Managerial Economics for Public Administration
Managerial Economics for Public Administration PPA 723
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This 249 page Class Notes was uploaded by Harmon Price on Wednesday October 21, 2015. The Class Notes belongs to PPA 723 at Syracuse University taught by John McPeak in Fall. Since its upload, it has received 35 views. For similar materials see /class/225664/ppa-723-syracuse-university in OTHER at Syracuse University.
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McPeak Lecture 7 PPA 723 Firms and Production Firms Three main kinds 1S ole proprietorships 2Partnerships 3Corporations Limited Liability Objective of the rm make decisions so as to maximize pro t Pro t is de ned as revenue What it eams from selling the good minus costs What it costs to produce the good an C or in slightly different form TCp fX W X Necessary vs sufficient conditions A necessary condition is in the nature of a prerequisite Statement A is true only if another statement B is true then A only if B or If A then B If a person is a father then they are a male If Felix is a cat then Felix hates baths Felix is a cat only if he hates baths If A cat then B hates baths Can we turn it around If B hates baths then A cat If Felix hates baths can we assume Felix is a cat No Felix might be a four year old boy for example Felix hating baths is a necessary condition for Felix to be a cat but it is not sufficient It is one characteristic of being a cat but this characteristic is shared by noncats as well Consider the situation Where A is true if B is true but A can be true When B is not true B is a suf cient condition for A A is one can get to Chicago from Syracuse B is One can take a plane to Chicago from Syracuse then the truth of B suf ces for the establishment of the truth of A but is not a necessary condition for A to be true B is a suf cient condition for A but not a necessary one Consider Where A and B imply each other A is it is the month of February B is there are less than 30 days in the month A is a necessary and suf cient condition for B and Vice versa Back to economics The point X1 X2 being on the budget line is necessary but not suf cient for the point X1 X2 to be the optimal bundle Yes it has to be on the budget line but other conditions need to be met as well A lot of non optimal bundle points are on the budget line as well We need to get a condition that takes care of these The reverse statement is a suf cient condition the point Xlx2 is the optimal bundle therefore it lies on the budget line The point XlX2 is the point Where MRSMRT implies the point Xlx2 the optimal bundle MRSMRT implies optimal bundle and optimal bundle implies MRSMRT Technologically ef cient production is a necessary condition for pro t maximization Pro t maximization is suf cient for technologically ef cient production Pro t max implies we are technologically ef cient but being technologically ef cient is not enough to know we are producing at a pro t maximizing level Technologically ef cient production the rm can not produce more output given the amount of inputs it is using and the rm cannot produce the amount of output it is producing by using fewer inputs Show sets Production function A rm gathers together inputs or factors of production The rm then applies a technology or production process to these inputs The result is an output can be a good or a service No costs of input are involved yet No selling of the product is going on yet Just boring old production l De ne a production function QfKLEM Q is output of the good in many studies people use Y rather than Q means the same thing K is capital L is labor E is energy M is materials f de nes the relationship between the quantities of inputs used and the maximum quantity of output that can be produced given current knowledge about technology and organization What is the nature of the f It can take on lots of different forms An important part of econometric work is to estimate the nature of the production function We can treat inputs in the production function as xed or variable inputs In the short run factors of production that can not easily be varied are viewed as xed inputs A factor for Which it is relatively easy to adjust the quantity quickly is a variable input The long run is the time span required to adjust all inputs There is no precise definition of time period applied to these terms It is a relative relationship All inputs are variable in the long run there are no fixed inputs in the long run An example A commonly made assumption is that labor is the most variable of inputs so we de ne it to be the variable input hold the others constant in the analysis No law here but convention Q MEL EM K bar E bar M bar mean xed in short run Holding xed inputs constant in the book Perloff de nes a labor output table ll in units and total rst then revisit marginal and average Labor units Total Marginal Average Output product product 0 0 NA NA 1 5 5 5 2 18 13 9 3 36 18 12 4 5 6 20 14 5 75 19 1 5 6 90 1 5 1 5 7 98 8 14 8 104 6 13 9 108 4 12 Marginal product of Labor the change in total output resulting from the use of an additional unit of labor all else constant g Note that this contrasts With the average product of labor the ratio of the output to the number of workers used to produce this labor Q Note further that there is also a marginal product of capital of materials of energy We are focusing on labor but other inputs also have marginal and average measures as we have just de ned for labor ll these in on chart Production Function 120 Total N 100 I Marginal Average 80 60 40 20 r 39 0 Am I I I I I I I I l39l 012345678910111213 Outputs Labor Units We can draw a graph of this information Why these shapes At low levels of labor workers help each other do tasks that are hard for one person to do or conversely they specialize This gives us initially a convex function Then after we reach some critical level of labor They have to wait for each other to nish at a machine or they get in each other s way then we get a concave function If MP curve is above AP curve then AP is upward sloping If MP below AP then AP downward sloping Think of heights for the intuition Geometrically if you draw a ray from the origin to any point on the Total Product curve you nd the average product at that point If you identify the slope of the total product curve at this point you nd the marginal product If AP steeper than MP then AP gt MP If AP atter than MP then AP lt MP At some point APMP The law of diminishing marginal returns If a rm keeps increasing an input holding all other inputs and technology constant the corresponding increases in output will become smaller eventually Not diminishing returns but diminishing marginal retums Long run production That was a discussion of variation in output due to different levels of labor holding other things K E M constant Now we are in the long run so all inputs are variable Note that the short run implies that at least one input is being held fixed Do not come away from this with the impression that the difference between the short run and the long run is one versus two inputs That is not right In the short run at least one input and potentially more than one input is held constant while one or more other inputs are allowed to vary In the long run all inputs are allowed to vary However to keep things simple we are going to assume there are only two inputs used in production of our good We will call them capital and labor More than two are possible likely in reality We focus on two because it is easier to draw and the logic carries through to higher dimensions We can combine different quantities of these inputs in a variety of ways to produce a given level of output Define l3 a curve that traces out the minimum combinations of inputs required to produce a given level of output This is an isoquant Again if you want to think of this as a contour line it is a contour line on the production function in 3D space Properties 1 The farther an isoquant is from the origin the greater is the level of output remember more is better than less 2 Isoquants do not cross as that would imply inef ciency remember transitivity 3 Isoquants slope downward as they are efficient levels of production remember there are tradeoffs Draw an isoquant What will in uence the shape of the isoquant How substitutable are inputs Production function of processed pork Processed Pork pigs bought in New York pigs bought in Pennsylvania Straight line graph Production function of peanut butter sandwiches Peanut butter sandwiches minimum dollops of peanut butter slices of bread 2 I have 10 dollops of peanut butter and 4 slices of bread I can only make 2 sandwiches Leontief graph Most lie intermediary to these two extreme cases Show contrast on single graph note nature of subs connect at upper and lower extreme The slope of the isoquant is called the marginal rate of technical substitution This tells us the trade off between inputs in production It is measured as the number of units of one input that have to be given up While increasing the other input to continue to produce a given level of output The MRTS like the MRS is a negative number since it is implicitly a tradeoff Here we define it for the capital to labor MRTS change capital amp MRTS KL change labor AL Unless goods are perfect substitutes MRTSl or perfect complements MRTSoo undefined or 0 the MRTS varies as different points are considered on the isoquant Remember we are on an isoquant The quantity of output stays the same Therefore we know that if we change labor and change capital on a given isoquant the total output should not change ATP K Recall that AK and a s1m11ar express1on exists for the marginal product of labor So if we know the change in total product is zero by de nition and we know the de nition of the marginal product is what we just saw we can add zero plus zero to nd the following AK1IPKALMPL ATP0 Show math note connection to calculus and answer zero minus zero question if it comes up Also note connection back to MRS and the Marginal Utility equations developed earlier While not overwhelming exciting this allows us to gain the insight that the marginal rate of technical substitution is equal to the negative of the ratio of the marginal products important note the numerator denominator relationship AK NIP MRT sKL L AL lPK From an intuitive point of view the movement along an isoquant is related to marginal changes I am getting this level of output using a speci c mix of inputs now I want to move over there to another mix of inputs holding output constant That is a marginal change Returns to scale Up until now we have been considering adjustments to our input bundles holding output constant That is how we have de ned an isoquant Or we have been changing one input at a time holding others constant That is how we thought about a production function Now however we want to turn to the question of how changes in the total input bundle are related to changes in output What can we learn by comparing different isoquants rather than looking at movement along a given isoquant We are going to look at a speci c type of change to the input bundle blowups Equal percentage change applied to all inputs I use labor and capital to produce my good Let s say we can continue to ignore other inputs like materials and energy for production of our good What are the implications of different production functions for changing input levels Say I use 2 units of labor and 3 units of capital to produce 6 problem sets In this case assume the production function is de ned by capital times labor If I double both units 4 units of labor and 6 units of capital I get 24 units of problem sets 236 new output 22324234624 Doubling inputs gives a fourfold increase in output 2464 Increasing Returns to scale Doubling inputs leads to a more than double increase in outputs f2K2L gt 2fKL 20 Say instead that the production function is capital plus labor perfect substitutes in production 235 new output2223223 10 Doubling inputs gives a doubling of output 105 2 Constant returns to scale Case two additive production function Doubling inputs leads to a doubling of output f2K2L 2fKL Finally assume we have a production function that de nes output as the natural log of capital times labor ln23l79 New output ln2223ln463 18 Doubling inputs increases output by 78 318l79l78 Decreasing returns to scale Doubling inputs leads to a less than double increase in output f2K2L lt 2fKL 21 Technical note CobbDouglas production function is useful as it embeds these three cases q vL KB IfaBgt1IRS IfaB1CRs IfaBlt1DRs While this defines the relationship between scale and the production function as either one or the other it is important to note that there can be variation over the scale of production in the returns to scale In other words returns to scale can depend on where you are in the production function A common pattern is IRS over low levels of input CRS over moderate levels and DRS with high levels of input If we think of isoquants as contour lines they are close together near the origin and spread further apart as we move away from the origin 22 Show graph from book that illustrates IRS over low ranges CRS mid range and DRS higher range Innovations Technological progress is one of the main driving factors of economic growth Different types Neutral technical change All inputs are equally affected Allows same input bundle to be used but generates more output Nonneutral technical change The innovation affects inputs unequally This alters the proportions of the input bundles when generating more output 23 McPeak Lecture 4 PPA 723 Who gives a hoot about elasticities Well as a policy matter they make a big difference when considering the implications of implementing a taX What are things we might be concerned about when implementing a tax 1 What will be the effect on the equilibrium price What will be the effect on the equilibrium quantity How much revenue will be generated 2 Who will bear how much of the burden of the taX What share will be borne by consumers By producers 3 What are the implications of different types of taxes What is the difference between a taX on producers and a taX on consumers What is the difference between a taX that is xed at a given level per unit sold and a taX that is based on a xed share of the selling price Two types of taX to keep in mind 1 Ad valorem For every unit of currency spent on a good the government keeps a given fraction the producer keeps the remainder 2 Speci c tax For every unit of the good purchased the government collects a given amount per unit Let s start by looking at the speci c taX since it is easier Then we will consider the ad valorem In addition we can distinguish between a taX placed on consumers and a taX placed on producers A speci c taX is often denoted as a taX of size tau 1 Go back to the processed pork example Say the government decides to impose a taX per unit 105 per kg on processed pork First consider the case of a taX on the pork producer So whatever they sell for is the posttaX price the price they get to keep is going to be 105 less than this Let us look at the graph rst 9 Demand 8 Producer price supply 7 6 Seing price supply 5 4 x it r A f 3 I i g e e 0 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 28620P 53 48 43 38 33 28 What is the qualitative story If the taX is imposed consumers spend more per unit to get the good Producers receive less per unit than they did before the taX The market clearing quantity decreases from the pretaX level The government gets revenue where it did not get it before What is the quantitative story Solve by algebra The speci c taX creates a difference between the price received by producers and the price paid by consumers The size of this difference is tau So write P r PS This distinguishes between the price consumers pay from the demand curve and the price the sellers get from the supply curve that does not include the taX Here we are given 11 05 Q 28620P QS884OPS P l 05 PS In equilibrium Qc still equals QS so 28620l 05 PS 884OPS 2862120P8840P drop the s notation for simplicity Seller s price 295 8840295206 is quantity Check answer Buying price 295105 or 400 286204206 Here you have two different prices to keep in mind the price the consumers pay and the price the sellers get that is the residual after the taX is taken by the government Equilibrium is composed here of four elements a selling price a buying price a quantity and taX revenue P 400 PS 295 Q206 What is the taX revenue TRQr or 206 l 05 or 216 Summarize the outcome The consumer spent 330 per unit to get the good in equilibrium pretaX now they spend 400 per unit to get the good in equilibrium post taX The producer received 330 per unit to sell the good in equilibrium pretaX now they get 295 per unit to sell the good in equilibrium post taX The quantity sold purchased in equilibrium is 206 a decrease from 220 before Note if the policy maker had not been spending time drawing supply and demand curves in this class they could make a common mistake of estimating revenue would be 1 0522023 1 when if we take into account the behavior of consumers and producers in response to the higher price and the supply curve we nd in fact revenue is 105206216 Incidence how much of the burden of the tax falls on consumers and how much falls on producers Ap consumer pays AT Consumer incidence In the case of the consumer the change in p is 070 The change in the tax is 105 from zero to 105 Here we are looking at tax per unit and price per unit This means that when the tax is imposed 70105 or 23 of the tax falls on the consumer The incidence of the tax on consumers is 23rds The price received by the suppliers falls by 035 The share of the tax burden falling on the producers is 35105 or U3 The incidence of the tax on producers is 13 The relative share of the incidence depends on the elasticites Consider atter demand curve introduced before and the same tax on ers 180 190 200 210 220 230 Demand I Starting Supply Ending Supply O MQJLLDCDV These cross at 365 192 after the taX is imposed and the equilibrium before the taX was our old friend 330 220 How 48480 Q80 Q40 8840 105 In this case the price to the consumer has changed from 330 to 365 a 35 cent increase for the consumer The price for the producer has decreased from 330 to 260 a drop of 70 cents Here the incidence on the consumer is l3rd the incidence on the producer is 23rds In this case the attest case considered in the demand curve comparison recall we calculated a price elasticity of demand of 3 12 Also recall that the baseline demand curve had a price elasticity of demand of O3 The price elasticity of supply for our baseline case was eta 06 we got 59 but let s round SHORT CUT Incidence on consumers eta etaepsilon 66 323 661213 If you really want to get into it state this in terms of Ag Ii APs Qquot HE AQ s d AP Q AP Q and look at appendix 3A This short cut tells us that the incidence that falls on consumers can be computed from the relative elasticities However rather than memorize the formula I want you to get the more important issue here the relative elasticities tell you what burden of a taX will fall on consumers and what burden will fall on producers A common assumption is that a taX on producers will lead producers to pass along the taX to the consumers This means that the analyst believes that producers can add the taX to the selling price without experiencing a change in the price they receive In what case can they do this Only if the price elasticity of demand is zero and or the price elasticity of supply is in nite The price elasticity of demand equal to zero means that no matter what the change in price consumers demand a given quantity This is REALLY inelastic The supply elasticity equal to in nity means that a really small change in price leads to a huge increase in supply Show each on a graph 10 9 8 7 w 6 Demand g 5 Starting Supply 039 4 EndingSupply 3 2 1 0 rv r6 r9 rvq rvq r9 vii r9 r193 Quantity p220330 10q 00015 P 434 PS 329 Q220 2197 TR231 Demand 39 Supply Supply with tax O MQJLLDCDVOJQO supply pQ129804000 n60 P 434 PS 329 Q199 TR209 In what case do producers bear the entire burden The opposite A price elasticity of demand that is in nite at demand curve or a supply elasticity that is zero steep supply curve Think these through Does it matter whether you put the taX on consumers or producers Somewhat surprisingly in the case of a speci c taX no 9 8 7 6 5 4 3 2 1 0 130 140 150 160 170 180 190 200 210 220 230 240 250 Quantity If you put the taX on consumers the shift in demand re ects the quantity price schedule after the taX is collected by the government and the original demand curve re ects the quantity price paid by consumers when the taX is included Take the basic elements of the problem solved before for putting the taX on producers but now put the taX on consumers Solve by algebra The speci c taX creates a space between the price received by producers and the price paid by consumers The size of this space is tau So write Pdr P Here we are given 11 05 Q 28620p QS8840pS P 105 P In equilibrium Qd still equals QS so 28620P 88l 40 X PS 28620P 8840 P 105 28620P8840P42 This solves for a consumer equilibrium price of 400 and a seller equilibrium price of 295 Should be familiar The shift in the demand curve takes you to an equilibrium quantity of 206 At this point the producer gets 295 per unit the consumer pays 400 per unit and the government gets 105 per unit and the taX revenue is 216 That is where we got when we taxed the supplier What about the ad valorem tax This takes a speci c amount per dollar so for every dollar spent a certain number of cents goes to the government Let s say we have a 20 sales taX so for every 100 spent the producer gets 080 the government gets 020 Note there is a slight difference I how this policy can be de ned In the US example with a sales tax we de ne pc 1 0 39 p5 This is different from a VAT that is de ned by p5 pc 391 a We will present the latter here 9 8 7 Demand after 6 governement takes 8 5 tax E 4 l Demand including 3 tax 2 1 0 Supply 0 Q Q Q Q Q Q lt5 a a e 9 rib in Quantity including tax How do you solve one of these by algebra This works better if you have the inverse demand curve handy Remember Q 28620Pc could be written Pc 28620l20Qc The point of this taX is that while that is the price the consumer pays for the producer they only get some fraction of this and the government gets the rest So if we think about it the sellers are going to get PSP l0t which by substitution is PS28620l20Q l0t If the taX is a 20 taX the sellers get 80 of the price paid by consumers and the price derived from the inverse demand curve So while Pc 28620l20Qc is the demand curve that characterizes consumer behavior ps28620l20 Q l 0t is what characterizes consumers behavior after the government takes the taX revenue according to the producers perspective To make a long story short we use the condition that the quantity supplied equals quantity demanded and we rearrange terms to get 28620PSl2884OPS 28625PS8840PS PS305 P 3 81 If PSP 1 a P PSlot P 3058 q210 286203058210 8840305210 r 0Lp 076 TR 076 per unit gt 210 units or 147 This is algebraically more complicated than the speci c tax but the idea is the same The tax creates a condition where the price that the consumer pays and the price that the producer receives differ Using the information that the quantity demanded and quantity supplied and the exact nature of this price difference we can solve for post tax equilibrium What is the incidence in the ad valorem case Well first what is the tax Consumers pay 381 per unit the producers get 305 076 is the tax What is the change in consumers price 381330 or 051 23rd of the incidence is borne by consumers Recall the speci c tax and contrast the tp 105 4 26 implicit tax rate that came out of the specific tax example with the 20 example used for the ad valorem example here If we crank up the tax rate used in our ad valorem example from 20 to 26 it will take us to the same point as the specific tax although other points on the line will differ some rounding going on here 0t26 28620pl268840p 28627p8840p p295 q206 Some basic ideas to take away Why do we tax Change behavior Generate revenue Compensate for extemalities more on this later The more inelastic demand for a good is the more taXing it is good at generating revenue The more inelastic demand for a good is the less taXing it is good at changing behavior If we want to generate taX revenue without causing much of a change in the equilibrium quantity taX a relatively inelastic good Different taxes forms eXist but under particular conditions we looked at lead to exactly the same outcome The relative elasticities of the supply and demand curve play a critical role in determining the incidence and these elasticities are determined by the nature of the good in question If we want to know who bears the greater burden of a given taX consumers or producers then we should identify who is the more inelastic party The more inelastic party will bear a higher share of the burden McPeak Lecture 10 PPA 723 The competitive model Marginal willingness to pay WTP The maximum amount a consumer will spend for an extra unit of the good As we derived a demand curve for an individual s preferences we can interpret the demand curve tracing out the consumer s marginal willingness to pay at different levels of consumption Consumer surplus CS the monetary difference between what the consumer is willing to pay for a given quantity of good and what the good costs show graph Relies on the fact that the demand curve is downward sloping and that the price for purchasing is the same for all units The area under the demand curve and above the price line The area below the price line is expenditure p times q If price increases and demand is constant consumer surplus falls The decrease in consumer surplus for a given price increase will be larger 0 The greater the initial expenditure on the good 0 The less elastic is the demand curve Producer surplus The difference between the minimum amount necessary for the seller to be willing to produce the good and the selling price show graph Producer surplus is revenue minus variable cost Since pro t is revenue minus cost the difference between pro t and producer surplus is xed cost in the short run and there is no difference in the long run The maximum societal welfare comes from maximizing consumer surplus plus producer surplus Why are there gains to trade show graph of when quantity is too low show graph of when quantity is too high Monopoly There is only one supplier of a good for which there is no close substitute How can such a thing happen 1 Technical reasons a Economies of scale A natural monopoly eXists when one rm can produce at a lower cost than several rms producing the same good and total output level AC is downward sloping over the feasible range of output b Large Sunk costs 2 Legal reasons a Patents b Franchises c Legal barriers Marginal revenue as you recall is the change in revenue divided by the change in q In the competitive model the price taking rm faced a marginal revenue of p since price did not change with the output level of the rm Now the monopoly rm faces the entire demand curve This is downward sloping so by picking a level of q there is also an associated p the whole demand curve is de ned by p761 pairs show graph Price I Discrete MR Bisection Discrete Bisection MR MR Price TR 1 23 23 2 22 44 21 20 3 21 63 19 18 4 20 80 17 16 5 19 95 15 14 6 18 108 13 12 7 17 119 11 10 8 16 128 9 8 9 15 135 7 6 10 14 140 5 4 11 13 143 3 2 12 12 144 1 0 13 11 143 1 2 14 10 140 3 4 15 9 135 5 6 16 8 128 7 8 17 7 119 9 10 18 6 108 11 12 19 5 95 13 14 20 4 80 15 16 21 3 63 17 18 22 2 44 19 20 23 1 23 21 22 24 0 0 23 24 Note there is a difference between calculating the MR from one observation to the next compared to the MR at a given point Bisection rule Marginal revenue for a linear demand curve de ned by pabq is MRa2bq For a linear demand curve the marginal revenue curve bisects the demand curve Why Well demand is 24qp in the example above and we know pq is revenue So pq is the same as 24qq or 24qq2 The marginal of this is the derivative with respect to q or 242q The competitive rm choose q given p Here the monopoly chooses p and q based on information about the entire demand curve It is making its choices in the awareness that increasing q decreases price and that marginal revenue is a function of the quantity they pick Pro t maximization steps for the monopolist 1 Identify q that determines where MRq MCq 2 Calculate what is the implied p for that q from the demand curve 3 Calculate pro t which is de ned by p times q minus cost at qquot 4 Shut down produce q0 if p is less than average variable cost SR or average cost LR Simple example Demand is de ned by p24q and total cost is de ned by TCq2 so that MC 2q you will be given this not be expected to derive it If we know that p24q we can use the bisection rule to de ne lR242q since Rpq 24q qz Where is lRMC Where is 242q2q 244q or q6 At a quantity of siX I plug back into the demand curve and nd that p246 or 18 note a common mistake is to plug back into MR curve to solve for price Pro t for me at this point is revenue minus cost or 186 66 or 72 To make life easier on us I will tend to give you a constant marginal cost but the procedure is the same How does this differ from a perfectly competitive market in terms of outcome If we use the given demand curve and recall that the MC curve traces out the supply curve in a perfectly competitive market we find 24q2q where supply and demand meet at a pq pair which solves for q8 implying that pl6 show on graph There is a deadweight loss of monopoly The market structure makes it so that transactions that would occur in a perfectly competitive market do no occur thus reducing total societal welfare Note ef ciency equity distinction Now we can modify the example If we assume perfect competition and the conditions for a horizontal supply curve discussed last class we can de ne a cost curve as 2q so the MC is a constant 2 242q2 when ql l which is where pl3 In perfect competition by contrast 24q2 when q22 so that p2 PS with perfect competition is the area below the price line and above the supply curve 0 PS with monopoly is the area defined by pInOIlOpOly m n P 1y or 13 211 121 mcq CS with perfect competition is the area above the competition price line and below the demand curve a triangle When q0 p24 by the demand curve So we h av e pwhen q0pcompetition qcompetition 4 22212242 CS with monopoly is the area above the monopoly price line and below the demand curve a triangle pWhen q0 pm n P lyqm P ly1224 13 1 1 1260 12 Total welfare under competition is O242242 Total welfare under monopoly is 1216O 12 or 1805 This illustrates a general result total welfare is reduced under monopoly market structure compared to a perfectly competitive market So what can we do about a monopoly 1 Optimal price regulation which sets a price ceiling What would the equilibrium market clearing price quantity pair be if the market was competitive Set the price ceiling at this level so that the demand curve facing the monopolist is modified to have a at spot then decrease after passing to the right of this p q pair show graph show graph when the price ceiling is set too low This is very dif cult to get right if you don t know the actual demand and cost curves Also may have a natural monopoly that is de ned by decreasing average costs over the total range of feasible output levels This means MC is below AC over this range as well since if AC is downward sloping that means MC is below it A policy that sets the price ceiling based on the marginal cost curve would make it better for the monopolist to shut down rather than produce thus losing whatever consumer and producer surplus we are getting under the monopoly situation McPeak Lecture 5 PPA 723 Consumer choice Model premises 1 Tastes for a consumer are given They may vary across consumers but for our purposes are treated as xed for a given individual We don t really care where they came from 2 There are constraints on the choices an individual can make either through regulation or budget limits 3 The consumer makes choices that maximize their wellbeing The goal is to understand and predict behavior Very exible very broad How does a consumer choose one bundle of goods over another We assume they are guided by their preferences Preferences obey three properties by assumption 1 Completeness For any two bundles of goods call 2 3 V V them bundle A and bundle B one and only one of the following statements is true a A is preferred to B b B is preferred to A c The consumer is indifferent between A and B meaning no I dunno s TransitiVity Preferences are logically consistent If I prefer bundle A to bundle B and prefer bundle B to bundle C then I also prefer bundle A to bundle C meaning if I prefer cranberry juice to orange juice and orange juice to apple juice then it is safe to assume I prefer cranberry juice over apple juice More is better than less Assume the commodity in question is a good rather than a bad and that there is free disposal if all else fails meaning if you see me drinking cranberry juice it is fair to assume that another glass will make me no worse off if I can consume it give it to somebody or pour it down the sink With these three assumptions we can proceed to map a consumer s preferences First if we are given a point that corresponds to a consumption level of two goods our bundle if composed of two goods we can partition space to tell us where the consumer is better off where the consumer is worse off and where we need to know more info Graph here We can put more precision on preference maps through the use of indifference curves These tell us the different combinations of the two goods in question that make the consumer equally well off The consumer is indifferent between any of the bundles that define the line hence the name Indifference curves are the contours on our map of happiness Each traces out a line that tells us consumption bundles that take us to the same happiness height Indifference curve properties 1 Bundles on a curve further from the origin consumption bundle equals zero for both goods are preferred to those on curves closer to the origin 2 There exists a curve passing through every bundle 3 Indifference curves can not cross 4 Indifference curves slope downward and for our purposes are convex to the origin though this last bit need not hold Draw indifference curve The slope of the indifference curve is defined as the marginal rate of substitution This tells us the maximum amount of one good the consumer will sacrifice to obtain one more unit of the other good The trade off for a marginal increase in one good in terms of a marginal decrease in the other AXZ 1 assuming rise is measured in good two run in good one What sign should this have We assume indifference curves are convex to the origin re ecting a diminishing marginal rate of substitution The less you currently are consuming of a good the more valuable an additional unit is to you More on this in a moment Alice MRS Abeans What does the indifference curve for perfect substitutes look like price chopper milk byrne dairy milk Graph What does the indifference curve for perfect complements look like left glove right glove Graph Most things fall in between Utility A numerical value that re ects the relative ranking of various bundles of goods How many utils of happiness does a given market bundle give you Ordinal rather than cardinal which means the absolute number of utils and the distance in utils between two bundles is not meaningful in and of itself It orders the bundles Utility is often represented by a utility function and we assume utility is concave to the origin Utility in two goods has three axes to be concerned about good one good two and the utility derived from the combination of the goods For example u x1x2 For X1 from 1 to 10 and X2 from 1 to 10 M ogg o quot 3 9233 3d View looks like a wedge from an upside down bowl Note the contours that is like the indifference curve View from above excel puts the label on the rhs but same idea here 012345678910 This makes it easy to pick out the indifference curve shape If we pick one value of good one and consider how utility changes as we increase good two we get something like this using the info in the surface map side View of utility function hold other good constant Utility increases as we consume more of the good but it is assumed by a decreasing rate Decreasing marginal utility Distinguish between decreasing utility and decreasing marginal utility From 0 to 1 utility increased by 07 From 1 to 2 utility increased by 05 From 2 to 3 utility increased by 04 AU Marginal utility AX Note that this is assumed positive The marginal rate of substitution MRS is equal to the negative of the ratio of the marginal utilities MRS MU AXI MUX2 At some level you just have to accept this AU AXi 39MUx AXz MUM but change in Utility 0 on an indifference curve so rearrange terms For a more detailed explanation see the following From a calculus point of view it makes sense UUX1 X2 The total derivative dUdUdX1dX1dUdX2dX2 If we move along an indifference curve we know that dU0 so that dUdX1dX1 dUdX2dX2 and we rearrange terms from there However we don t have that calculus option so my best intuitive try here Take yourself back to the 3d graph If we change X1 positively it will have a positive impact on utility change in X1 moves us sideways but also up If we want to get back down to the utility level we started at we need to change X2 negatively until it moves us back down on utility change in X2 moves us sideways but also down So loosely stated we have to balance the total impact of the change X1had on us in 3d space by changing X2 enough to bring us back down to the same utility level as we started at but at a different consumption bundle Budget constraints Assume away savings and dynamic aspects and to keep things simple assume that the budget constraint is the income received in a given period Now we have two goods so let s de ne Y as income p1as the price of good one X1 as the quantity of good one consumed p2 as the price of good two and X2 as the quantity of good two consumed p1gtllt X1 p2gtxlt XZZY The budget line budget constraint The plot of all possible combinations of goods X1 and X2 that can be purchased at given levels of Y p1 and p2 The opportunity set is all bundles on or below the bundle line YlOO p1lO and p2 5 131 X1 132 X2Y 10 X1 5 X2lOO Max X1Yp11001010 Max X2Y p2lOO520 Draw this note opportunity set Slope Change in X2change in X1 20102 Or p1p2 4 2 Why As graphed X2 is a function of X1 So we can write X2Y P239 p1 P2 X1 x2100 5 10 5 x1 The marginal rate of transformation is the slope of the budget line It re ects the trade offs the market imposes on the consumer in terms of the amount of one good the consumer must give up to obtain more of the other good What is the impact of a change in price on the budget line If price of good one increases from 10 to 20 Slope is now 4 20 X1 5 X2lOO Draw What is the impact if the price of good one decreases to 5 from 10 Slope is now 1 5 X1 5 X22100 Draw What is the impact of a change in income on the budget line 10 X1 5 X2150 Income goes to 150 from 100 Does this change the slope No outward shift What happens to the budget line if income doubles What happens if the price of all goods is halved Takes you to the same place 10 X1 5 X2100 10 X1 5 X2200 10 X1 5 X2100 5 X1 25 X2100 McPeak Lecture 9 PPA 723 Competitive rms and markets Recall the conditions for a perfectly competitive market 1 Goods are homogenous 2 Large numbers of buyers and sellers freedom of entry and exit price takers 3 Perfect information by both buyers and sellers 4 No transaction costs Focus on the point that firms are price takers in both output and input markets That is to say a firm can set a selling price higher than the market price or offer to pay less for inputs than the market price but nobody will buy their product or sell them inputs if they do so 7 Profit maximization Pro t Revenue costs Questions to be asked when considering prof1t maximization 1 Should I produce at all 2 If so how much should I produce To begin with let us focus on the case when we should produce an amount larger than zero and then later consider what would lead the rm to be better off producing zero I am going to also assume now that we are in the long run and we will introduce short run issues later I should produce to the point where pro t is maximized Show graph with derivatives May not know the shape but you could think of this shape coming from experimentation At the peak of the curve marginal pro t equals zero increasing to the left of the maximum decreasing to the right of the maximum Since we know that HQRQ CQ we can think of the marginal representation of this as AHAR AC MHMR MC or AQ AQ AQ We can elaborate on this expression a bit since we know that HRC can also be expressed as HpfX wX O HpQCQ r We can see that each additional unit of Q represented here by fX or Q generates an additional revenue of size p So in fact MR p The competitive rm will produce at output level Q where MCQ p Since p MR and assuming p is greater than or equal to ACQ as we will see in a moment MHO where MRMC and with MCp we have pMC Show graph If we want we can think of pro t per unit in this case as equal to ARAC or price minus average cost Then pro t is Q pro t per unit What if price is not greater than average cost Long run production level decision Consider the point Q where MCQ p If this point is above AC then the rm stays in production If not shutdown Note that p is both MR and AR if that helps Now consider the same type of decision but consider the example of a short run setting where xed costs eXist HQRQVCQFC Find Q where pMCQ noting that this is where AC AVC p AQ AQ If at this point variable costs are greater than revenue then shut down It is already bad producing makes it worse If variable costs are less than revenue then stay open and produce You will at least be eating into your losses if not earning positive pro t Show graph If when I determine a quantity level Q that sets MCQ p MC is below the AVC curve note not the AC curve then I should not produce anything set QO and hope for better times in the future If when I choose the quantity level Q that sets MCQ p MC is above the AVC curve then I should produce Q I will minimizing loss maximizing pro t at this point The competitive rm s short run supply curve is the marginal cost curve above the average variable cost There is a discontinuity jump gap Show graph The market supply curve is the horizontal sum of all the individual rms supply curves Supply goes up as selling price increases due to a miX of rms entering the market and rms already in the market supplying more show derivation Think about supply shifts when input costs go up Show graph Supply slopes up due to the diminishing marginal returns to an input in this short run context which is why the marginal cost curve is upward sloping The competitive rm s long run supply curve is the marginal cost curve above the average cost There is still a discontinuity jump gap Show graph In the long run there is no xed cost variable cost distinction so the diminishing marginal returns explanation for the upward sloping curve is not going to hold The long run market supply curve is at a horizontal line at the minimum point of AC where MC and AC cross if and only if 1 Firms can freely enter and exit 2 Firms are identical 3 Input prices are constant What would make entry limited Production requires a limited resource Government regulations Entry is costly This makes it slope up See p 243 for entry and exit rates What would make rms not be identical Location production and regulation environment climate This makes it slope up What would make input prices vary across rms If there are only a few rms who use the input jet engine example increased demand by competitors should drive up the price of the input compared to the receptionist example If there is something about the scale of production allowing different technologies to be used PC is output oppy disc is input example then we can have decreasing input cost as quantity expands Competitive rms earn zero economic pro t in the long run If rms are earning higher than average return to capital 105 in the current text over the past ve years on page 255 though this is bound to come down given the recent turmoil other rms will move in bringing down the price bringing down the rm s pro t If rms are earning less than the average return to capital some rms will drop out and reallocate capital to a more attractive sector bringing price up Even without entry and exit we still have zero economic pro t however If there is a restriction the market nds a way to extract the value of the xed input Permit value Capitalized present value If a rm does not maximize pro t they will be losing money and be driven from business Summary A pro t maximizing rm must then choose the level of quantity it produces in a way that Uses inputs in a technologically ef cient fashion production function Uses an input miX that is selected to minimize the cost of producing Q isoquant isocost Compares the marginal cost of producing at that level to the marginal revenue of producing at that level pro t maximization McPeak Lecture 14 PPA 723 Costs and Bene ts A cost is anything that reduces an objective and a bene t is anything that contributes to an obj ectiVe For society as a whole increasing national income is the obj ectiVe Anything that reduces national income is a cost and anything that increases it is a bene t Anything that reallocates it from one party to another is a transfer Compare to nancial analysis where a dollar is a dollar There we would worry about taX taking money from us to give to them Here it is not an issue return to DWL argument and can use example of user fees in the commons Transfers Tax payment Subsidy Credit payments These don t create or diminish national income they just move it from one party to another What is done with the money loan money to buy fertilizer fertilizer is a cost increased output is a bene t impacts national income but the loan payment does not Real resource ows are critical to identify A taX is a claim on a real resource ow We are looking to identify uses of the resources Steps to CostBene t analysis 1 De ne the situation 2 Identify and value the costs 3 Identify and value the bene ts 4 Discount future cost and bene ts to identify net present value 5 Consider the implications of the choice made on NPV income terms for other objectives equity for example 6 Sensitivity analysis 7 Interpret results 1 De ning the situation What is the community whose resources are relevant to the program being evaluated What is the spatial extent of the proposed project What are the current resources in this community in terms of money property labor environmental amenities and government services for the community What will happen if the project is not implemented Identify and value the costs and bene ts that arise with the project and compare to the situation without the project This is not the same as before and after Incremental net bene t with and without project Patterns With grows at a faster rate than without With stops a decline that will happen without With leads to an increase without a decrease 2 Identify and value the costs Physical goods Materials that are easy to identify Labor People working and getting paid for it Land The place where the project is taking place Contingency allowances Recognizing that there will be changes in physical conditions or prices over the course of the project and putting that in Intangibles Traf c delays noise Externalities omit taxes debt service sunk costs To value these we return to the concept of economic cost Here we expand it some since we have now considered extemalities The shadow price of an input re ects its value to society as a whole the full social accounting of the marginal cost of using the input If there are market imperfections it is not the same as the market price If the market is perfectly competitive and there are no extemalities then it is the same as the market price the next best alternative as re ected in the market de nition 3 Identify and value the benefits New production or increased production from current level Quality improvement Ability to access higher return markets Cost reduction Avoided losses These again in the absence of externalities can be valued through market prices Some bene ts are dif cult to re ect in market prices civic pride reduction in pollution To approximate these we use a variety of techniques to estimate the community s willingness to pay 4 Discount future cost and bene ts to identify net present value Many projects have bene ts and costs that will be realized over time How do we compare these values and arrive at a single measure of the ow of costs and bene ts over time We compute a single measure of these ows as the present value We discount future bene ts and future costs to arrive at a single statement of the net present value of benefits minus costs Why do we discount Impatience Having it now is more valuable than in the future Longer time to be with the benefit and also conditional continuation probability factors in here In ation Dollar today is not the same as a dollar in the future Opportunity cost I could have invested the money and earned returns so this is the economic standard by which I should evaluate future returns General form for discounting r is the discount rate usually expressed in annual terms De ne future value by FV and present value by PV t is a time index and in our case is indexed in years Fvt on 1 rt or m on 1 rt If I promise to pay you 100 20 years from now and the discount rate is 6 what is the present value In other words what amount could you give me now I invest in a sure bet 6 rate of return bond and have it pay off 100 in 20 years 100l06203118 If it is current year 551001060 100 since anything raised to the zero power 1 by convention If it is a stream of payments we sum them over time Xt2 Xt3 Xts PVXL11 2 3 lr lr lr lJrrs For future reference if payments are equal over time and it is over an in nite time horizon we can use the following result 1 m 1 m a 7a Zak S kl lea 1 1 1 no 71 w i 0 1 7 10 1r 1r 511rs 17 1 1r71 l 1r lr 1 Distinction between the nominal rate of interest and the real rate of interest The nominal rate includes in ation The real rate is in terms of in ation adjusted units Let gamma be the in ation rate and i is the real rate of interest The nominal rate of return can be stated 1 1 iXHVFHitVtW That means the real rate of interest is nominal rate of interest in ation diVided by 1 rate of in ation Roughly speaking we can use nominal rate minus in ation rate to get real rate if in ation is small Real present value discounts for both real interest rates and in ation If your future monetary values are stated in real terms you do not discount for in ation They have already been discounted If your future monetary values are stated in nominal terms you need to discount for both in ation and real rate of interest Is the contract you signed for a 100 bill to be handed to you each year or for the equivalent of 100 in today s money to be handed to you each year The discount rate you choose depends on whether the values you are using for costs and bene ts are in real or nominal terms In ation rate is 5 Nominal rate of interest is 8 108 1051i real interest rate is 29 Is promise to pay 100 bill next year Then 100108 worth 9259 today Is promise to pay the equivalent of 100 next year Then 1001029 worth 9718 today How do we choose r A different r may change the relative evaluation The discount rate re ects the relative value a person places on future consumption compared to current consumption Lower values show a greater preference for future consumption Example suppose I will give you 100 today or 1001r next year Today R Next year 100 0 100 100 2 102 100 5 105 100 10 110 The point at which you become indifferent between the two choices is your discount rate Why the discount rate matters Discounting affects the value placed on future bene ts and costs Higher discount rates place less importance on future benef1ts costs A lower discount rate increases future values in terms of current values Recall F V t t PVO I r Consider a program with 20 years of bene ts at 1year PV 20 with 0 discount rate PV 159 with 3 discount rate PV 135 with 5 discount rate PV 116 with 7 discount rate PV 95 with 10 discount rate What about using market interest rates Economists sometimes use the rate of return at the US Treasury Investors looking for a safe return invest in government securities DATE 3mo 6mo 1yr 2yr 3yr 5yr 7yr 10yr 20yr 30yr 11011990 728 738 732 768 788 815 842 857 863 870 11011995 548 549 546 552 562 574 586 598 636 629 11011999 516 532 547 583 593 600 623 606 655 619 11012002 144 143 142 146 176 214 292 354 401 507 A problem occurs if when comparing two options one is riskier Using a riskfree rate favors the riskier project Another a1temative is to consider where the funds for a project come from If some of the funds come from the private sector we should consider the opportunity cost of using those funds This is a good estimate of the opportunity cost of the capital you are using Rate of return on capital is around 10 so we use 10 The Office of Management and Budget directs agencies to use a 7 real discount rate This rate approximates the marginal pretaX rate of return in the private sector Might the social discount rate deviate from these market rates Social discount rate the interest rate at which society is willing to trade future consumption for present consumption Some economists argue that the opportunity cost of foregone future consumption might differ from the opportunity cost revealed in the markets Reasons social discount rates may differ from market rates 1 Concern for future generations Private sector may save too little because it doesn t care about future generations Thus the government acts as an advocate for future generations who are not represented in the marketplace Estimate by Costanza et al 1997 of the value of the annual ow of goods and services from the environment 33 trillion Years 5 discount 10 discount 1 31390571008524 29859634795187 10 20015511770517 12140021558658 100 222352250970 1498197682 200 1498197682 68018 300 10094777 3 400 68018 O 500 458 O 600 O O Discounting can lead to outcomes that are pretty grim for future generations 2 Market inef ciency Investments create knowledge a positive externality spillovers leaks Thus one can argue that rms underinvest Sometimes you see a 10 rate by convention Example Compare costs of paving a road and gravelling a road Present Value Cost computation Gravelling costs 28000 to do now and requires 2000 per year upkeep for the next 10 years Paving costs 35000 to do now and requires 1000 per year upkeep over the next 10 years Discount rate is 10 Say this is the nominal rate of return on capital and these values are nominal values signing a contract Gravel Pave Now t0 28000 35000 1 20001111818 1000111 909 2 20001121653 1000112 826 3 20001131503 1000113 751 4 20001141366 1000114 683 5 20001151242 1000115 621 6 20001161129 1000116 564 7 20001171026 1000117 513 8 2000118 933 1000118 467 9 2000119 848 1000119 424 10 2000111 771 1000111 386 GRAVEL 40289 PAVING 41144 Gravel is less costly than paving in PV terms If we add in bene ts we can arrive at net present value Assume the impacted population is of size 1000 Also assume we did a study that indicates that the average monetary value per year the population of 1000 of an improved road is 8 if paved and 6 if gravel each So the total annual bene ts of the gravel road are 6000 and total annual bene ts of the paved road are 8000 10 10 NPpaving Z 2 1rt 1rt 10 1 NPvrave 26000 g 1 t 1rt 10 28000 2000 1 rt If the discount rate 6 then NPVpavi11g 16520 while 11gravel 1 If the discount rate 10 then NPVpavi11g 8012 while NPVgravel393a422 Note that as the discount rate increases future net bene ts have less weight against the current period costs Choice of discount rate can in uence which project is selected in Cost Bene t analysis though not in this case Another measure is sometimes used the internal rate of return What r leads to PV bene ts equal to PV costs For the paving project just over 15 makes NPVO For the gravel project it is a bit over 7 Solve for the r that makes 10 1 7000 35000 g 1 rt 10 40002 1 t228000 t11r Also note we can consider the bene t cost ratio under the rule that if it is greater than one the bene ts outweigh the costs 10 1 8000 Z 1 y tl B C ratiopaving 10 35000 1000 it H l r The ratio is 140 at a discount rate of 6 for the paVing project 5 Consider other factors that weigh in the decision Equity impact on subgroups things like this While the average bene t is indeed 6 or 8 for our community members this is highly skewed as only 500 people have vehicles The other members will not have any direct bene t from road improvement but will have to pay the costs The gravel road will not be strong enough for the family farm to drive their tractor on so they will not bene t from this but will bene t from the paving 6 Sensitivity of results As you have seen by now the assumptions can lead to changed assessment With regard to the discount rate it is sometimes useful to identify where is the crossing point If we keep the original values it is never going to make more sense to gravel than pave given these values If we change our original problem and make the cost of gravelling cheaper say it is 18000 rather than 28000 we choose paving when r is less than 12 and gravel when r is greater than 12 Also the values we came up with for our bene ts could be off Say the costs were as reported in the original problem but the bene ts of the gravel and paved road were overstated by half like in the windmill example NPV for the gravel road is 20640 while for the paved road it is 12920 Neither project makes sense at a discount rate of 10 alternative uses of the resources offer better options One other source of uncertainty as if ambiguity about the discount rate the way we can make the prediction change by changing the bene t estimation is not enough is the length of the time horizon Are we really sure the time horizon is 10 years If for example we use the 6 rate and have a horizon of 2 years it is better to gravel than pave recall we picked pave If it is anything more than 10 years we have understated the NPV for example the paved road NPV if it lasts 20 years is 27 times as large as the NPV if it lasts 10 years Longer time horizons tend to atten out future costs and bene ts as suggested by the Costanza et al result above NPV Cost for Gravel Road 60000 50000 tn 5 40000 Do NPV Cost gt 20000 10000 0 quot Q 393 13 S5 b5 b9 6 6 F5 6quot Q9 b0 amp Years 7 Interpreting results Look at NPV and if you want other perspectives the internal rate of return and the bene t cost ratio Consider how sensitive the results are to your assumptions and how sure you are of your assumptions Consider the NPV result as statement of economic ef ciency and balance this against other objectives that may be important equity targeting speci c subgroups righting historical wrongs political stability whatever Realize that as a producer of this information how important it is for you to act carefully and ethically Realize that as a consumer of this information that the careful ethical approach is not always adopted McPeak Lecture 11 PPA 723 Monopsony There is only a single buyer in a market and this single buyer chooses the price quantity pair from the supply curve It buys at a price below what the price would be in a competitive market Supply curve is of the input the demand curve is the demand of the monopsonist Without getting into the details it is conceptually similar to the monopoly case though the focus is on the supply curve marginal expenditure curve rather than the demand curve marginal revenue curve Know there is a conceptual distinction Strategic interactions and Game theory Game theory is a tool to understand why outcomes with higher payoffs may not be possible to obtain if each individual acts in his or her own best interest How we understand why a failure to coordinate actions when there are strategic actions leads us to an outcome that does not maximize welfare of the decision makers A set of strategies is a Nash equilibrium if holding the strategies of all other players constant no play can obtain a higher payoff by choosing a different strategy Each rm is playing a best response strategy Chicken game Best response strategy lists out the options If LFG swerve KB straight If LFG straight KB swerve If KB swerve LFG straight If KB straight LFG swerve Neither option is dominant as a pure strategy Prisoner s dilemma Both quiet lesser charge One squeals gets let off gives evidence on other so that they face a higher charge Both squeal medium charge If I squeal you squealing is BR If I am quiet you squealing is BR If you squeal me squealing is BR If you are quiet me squealing is BR Say it is a question of entering a market Ford GM example If GM enter F enter If GM plays not enter F enter If F enter GM don t enter If F plays not enter GM enter Ford enters GM does not Say it is the choice of a level of quantity to provide UA AA example If UA chooses 64 AA chooses 64 If UA chooses 48 AA chooses 64 If AA chooses 64 UA chooses 64 If AA chooses 48 UA chooses 64 If they could coordinate then they could offer a lower quantity and earn higher pro ts Note collusion on supply and demand graph Detection as a preventative means Inspection of each other s books Price matching eX post Tracers in products Types of oligopoly solutions 1 Cournot quantity setting oligopoly Each rm chooses output level as a best response to the other rms strategies 2 Stackelberg quantity setting oligopoly One rm has rst mover status in a quantity setting game 3 Bertrand price setting oligopoly Each rm selects price as a best response to the other rms strategy Math appendix to contrast market structure p3397q c147q2MC147 If the market is perfectly competitive Supply equals demand q Zqi where i is each individual rm 3397q147 gtql92pl47 H19214771921470 cs18432PsoTw18432 If we have Cournot oligopoly competition say 2 rms p 339 7 qr qz 111 339 Q1 quot12 quoth 14739Q1 R339q1q12q1q2 MR3392q1qz MC147 MRMC implies 3392q1qz147 0r q1965qz If rms are symmetric q1965965 ql or q1965965 ql 0r q1964825 q1 or 75 q148 0r q164 Both produce this level so total quantity is 6464 or 128 This implies price is 211 Pro t for each rm is thus 2116414764 or 135049408 or 4096 CS can be calculated as 8192 PS is 8192 total welfare is 16384 If Stackelberg give rm 1 rst mover status p 339 7 ql qz 111 339 Q1 quot12 quoth 14739Q1 Firm one knows rm two is reacting to one s decisions by qz965q1 S0 plug this in R339Q139Q12391196395Q1a 243Q139Q123996Q15 Q12243Q1395 112 MR243 q1 MC147 so if MRMC q196 This then implies that qz96596 or 48 Pro t for rm one is 4608 pro t for rm two is 2304 total of 6912 CS 10368 Total welfare is 17280 If a monopoly Bisection rule gives us MR3392q and MC 147 Monopoly q 96 Monopoly p 243 Pro t is 9216 CS4464 Total welfare is 13680 General rule Welfare and quantity are highest in perfectly competitive market lowest in monopoly Oligopoly of different forms lies in between McPeak Lecture 8 PPA 723 Costs We are leaving selling price revenue out of the picture for the moment but we are adding in the issue of input costs Economic cost Includes both the eXplicit and the implicit cost Full accounting of cost to society There are counterfactual competing allocations that underlie this concept Opportunity cost of time is the idea for the implicit cost What you could have done with that time the cost of leisure includes the foregone income if you could have had if you worked instead the cost of staying home to care for children includes the foregone wages you could have gotten the cost of studying includes the foregone income you could have gotten These costs plus the explicit costs leisure the cost of the gas and bait and dock fees for your shing trip child care the strollers slings toys for home the studying the books tuition fees lead to the full cost Coming to study here for a year has both an explicit cost of what you pay to attend and an implicit cost in terms of the foregone earnings opportunity of the year you spend here You bought that year from yourself in a sense This gets us towards thinking about zero economic profit The next best alternative is another form of investment that earns a positive rate of return more on this later If you own a piece of land and choose to build a house on it the full cost of building the house are the material labor costs plus the current value of the land by building you are not selling the land In a perfectly competitive market with no externalities and no dynamic implications market price re ects economic cost If this is not the case economic cost can deviate from market prices Historical cost is not important but actual cost is Concept of sunk cost an expenditure that can not be recovered but for scrap value 486 computers Soviet economic planning details The value of these is what the market will bear currently not what it cost when you obtained it Short run costs Fixed cost the production expenses of the rm that do not vary with output Costs of inputs the rm can not feasibly vary in the short term Variable cost production expenses that change with the quantity of output produced Total cost is variable cost plus xed cost Three average cost measures are derived from the fact that TCVCFC Divide through by q TCq is average cost Total cost divided by units of output produced VCq is average variable cost Variable cost divided by units of output produced FCq is average xed cost Fixed cost divided by units of output produce ACAVCAF C In addition we can add in one more cost concept Marginal cost is the amount by which the rrn s cost changes in order to produce one more unit of output Mcz z Aq Aq WARNING FOR THE FIRST TIME WE ARE PUTTING CHANGE IN Q or Q IN THE DENOMINATOR THIS IS IlVIPORTANT TO KEEP TRACK OF Exam ole from the book Output Fixed Variable Total Marginal Cost AFC AVC AC Cost Cost Cost 0 48 O 48 NA NA NA NA 1 48 2 5 73 25 48 25 73 2 48 46 9 4 21 24 23 47 3 48 66 1 1 4 20 16 22 38 4 48 82 13 O 16 12 20 5 325 5 48 100 148 18 96 20 296 6 48 120 1 20 8 20 28 7 48 141 1 21 6 9 20 1 27 8 48 168 21 6 27 6 21 27 9 48 198 30 5 3 22 273 23456789 Fixed Cost I Variable Cost Total Cost Marginal Cost l AFC AVC AC 8 9 The average cost curve is the vertical sum of the average variable cost curve and the average xed cost curve look back at numbers in table and this graph The minimum of the average cost curve is where the AC curve is crossed by the MC curve look back at numbers in table and this graph AVC and AC fall when MC is below them and rise when it is above them if the cost of producing one more unit of output is below the current average the average calculated at the next point will be lower if higher then higher can recall example of marginal person entering the room and changing average height in the room Return to the production function idea and recall diminishing marginal returns to production Show production function XaXis is input level Multiply by cost of the input Then we have output as a function of input cost Tip it over and we have cost as a function of output Given input prices the shape of the cost curve is determined by the production function The shape of the production function is determined by marginal returns with the possibility of increasing returns to scale over low range of output and decreasing returns to scale over high ranges of output show graphs This relationship between the production function and the marginal cost curve leads to the following relationship MCchange in cost change in quantity Cost is VC or C MC cost of input times change in input change in quantity Remembering marginal product is change in quantity divided by change in input we can state MC cost of input MP A similar process holds for the Average Variable Cost so that we can say AVCVCq or cost of input gt input level output level This means AVC input cost AP Summary 7 short run cost concepts Total cost Fixed cost Variable cost Average cost Average xed cost Average variable cost Marginal cost Long run costs What is the value of xed cost F in the long run when there are no xed inputs Zero since all inputs can be adjusted Note idea of avoidable cost There may be costs in the long run that do not vary with output except in the binary sense Three long run cost concepts Total cost Average cost Marginal cost An isocost line A line tracing out different combinations of inputs with given input prices that can be obtained at identical total cost The maximum amount of inputs that can be bought given input prices at a given total cost level Draw example for C10 w2 rl Then C20 Again note that we are saying it is long run cost since two variable inputs but could also have two variable inputs in short run if a third is xed The key here is that we assume there are two inputs to production and both of them are variable K and L The slope is determined by the negative of the relative price ratio Discussion here of deriving the slope of the budget line from the cost function and why the expression depends on whether you put K or L on the yaxis An isoquant is like an indifference curve An isocost is like a budget line However there is a difference in how we treat a budget line and an isocost line Remember the consumer had xed income Y in the consumer theory section Here there is nothing exogenous to cost so we have to think about it differently Firms are choosing cost level while the consumer was not able to choose income level Producing in a way that is technically ef cient meaning and in a way that is cost minimizing is economically ef cient We are technically ef cient on the isoquant curve remember Draw isoquant isocost and contrast points 3 ways of conceptualizing how we arrive at an economically ef cient cost minimizing point 1 Lowest isocost rule Minimum cost subject to producing a given output level ef ciently being on an isoquant 2 Tangency rule The point where the isoquant is tangent to the isocost line Where the slope of the isoquant MRTS is equal to the negative of the input price ratio AK MPL wage w MRTS AL MPK rental r 3 Last dollar rule Pick input bundle so that the last dollar spent on one input adds as much output as the last dollar spent on the other input MPL MPK W I39 The expansion path traces out the cost minimizing combination of inputs for each output level If we look at the line traced out by the tangency points we trace out a line of economic efficiency We can take the information from the expansion path to trace out a long run cost curve note the use of the isocost and isoquant labels which differs from what we did for the demand curve derivation show derivation Lecture 1 PPA 723 McPeak Microeconomics The study of the allocation of scarce resources amongst competing alternatives The study of how best to use limited means in the pursuit of unlimited ends The ideas of optimization and constraints are critical here the idea is constrained optimization Optimizing we do the best we can Constraints given the limits we face The study of tradeoffs and the factors that in uence these trade offs Perloff notes three categories of tradeoffs 1 What goods and services are produced with the given resources that we have 2 What particular miX of resources will be used to produce these different goods and services 3 What will be the distribution of the goods and services we produce Decision makers are assumed to make rational decisions that are most effective in helping them meet their own objectives Whatever they may be Models and assumptions are critical to economic analysis Models are designed to illustrate and understand relationships between different economic variables They are based on simplifying assumptions The main goal of model building is to predict how changes in one variable will impact another variable of interest Key is to model relevant features not every detail Although these models may simplify in ways that eliminate some realistic aspects the goal is to focus on only the aspects of the problem that are relevant Do the predictions change significantly if specific underlying assumptions are relaxed Theories lead to predictions that can be tested We do this by looking at actual data Our rst model i the perfectly competitive market So let us begin by considering the economic model of a perfectly competitive market This is a model of how goods are exchanged between people that have them suppliers sellers and people that want them demanders buyers What assumptions underlie a perfectly competitive market 1 Both buyers and sellers are price takers No individual buyer or seller has enough market power to determine the going market price 2 The good in the market is perfectly homogeneous Different suppliers are providing a good that is identical from the point of view of the consumers 3 Both buyers and sellers have full information about the quality and price of the good in the market 4 There are no costs to completing an exchange that are relevant besides the market price Such costs if they exist can be called coordination costs These can be defined as costs of obtaining and processing information related to the exchange see point three costs of negotiation monitoring agreed upon behavior or enforcing contracts In addition you might wonder Are there spatial aspects to markets We assume they are not relevant in our basic model but there may be things to think about here in reality Think real estate Are there temporal aspects to markets We assume they are not relevant to our basic model but again worth thinking about Is the market appeal of a SUV at low gas prices the same as at higher gas prices Is the market a selfcontained universally defined entity or is it embedded in institutions cultural practices law ways of doing things 7 We assume the model can proceed Without eXplicit reference to these But particularly with regard to point four in the definition can markets eXist Without supporting institutions You can probably think of other aspects that have implicit assumptions Note this is a set of assumptions and these assumptions can be relaxed But it is better to start simple with lots of assumptions and then see What happens when these assumptions are violated We can begin by considering half of the market we just described the buyers This we call the demand side The key element of a model of the demand side is a demand curve It helps if you think of it as a demand schedule that tells you what will happen under a variety of different circumstances It tells you the quantity that will be demanded for a given price level and traces out this information for a range of plausible price levels Example Say the price of NYS red wine is 900 per bottle How many bottles per day will be sold in Syracuse Let s say 1000 What about if it goes to 1000 per bottle Let s say it goes to 950 since a few people buy California red instead of NYS red note CA red is a substitute for NY red Assume that over a period of time we have observed the following relationship and we are reasonably confident that all else has remained constant during this period of time Consider the following table Price Per Bottle Bottles per day demanded 900 1000 1000 950 1100 900 1200 850 1300 800 What does the graph look like Draw graph What is on the XaXis What is on the yaXis What explains the slope note use this to review and eXplain What is meant by slope rise over run XaXis and yaXis and also stress importance of labeling In the example above it was noted that the analysis went forward all else held constant other than the relationship between price of the good and quantity demanded of the good What varied was the price and the corresponding level of demand as measured in quantity If price changed we moved along a demand curve A given demand curve is a relevant statement about the relationship between price of the good and the quantity demanded holding a variety of factors constant Changes in these other kinds of factors lead to a shift in the demand curve so that the original curve is not longer applicable What are these all else constant factors Some examples of things that lead to a shift in the demand curve Take the example of red wine produced in the Finger Lakes Note in this example increase demand means at a given price a greater quantity is demanded decrease demand means at a given price a smaller quantity is demanded 1 Change in consumers tastes a Increase demand Consumers demand more domestic red wine since we are mad at the French b Decrease demand Consumers have decided drinking NYS red wine is so 2007 and moved on to the new trend of drinking NYS honey beer 2 Change in information a Increase demand A study was just released finding one glass of red wine per day is good for coronary health b Decrease demand A study was just released finding NYS red wine makes your teeth turn green 3 Change in the prices of other goods that are logically related to the demand for the good in question a Substitutes A good that can replace the good in question Increase demand A bad year for the Finger Lakes Chardonnay production increases the price of white wines from the area thus leading those NYS wine diehards to switch to reds Decrease demand California red production is abnormally high given weather patterns decreasing the price of California red b Complements A good that enhances your enjoyment of the good in question Increase demand A bumper wheat harvest makes crackers less eXpensive Decrease demand Cheese price goes through the roof as cows go on strike 4 Income a Increase demand Rapid economic growth due to Destiny USA construction leads to massive income increases and people buy more red Wine b Decrease demand The slowing down of the national economy leads consumers to move from NYS red Wine to Milwaukee s Best beer 5 Government rules and regulations a Increase demand The state government reduces the drinking age to 18 so college students from around the Finger Lakes go on Wine tasting tours and develop a taste for NY Wines and buy them regularly b Decrease demand The state government cracks down on underage drinking on Finger Lakes Wine tours Take a numerical example Perloff s Pigs from the book We are going to stick with this example for a while so let us go into it in some depth NA quot46quot U Quantity demanded of processed pork Quantity demanded Q is a function D of the price of pork pp the price of substitutes like the price of beef pb and the price of chicken pc and the income of consumers Y QDpppbpY Notez describe what is meant by a function and how to interpret this equation Using statistical techniques some economists came up with a linear approximation of this function Ql7l 20pp 20p 3p 2Y If we just want to focus attention on the relationship between the price of pork and the quantity demanded of pork we hold other prices and income constant Pb4 Pc3333 Y125 again all this is from the book Q171 20pp 204333332125 Ql7l20pp801025 Q 286 20pp Make a table of this Price in kg Quantity in millions of kg year 5 286205 186 4 286204 206 3 286203 226 2 286202 246 l 28620l 266 This is the same kind of demand schedule as we were looking at in the previous discussion of red wine in NYS Draw this on a graph What is on the yaXis The XaXis What is the slope of this line What happens if the price of beef goes from 4 to 5 Think about it first if the price of beef goes up should more or less pork be demanded at a given price More a shift out in the demand curve At a given price more pork will be demanded At a given quantity the price per unit will be higher Check the intuitive answer by working through the math From the book Ql7l 20pp 20p 3p 2Y Let p be the price of pork after substituting other values Original scenario Ql7l20p20433332 125 Q28620p Compared to Ql7l20p20533332 125 Q30620p If the price of beef goes from 4 to five and chicken price and income is constant Price Quantity 306205 206 306204 226 306203 246 306202 266 l Nwlkm 30620l 286 Draw graph Show shift Note the distinction between a shift in the demand curve and movement along a demand curve This is critical for your understanding of supply and demand so make sure you have it clear A movement along a demand curve means all else is being held constant and we are moving from one point to another on a given demand schedule like in the charts we used before Another way to think about it is that there is a shift in the supply curve leading to movement along the demand curve Whatever changed shifted supply not demand A shift in a demand curve means something in the all else held constant has changed so the entire schedule has shifted and we now have a new schedule Note some types of change can lead to a shift in both supply and demand think about the price of gas for example We will not worry about that in this course and only focus on one shift at a time Supply Supply curve traces out the amount of the good firms are willing to sell at a variety of different price levels Geometric representation of an underlying supply schedule that describes the quantity supplied at a variety of given prices per unit all else held constant Again the focus is on the relationship between the selling price of the commodity and the amount sold of the commodity all else held equal A supply curve tends to slope upward Why as we will go into detail later as price goes up more firms can enter the market or eXisting firms can produce more since they bid away resources from other alternative uses Corn fields turned into vineyards Cattle farms turned into pig farms Draw a basic supply curve Again we have an underlying relationship between price and quantity all else held equal What else might matter that we are holding equal in that all else equal Let us continue to think of pork since we are on a roll and call decreased supply less quantity at a given price supply shift up or in and increased supply more quantity at a given price supply shift down or out 1 Cost of inputs used in production a Decreased supply pig disease wipes out hog supplies raising the price of hogs used to make pork b Increased supply gas prices go down making it lest costly to ship pigs to the pork factory 2 Technology of production a Technology is usually an increased supply story Cornell researchers develop a new pork processing machine that reduces processing waste by 4 for the same amount of input 3 Government rules and regulations in uencing production a Decreased supply Government regulations on sanitary standards in processed pork plants become stricter and more costly to meet b Increased supply Government regulations on overtime pay change reducing total labor costs without reducing labor 1nput Consider the example of the supply of processed pork presented in the book Q5 Sppph Where QS is the quantity supplied of processed pork S is the supply function pp is the price of processed pork and ph is the price of hogs Note the example does not follow exactly the three in uences described above it is assumed there is no variation in technology or regulations and the only relevant cost of production is the cost of hogs Through the magic of empirical methods which you are learning in other classes and is not what we are worried about here the following approximation of the supply function was estimated Qsl7840pp60quot p1 What does this tell you The price of processed pork goes up the quantity supplied of processed pork goes up The price of the input used to make pork goes up the quantity supplied processed pork goes down There is something to the idea that economics is formalizing the obvious You are learning the language of economics but this should be pretty intuitive Like we did before we can simplify by using the sample average price of hogs of 150 This gives us the simple relationship QS884Op Price Quantity 88405288 88404248 88402168 5 4 3 88403208 2 l 88401128 We can draw this graph Now return to the idea that we had the all else held equal condition applied to the price of the input of hogs What if it goes up Let us say it goes from 150 to 200 Qsl7840pp60quot p1 We go from QS884Op to QS584Op Price Quantity 5 58405258 4 58404218 3 58403l78 2 58402l38 l 5840l 98 Shift is up left Less is supplied at a given price graph Note on supply and demand graphs The first people in economics to draw these drew it backwards from the way math works and from the way we have been talking about it Usually in math the X aXis is the variable and the y aXis describes a function of this variable as in yfX Here we talk about quantity as a function of price q fp but price is on the y aXis and quantity is on the X aXis Economists are a funny bunch However recall that these curves describe the relationship between quantity and price We can think about a change in quantity leading to a change in price or a change in price leading to a change in quantity either direction of causality could apply We could redefine QS884Op and QS584Op by rearranging terms QS884Op so divide through by 40 140QS88404O40p so 140QS22p SO pwhen price of hogs 150 l40QS22 QS584Op repeat same steps if needed Leads to pwhen price of hogs 200 l4OQS145 p0 intercept for 150 graph is 88 p0 intercept for the 2 graph is 58 Of course p is not ever zero so we should think of this as the logical extension of the line but not a prediction Sometimes called the tyranny of the straight line or less dramatically being off the support of the data Sometimes this helps make sense of the math relating to the graph 20 McPeak Lecture 6 PPA 723 Constrained consumer choice What is the optimal bundle The bundle of goods that makes the consumer as well off as possible given a particular budget constraint The bundle consumed at the point where the indifference curve is tangent to the budget line Graph with points a b c d B is the optimal bundle C is not as it is not in the opportunity set A is in the opportunity set but has less of good 1 and 2 than b so must be worse D is in the opportunity set and has more of good one less of good 2 By looking at the indifference curves and knowing their properties we can rule it out Technical note A solution is an interior solution if the optimal bundle involves the consumer consuming positive amounts of both goods A solution is a corner solution if the optimal bundle involves the consumer consuming zero of one of the goods We will focus on interior solutions For an interior solution the marginal rate of substitution equals the marginal rate of transformation We know these expressions have other forms so we can write the expanded equality for the condition of an interior solution as follows MUX1 AX2 3 MRS MUXZ AXI P2 MRT A nice way to think about it is that the optimal bundle equates the marginal utility per dollar spent on good 1 with the marginal utility per dollar spent on good 2 Mle MUX2 P1 Pz Example Price of apples is 050 price of oranges is 080 Consumption bundle is 4 apples and 10 oranges Income is 10 MUapplesapples4 oranges103 MUorangeSapples4 oranges104 First is the consumer on the budget line at the consumption bundle in question What does a budget line look like P1 39X1 132 39X2 Y or 05039408010 10 OK so on the budget line not above not below Draw with oranges on y aXis apples on X aXis What is MRS at observed consumption bundle MUapples MUoranges or 2075 What is MRT at observed consumption bundle price of apples price of oranges or 0508 or 0625 Market says I have to give up 625 oranges to get 1 more apple My preferences say I am willing to give up 75 oranges to get 1 more apple to be equally happy I can give up less than that and have some left over to make me move up to a higher indifference curve Or MRS at that point says give up 3 oranges to get 4 apples MRT says give up three oranges to get 48 apples Why give up oranges to get more apples and not the other way MUX1 Msz around p1 p2 MUapples MUoranges papples pomnges at optimal bundle but MUaPples 3 6 gt MUorangeS 4 paPPIeS pomnges at current bundle I need to bring down the marginal utility of apples bring up the marginal utility of oranges By diminishing marginal utility I get higher marginal utility by consuming less of a good lower marginal utility by consuming more of a good So to bring MUapples down I need to consume more apples To bring MUmnggS up I need to consumer fewer oranges Thus more apples fewer oranges say 12 apples 5 oranges which satis es the budget constraint and under the assumption that MUappl6S apples12 oranges 5 275 MUmngS apples12 oranges 5 44 Remember MRS is the rate at which a consumer is willing to give up one good to get more of the other It comes from the underlying preferences of the consumer MRT is the rate at which prices let a consumer give up one good to get more of the other It comes from the underlying market conditions and has nothing to do with the consumer s preferences Show comer solution In this case the indifference curve is not tangent to the budget line since reality intrudes The underlying preferences cause this and since we take preferences as given we can run across this It happens when the consumer has a strong preference for one good as compared to the other Food stamp example Consider good 1 is food good two is all other goods Food stamps are given to the consumer and the value of the stamps can only be spent on food 100 worth let us say Consider extreme examples where all is spent on one good or the other again However note there is an issue about the constrained nature of the food stamp program Graph Shape of indifference curves matters here Is the consumer better off getting 100 cash or 100 in food stamps better off with food stamps than without in either case Graph for equally well off whether the transfer is in cash or in food stamps Graph for worse off when the transfer is in food stamps rather than cash Note in both cases consumption of the other good has increased in spite of the fact that the program is targeted at food General result a subsidy program that constrains consumer choice will do worse or no better than an unconstrained transfer Why do we constrain the transfer in the case of food stamps then What is the impact on the budget constraint of a black market in food stamps that lets you get 30 cents on the dollar face value Show graph Chapter 5 How do we derive a demand curve Remember that we began the course by taking a supply curve and a demand curve as given Now we are going to nd out where a demand curve comes from Ingredients Budget line Indifference curves Variation Go back to our basic budget line pp X1 p2 X2Y rst with Y100 p125 and p2 10 Then consider Y100 p15 and p2 10 Y100 p110 and p2 10 On the same graph X2 10X110X2100 0 2 4 6 810121416182022242628303234363840 graph X1 Draw some indifference curves on this 10X110X2100 low I middle 0 2 4 6 8101214161820222426283032343638 X1 The line connecting these points traces out the price consumption curve 55 105 20 5 In this case it is a horizontal line due to the simple form I picked for utility P1 5 10 20 X1 We can summarize the information in this form All else constant how does a change in price impact the quantity demanded for a given good Sound familiar This is the derivation of the individual s demand curve for a particular good The line traced out by this the price consumption curve will re ect the individual s underlying preferences For a different individual one who has less of a preference for X2 than the individual just considered we would get the following result 10 x110 x2100 100 25 X110 x2 low Imiddle 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 X1 Q of goods Price 6 4 1 0 1 4 3 5 283 25 Now if we take each indiVidual s demand curve and sum them horizontally we end up with the market demand At a price of 10 consumer I wants 5 and consumer 2 wants 6 1 1 At a price of 5 consumer I wants 10 and consumer 2 wants 14 24 At a price of 25 consumer I wants 20 and consumer 2 wants 28 48 What about a change in income 131 X1 p2 X2Y rst with Y50 p110 and p2 5 Y100 p110 and p2 5 Y150 p110 and p2 5 10x15x250 low middle 0 012 3 4 5 6 7 8 910111213141517192123 The line connecting the optimal bundles de ned by increasing income is the Income Consumption curve At a given price of 10 for good one we can draw these quantities on a price quantity graph to illustrate the idea of demand shifts 12 10 The graph traced out by placing income on the y axis and quantity on the X axis is called an Engel curve It traces out the relationship between the quantity demanded of a single good and income Remember the idea of income elastiticites from before Here is where they come from A normal good has a positive income elasticity an inferior good has a negative income elasticity What is the formula for an income elasticity change in q diVided by change in income A good can be normal for one person and inferior for another A good can be normal for one person at one point in their life and inferior at another A good can be normal at one level of income and inferior at another We can block out space from an optimal bundle to areas where both goods are normal one good is normal and the other inferior Can both goods be inferior Show on graph What is the impact of a price change First we identify the change in the quantity demanded as a result of a price change as the total effect We decompose this total effect into two distinct components 1 The substitution effect If utility and the price of the other good are held constant as the price of one good rises consumers substitute between the two goods to re ect the new price ratio Since MRSMRT price change leads to a change in MRT the consumer will adjust the consumption bundle along the indifference curve to reequate MRS and MRT 2 The income effect A change in price changes the consumer s buying power Recall the example of how a halVing of prices is equivalent to a doubling of income This is the core idea here If the price of good one goes down all else held constant that is going to increase the consumer s buying power which is like increasing their income Total effect substitution effect income effect Since indifference curves are downward sloping can we predict the sign of the substitution effect The change in price and the substitution effect should have opposite signs An increase in price leads to less of the good being consumed A decrease in price leads to more of a good being consumed Show graph However the income effect depends on whether the good is a normal or an inferior good A Giffen good is one for which a decrease in price causes quantity demanded to fall the income effect outweighs the substitution effect making the total effect negative Not observed in reality but an interesting example Show graphs for substitution effect for normal good inferior good and Giffen good For edi cation inoculation This graphically represents what in economics is known as the Slutsky equation It describes the relationship between two different approaches to deriving the demand function One a money income held constant derivation the Marshallian and a second utility held constant derivation the Hicksian Show three graphs for a price decrease One 8 IT39 Two 8 1 T39 Three 8 1 T McPeak Lecture 13 PPA 723 Public Goods Go back to the idea of goods being categorized by rivalry and exclusion Exclusion No Exclusion Rivalry Private Good Open Access No Rivalry Club Good Public Good Private good candy bar Open access good sh in the ocean Club good concert movie country club Public good national defense clean air city park A commodity or service for which the consumption by one person does not preclude others from consuming the commodity or service and for which it is not feasible to exclude any one individual from access to this commodity or service Provision of a public good creates positive externalities The value of the bene ts is not re ected in a market It does help some to think through the supply and demand for a public good The social demand curve for a public good is derived by the vertical summation of the individual consumers willingness to pay for the good in question for all consumers Recall that a private good had the horizontal summation for each consumer For a price of 2 I want 3 Whoppers you want 1 a total of 4 is demanded You and I are the only people and if one of us consumes it the other can not Now consider a public good The free rider problem leads to underprovision of public goods There is an incentive to bene t from a positive externality without paying the cost of public good provision There are two stores side by side but one entrance to the two stores Each store is deciding whether to hire a guard to sit by the main door Two guards are no more effective than one guard Costs 10 to hire Bene t of a guard at the main door is 8 to each store Baseline is no guard no bene ts 0 Hire Don t hire Hire 2 2 2 8 Don t Hire 8 2 O O Say we consider cooperating and splitting the cost Costs 10 to hire Bene t is 8 to each store Hire Don t hire Hire 3 3 2 8 Don t Hire 8 2 O O Still don t hire Show on graph The societal demand curve is arrived at by vertical summation by all who will bene t from the public good Ways to deal with the free rider problem 1 Social pressure 2 Mergers 3 Privatization 4 Compulsory provision Voting and public goods Finding everyone s valuation is dif cult if not impossible Even if you knew practical issues arise about charging different people different rates Usually we end up charging a uniform rate Median voter theorem A project will pass if the median voter s valuation is greater than the cost to that voter Project is atraff1c light Total cost of light installation is 300 There are 3 voters here who get bene ts and pay the costs Assume they split the costs evenly so each one pays 100 per light installed Three corners are being voted on and the following represents the voters WTP Fred Barney Wilma Corner A 50 100 150 Corner B 50 75 250 Corner C 50 100 110 Corner A has a total WTP of 300 Corner B has a total WTP of 375 Corner C has a total WTP of 260 Which ones will pass if we vote and people vote yes if their WTPcost is greater than or equal to zero Yes no voting ignores intensity of preferences If the valuation of the median voter is greater than the cost to that voter it will pass a vote with a majority How do we gure out WTP for public goods Some Methods 1 Hedonic Methods Information on public good demand is embedded in price and consumption levels for private goods Consider the case of environmental quality It is a implicit characteristics of a good you can buy in the private market We can disaggregate the observed selling price into its component parts We need to have some measure of the public good in question along with observed selling prices and observed characteristics of the commodity sold Price is a function of characteristics House purchaser maximizes utility subject to a budget constraint by selecting a house with a given set of characteristics and price Examples Houses next to parks Houses next to sewage treatment plants The debate over SU putting up fences and lights in the Hookway tract Case One Lakefront footage requirement on northern lakes in Wisconsin The county extension agent came to us with a question Counties in northern WI were considering raising the minimum frontage requirement from 100 feet to 200 feet There was debate about whether this was a good thing or a bad thing Externalities from zoning 1 Positive externality You look across the lake and see fewer houses If part of you enjoyment of you lakefront house is some kind of wilderness view this helps you Amenity effect Negative externality You can t develop your property in the way you could before the law changed The value of your property in development has been reduced Development effect 2 V What is the net impact 892 transactions for undeveloped properties between January 1986 and December 1995 o The amenity effect is signi cant and positive 0 The development effect is not signi cant but is negative 0 The 200 foot rule increases property values by 1582 per foot 123 0 Also an increase in the percent of lakefront that is held as public lands signi cantly increases the value of a property Case Two Permits to Graze on Public Lands in New Mexico Ranchers are allowed to graze on BLM Forest Service and New Mexico State land Permits are not bought or sold They have no explicit price They are transferred to the purchaser of a ranch when the ranch is sold A policy goal is to charge fair market value for the use of public lands There is a grazing fee associated with the use of a permit Fair market value in this case would be to set the fee so that there is no value to a permit positive or negative Permits are in terms of animal unit months 452 ranch sales between January 1979 and December 1988 Regress price on characteristics including permit Implicit value of a permit is signi cantly different larger than zero in ve out of 10 years for BLM permits 8 out of 10 years for forest service permits and 7 out of 10 years for state permits Also by investigating how permit value changes in response to grazing fees we find that if fees increase permit value decreases 2 Travel Cost methods If there is a site speci c public good you can look at the implicit cost of travel to the site as an implicit price of access to the site The individual s utility depends on the total time spent at the site the quality of the site the individual s opportunity cost of time and other stuff The individual maximizes utility subject to monetary and time constraints Case One Lake Michigan Anglers 97 anglers followed from May to September 1996 and 1997 We called every two weeks and recorded trip information At the end of the study we collected background demographic information including their income levels Mostly MilwaukeeRacine area anglers Estimated seasonal value of shing 500 to 700 dollars Current catch rates are on the order of 12 to 2 sh per hour depending on the day season year What is the expected bene t of increasing this rate by 1 sh per hour Findings suggest somewhere in the 10002000 range Most of the sh these people are shing for are raised in hatcheries What is the amount that should be spent on providing the public good of swimming easter eggs so that a higher rate per hour catch is possible 3 Private expenditures on a substitute in the absence of a public good Not as common in the literature but interesting results can be obtained The question here is how much do people pay privately in the absence of public good expenditure We each hire private security rms in the absence of public security We buy bottled water in the absence of a clean municipal water supply or how much do we spend per year boiling municipal water since it is not safe to drink unboiled We buy kerosene to fuel our lamps since there is no electricity Can you provide a public good that substitutes for what people are already paying for at a lower price than they are currently paying 4 Contingent Valuation Used to estimate values for environmental amenities and other nonmarket goods and services Surveys are designed to elicit monetary values for non market goods contingent upon creation of a market or other means of payment The transactions are hypothetical What are you willing to pay for a speci ed change or to prevent a speci ed change from happening The response is a direct measure of the individual s valuation of the non market good or service Case One Nonpoint Source Pollution and Present Values Lake Mendota Wisconsin DNR is worried about phosphorus loading in Lake Mendota The biomass in the lake responds to phosphorus through sudden and massive algal blooms These stink are ugly and take a lot of work to clean up Also there is an environmental impact through decreased dissolved oxygen content of the lake harming sh species and plant species in the lake Runoff from dairy farms Runoff from crop fields Runoff from yards and golf courses Increased pavement increasing runoff Proposal a program to reduce the number of blooms in the summer from one out of every two days to one out of every five days The proposal outlined specific measures that would reduce phosphorus runoff Spectrum of choices Would you vote yes or not if it cost 0 yes or no if 5 yes or no if 10 over 300 each year for each of the next three years Mean willingness to pay is 353 per year Case Two Willingness to pay for wind power Madison Gas and Electric was considering implementing a wind power program They were going to build some windmills If you signed up you would voluntarily pay more to help meet the costs of the windmill and decrease the use of coal to generate electricity We took this opportunity to compare actual willingness to pay with hypothetical willingness to pay We told one subsample they could sign up for 24 per year another at 48 per yearup to 288 per year They said yes or no The hypothetical group had the same intervals but it was phrased if we were to offer this and it would cost you would you agree to pay yes or no 7 How many actually signed up 24 How many said they would hypothetically 43 How much did people sign up to purchase on average 59 How much did they agree in the hypothetical case to purchase on average 101 We asked a follow up question about how certain they were about their answer in the hypothetical case For those who were more certain the actual and the hypothetical converged McPeak Lecture 3 PPA 723 Now we move to the topic of quantitative change Not only the question of which direction but how much in that direction We might be interested in the how much question For planning purposes we may be interested not only in what direction but how much in a given direction we will move as a result of a given policy For this we will see that the shape of the curves matter How steep are our curves Let us consider a shift in the demand curve Where the new equilibrium lies will depend on the slope of the supply curve Say for example that the price of beef goes up and we are still considering our processed pork example We could do it by an equation by equation approach or a graph by graph approach Review the impact of the price of beef going from 4 to 5 Ql7l20p20433332125 Q28620p Compared to Ql7l20p20533332125 Q30620p If the price of beef goes from 4 to five and chicken price and income is constant Price Quantity if pb4 Quantity if pb5 5 286205 186 306205 206 4 286204 206 306204 226 3 286203 226 306203 246 2 286202 246 306202 266 1 286201 266 306201 286 Supply curves Consider a supply curve de ned by QS5550p or 5 l 55 pTyQ E 1 88 Originally given QS8840p or PW39Q E Consider a supply curve de ned by QS12130p or l 121 FEQ E Price QS5550p QS8840p QS12130p at original steep 5 55505305 88405288 121305271 4 55504255 88404248 121304241 3 55503205 88403208 121303211 2 55502155 88402168 121302171 1 55501105 88401128 121301151 How did I get these supply curves I wanted them to all pass through 330 220 so I plugged these in and moved the slope from 40 to 50 and then to 30 and in each case solved for the intercept term To graph them I solved for p as a function of q for example p140q8840 7 Different Supply functions 6 i l x 5 o 4 2 a 3 5550p 1 z 12130p 0 i i i Q Q Q Q Q Q Q Q Q 0 lt5 quot03 Q 9 qgtQua i lbtity b if 9 Q N Add in the issue of demand shift 8840p x 55 50p 12130p 28620p 45 30620p 425 4 35 I 9 325 V Demand shift different supply 475 3 r 275 25 21 O 220 230 240 What are the different implications at77 30620p5550p p359 q234 original 30620p8840p p363 q233 Steep77 30620p12130p p370 q232 These are made up numbers but it does show that the underlying numbers that determine the shape of the curve matter for where you end up in equilibrium if things change In many cases we can use a simple measure of sensitivity to capture important information about quantitative change This is elasticity a unitless summary measure of sensitivity Elasticity The percentage change in one variable as a response to a given percentage change in another variable change x change y Supply Elasticity AQS Ap eta change in quantity supplied divided by the percent change in price The symbol for change is delta A AQS Qs AQp 7 ApQ Alternatively de ne it as p or Below one we call inelastic l is unit elastic Above one is elastic In nity extremes are perfectly elastic zero is perfectly inelastic Note 1 elastic inelastic elastic oo 1 0 l 00 2 Intuition behind word elastic 3 Calculus link at77 Try the calculation for QS 5550p that led us to the p359 q234 pair Remember that we moved from an equilibrium pair of 330 220 Change in q 220 to 234 14 units q Change in p 330 to 359 029 AQ A AQS S Q Q E n Ap s A Ap p Q I9 KG 330 J AQ 14KG 220KG 636 233231 029 220KG Ap 0 29 330 8 79 330 n072 original Consider the original curve Remember that we moved from an equilibrium pair of 330 220 to the equilibrium pair 363 233 when we used QS 8840p Change in q 220 to 233 13 units q Change in p 330 to 363 33 cents A AQ s 1 n S A Ap p Q I9 EKG 330 J AQ13KG220KG59 281 033 ZZOKG Ap03333010 330 n059 steep How about the Q12130p supply curve that took us to p370 q232 when demand shifted Change in q 220 to 232 12 units q Change in p 330 to 370 40 cents AQ A AQS s n 2 Q Q E Ap s A Ap p Q I9 IZKG 330 J AQ12KG220KG545 281 040 ZZOKG Ap040330121 330 n045 Which was the most sensitive to a change in price The one with the highest elasticity has the highest change in the quantity supplied for a given change in price That is our 5550p supply curve 7 Different Supply functions 6 i l x 5 o 4 2 a 3 5550p 1 z 12130p 0 i o o o o o o o o o 0 lt5 quot03 Q 9 qgtQua l lbtity 3 l3 l9 Q N This is a general pattern to keep in mind but don t get too caught up in A atter curve as drawn above has more response in quantity for a given change in price than a steeper curve Steep curves tend to be inelastic price change does not bring about much change in quantity Think of our steepest curve the coefficient on the price variable is 30 For our attest curve it is 50 Get the idea In demand analysis we are often interested in the price elasticity of the quantity demanded What is the percentage change in the quantity demanded diVided by the percentage change in the price Use the Greek letter epsilon 8 Recall that the symbol for change is delta A AQ 8224 Ap AV p Can state this in an equivalent fashion J9 AP Q Now in our demand shift case we don t have the information we need for the elasticity calculation from the preVious example where we calculated a supply elasticity NOTE THE PRICE ELASTICITY OF DEMAND IS ABOUT MOVEMENT ALONG A DEMAND CURVE NOT A SHIFT IN A DEMAND CURVE We had a demand shift giVing us two points on the supply curve in each case above to work with Now for the demand elasticity I have to generate some kind of supply shift to get a similar story going So go back to our original story yet again Qd28620p QS8840p Remember this took us to the equilibrium point p330 q220 Compare alternative demand curves as I did before for the alternative supply curves Iwill pick one steeper one atter 88 40p 1 18 40p 25310p 28620p 48480p 210 220 230 240 250 Supply gt If we have the given supply shift we can see along the alternative demand curves Recall that the processed pork supply curve was a function of the hog price Assume the hog price decreases from 150 to 100 This leads to a downward shift in supply I can produce more pork at a given selling price since my input cost decreased QS11840p according to the information in the book and again recall 330 220 is how we start Consider three alternative demand curves at77 The attest case is Qd48480p p605lt0125q Solve for the new equilibrium nd p305 q240 Change in q is 20 Change in p is O25 0 AQD AQ p g 2 MQD Q 39 Ap D A Ap p Q I9 MKS ZOKG 330 J AQ20KG220KG 91 325 025 220KG Ap 025 330 7 6 330 The original case Qd28620p p143705q Solve for the new equilibrium nd p280 q230 Change in q is 10 Change in p is O50 1 Ap Q g AQD Ap IOKG 330 J 050 220KG AQ 10KG220KG 45 Ap 050330 152 Steep77 Solve for Qd25310p p 2531q If you solve this one for the new equilibrium after the shift you get p270 q226 Change in q 220 to 226 6 units q Change in p 330 to 270 O6O 0 AQD AQ p g 2 MQD Q Ap D A Ap p Q l9 6K6 330 J AQ6KG220KG27 03960 ZZOKG Ap 060330 182 330 8O15 Recall elastic inelastic elastic oo 1 0 1 00 When elasticity is between 0 and l we call it an inelastic price elasticity of demand When elasticity is equal to l we call it a unitary elastic price elasticity of demand When elasticity is less than 1 we call it an elastic price elasticity of demand NOTE THE NEGATIVE SIGN Also can speak of elasticity in terms of absolute value Less than one in absolute value is inelastic greater than one is elastic Realize that a calculated elasticity may only be applicable in the neighborhood of the equilibrium not for the entire demand curve Note that these calculations are for a given point on the curve Take the example of the baseline curve that had a constant slope of l20 Qd28620p that is expressed as inverse demand of pl43005q Price Quantity if pb4 5 286205 186 4 286204 206 3 286203 226 2 286202 246 l 28620l 266 AD AQ p Q 8 l to 2 l 20 l 266 008 2 to 3 l 20 2 246 0 l6 3 to 4 l 20 3 226 O27 4 to 5 l 20 4 206 O39 A constant slope is not the same as a constant elasticity 20 unit change in Q is what of Q 100 80 60 40 20 0 QQQQQQQQQQ vbsxvx brtvbsgmgb L Qua ntity Elasticity is a result relevant to the area around you equilibrium Also note the concept of arc elasticity where you take the average of the starting and the ending points in de nin p and q Ap AQ Aye p Aye Q a 1 to 2 1 20 15 256 O12 2 to 3 1 20 25 236 O21 3 to 4 1 20 35 216 O32 4 to 5 1 20 45 196 O46 Arc elasticity 5P1P2 AP 5Q1Q2 Two other elasticities used in demand analysis now we are looking at sensitivity of shifts in the curve rather than sensitivity in terms of movement along in response to a shift A change in the all else equal set of variables Income Elasticity What is the percentage change in the quantity demanded divided by the percentage change in the income level that brings about this change in quantity demanded aQ WK Xl is the greek symbol used here Take the example of the pigs again Recall the baseline equation Ql7l 20pp 20pb 3p 2Y Pb4 Pc3333 Y125 Assume a one unit change in income from 125 to 135 so you can use the coef cient on the income variable in the quantity demanded equation Also recall the baseline equilibrium result of p q 330 220 220171 2033020433332125 222171 2033020433332135 Change in q 2 Q 220 Change in Y We assumed it to bel Y 125 0 AQD Y g A AQD Q AY D AY AY Q Y 2K6 MlWW AQ2KG220KG91 21322 101 100 220KG AY 1001250 80 1250 g 252200r 0114 A normal good is one for which the income elasticity is positive An inferior good is one for which the income elasticity is negative Inferior goods tend to be things like staple foods Not a bad mind you but something that you will consume less of as your income increases Brazil 197475 Income elasticity for cassava l59 for rice 0172 for milk 0147 for eggs 0630 Shows the relationship between income and quantity demanded holding prices constant Example of economic models of the demand for children are children a normal or inferior good 20 Cross Price Elasticity What is the percentage change in the quantity demanded diVided by the percentage change in the price of another good that brings about this change in quantity demanded AQI Q 1 8 Apz P2 Q171 20pp 20pb 3p 2Y Pb4 Pc3333 Y125 Where there are two goods good one and good two Think of the pork example and think a one unit change in the price of beef 220 171 20330204333332125 240171 20330205333332125 21 Change in Q 20 Q 220 Change in price of beef We pick 1 dollar for ease of computation Price of beef 4 0 AQD AQ p g 2 MQD Q 39 Ap D A Ap p Q 17 20m 400 J AQ20KG220KG91 2 100 220KG Ap 100 4 00 25 400 Mix ingredients and you get 036 If you want to practice try the chicken price changing by one dollar and you should get 0045 A complement of a good is one for which the cross price elasticity is negative A 1 increase in the price of bacon leads to a change in the quantity demanded of eggs A substitute of a good is one for which the cross price elasticity is positive A 1 increase in the price of bacon leads to a change in the quantity demanded of sausage What have we found with the beef example here a complement or a substitute for processed pork 22 What does an elasticity mean Let s go back to demand elasticities Goods that are relatively price inelastic mean that a large change in price leads to a relatively small change in the quantity demanded of the good Goods that are relatively price elastic mean that a small change in price leads to a relatively large change in the quantity demanded What determines the degree of elasticity l Closeness of substitutes 2 Time period over which these substitutes can be obtained 23 Long run versus short run elasticites Goods tend to be more price inelastic in the short run and more elastic in the long run Short Run Long Run Gasoline O2 O5 HH Electricity Ol l 9 Air Travel Ol 24 Intercity bus travel 20 22 Elasticity example Washington DC needed money in 1980 and they increased the excise tax on gasoline sold in the district by 6 If we use the short run elasticity example here what percent reduction in demand should we predict 2 change in Q6 a 12 reduction In the long run a 3 reduction What happened Well six months after implementing the policy sales of gasoline in the district had reduced 33 What is the implied price elasticity of demand 336 or 55 They repealed the tax after ve months What went wrong 24 McPeak Lecture 12 PPA 723 Externalities An externality occurs when an economic agent s consumption or production activities confer a bene t or impose a cost on other actors and this bene t is conferred or this cost is imposed outside of a market that is to say it takes place in a way other than through changing prices Alternatively an extemality occurs when a person s wellbeing or a f1rm s production capability is directly affected by the actions of other consumers or firms rather than indirectly through changes in prices A consumption extemality is an extemality generated by the consumption behavior of an economic actor Smoke Drunken louts Loud music Vehicle exhaust A production externality is an externality generated by the production activity of a rm Smokestacks Acid rain Noise and shaking houses Odors Externalities can be positive or negative An externality that harms others by imposing a cost on them is a negative externality An externality that helps others by conferring a bene t to them is a positive extemality What is a positive externality to one person can be a negative extemality to another wind chimes Positive externalities are sometimes called spillovers Positive externalities play a prominent role in growth theory and economic development Also can be used to explain endogenous neighborhood formation and the persistence of poverty over time in speci c areas We are going to focus mostly on negative externalities here Private cost diverges from social cost in the presence of an extemality and in the presence of a negative extemality SC is greater than PC Pareto optimality An allocation of resources is Pareto optimal when it is not possible through any feasible changes in the resource allocation to bene t one person without making at least one other person worse off If an allocation is not Pareto optimal it is not economically ef cient An allocation is inef cient when it is possible through some feasible change in the allocation of resources to make at least one person better off without making any other person worse off If an economy does not arrive at a Pareto optimal outcome it has suffered from market failure In the presence of an externality the harmed party is theoretically willing to pay the harming party to reduce the activity generating the extemality but no market exists for them to conduct such an exchange We may have moral objections here but the idea is that I am made worse off by the externality and there is some cash value I am willing to pay to eliminate the source of this reduction in my utility Market failure in a production setting occurs when rms equate private marginal cost with price rather than social marginal cost with price In a competitive market more of the good and more of the extemality will be produced than is socially optimal since private cost is less than social cost show graph Welfare is maximized when price equals social marginal cost 1 A competitive market may produce negative externalities thus making the market equilibrium not socially optimal 2 The optimal amount of pollution is greater than zero Can address by regulation Government can control the size of the extemality by imposing an emission standard that limits the quantity of the extemality imposing byproduct of production Can also charge an emissions fee that taxes the amount of the emission If such a taX is designed to fully internalize the externality it is called a Pigovian taX show graph Taxes on fuels Externality as a Tax as of price of price Natural Gas 11 64 Gasoline 167 166 Diesel 504 129 Coal 5280 359 Point source pollution is pollution that can be traced to a single point there is an identi able source of the pollution that can serve as the point of control It is coming from that smokestack over there Nonpoint source pollution is pollution that cannot be traced to a single point multiple small sources make it hard to identify where it originated It is coming from all these burping cattle Market structure and externalities Remember that a monopoly producer selected an output level below the level that would be arrived at in a competitive market thus leading to deadweight loss of monopoly Remember that a producer that generates negative extemalities is producing more than is socially optimal since MSCgtMPC Can these offset Potentially yes show graphs The monopoly output may be less than the socially optimal level equal to the socially optimal level or greater than the socially optimal level It will be less than would be generated in a perfectly competitive market The overall point is that in the absence of externalities social welfare is maximized under perfect competition This is not the case if externalities are present Coase Theorem In the absence of transactions costs and with symmetric information the initial assignment of property rights does not matter in determining the ef cient allocation of resources though it may matter from a distributional standpoint Cattle owner and a crop grower 1 Is the right to grow crops without bearing the costs of livestock damage 2 Is the right to graze without facing limits imposed by individuals planting elds The rancher is liable to compensate the farmer for damage in case one the farmer is liable to compensate the rancher in case two From an ef ciency standpoint the outcome will be the same Boat owner rents boats to cruise about Onondaga Lake Chemical rm dumps gunk in Onondaga Lake They choose levels of production and have the following payoffs Initially assume neither firm has the right to compensation Boat Company boats used 0 1 2 Chemical 0 0 0 0 14 0 15 tons dumped 1 10 0 10 10 10 5 2 15 0 15 2 15 3 Chemical firm has dominant strategy BR to anything the boat firm does is 2 Boat firm knows this chooses 1 1 boat 2 tons gunk Now assign right to boat firm that says they must be at 7 ton Boat 0 2 1 11 BR 1 1 1 1 ton Now assign chemical firm the right to be compensated for any reduction in gunk emission from 2 tons at 6 per ton Why might such compensation schemes not occur break down in reality 1 Transactions costs may be high How to bargain on behalf of one party if they are many 2 Lack of information What are the costs Do both sides know and agree on the MC of the externality Is the pro t matrix agreed upon Tragedy of the commons Where do we have common property resources When a good is rival and has no exclusion Rival means one actor s consumption of the good in question precludes another actor s consumption of the good the good is depletable Exclusion means that others can be prevented from consuming the good The sh in the ocean the grass in a pasture the water in a river the oil under the ground a seat in the lounge a quick trip down a road a quick download from the intemet There is a distinction between a commons and an open access resource In a commons the number of users is de ned leading to greater cooperative potential In an open access situation there is no restriction on the number of users Commons the academic village Open access Marshall street Hardin provided the example of a village commons where multiple users have the right to graze animals There is an incentive problem in the commons Each user has an incentive to add animals and does not take into account the externality imposed on others brought about by adding this animal only the direct costs they bear Note the distinction between an appropriation externality and a provision externality An appropriation externality is a static extemality and it is either your animals or my animals get the grass to produce milk in this setting A provision externality is a dynamic extemality and it is that together our animals impose a cost on the future provision of the good produced in the commons that is we can cause environmental damage through overgrazing There is one pasture we share in common and let s keep it simple and have it be just the two of us using this On this pasture milk production as a function of total herd size is as follows of animals Liters of milk produced 0 O 5 10 10 20 15 3O 20 36 25 4O 3O 44 0 5 10 15 20 25 30 For each livestock owner the share of this total milk produced they receive is a function of your share of the total herd The cash value of milk is 1 per liter For each animal put on the pasture it costs 1 in private labor costs 5 animals costs 5 10 animals costs 10 So if I have 5 animals and you have 5 animals my payoff is 510205 or 5 Ifyou had 15 animals and I had 5 then it is 520365 or 4 We can develop the following matrix of payoffs Hj 1 fhjh2 ch1 hf 142 to give the general form 0 5 10 15 0 0 0 0 5 0 10 0 l5 5 5 0 5 5 5 10 4 12 10 10 0 10 5 8 8 6 9 l5 l5 0 12 4 9 6 7 7 can extend down here to 20 160 25 150 30 140 Can go through and identify best response strategy There is a Nash equilibrium in pure strategies of 15 15 with a payoff of 7 to each Note however that if they could restrain their stocking levels to 10 they would arrive at a Pareto improving outcome What if I privatize and assign exclusive rights to one of the individuals O O O O 5 5 O 10 10 O 15 15 O 20 16 O 25 15 0 3O 14 O I arrive at the ef cient stocking level as pro t is maximized where total herd size for one individual is equal to 20 and the total payoff is 16 Not really very fair though is it What about if we give the exclusive land right to one of the herders on the condition that the other herder is allowed to use the land if he pays 80 cents per animal to herder one Herder one puts ten animals on gets 16 lO2036108 while herder two puts ten animals on and gets zero lO2036 108 So this is an alternative that takes you to the ef cient though not very fair outcome Also consider the possibility that we develop an outside agency say the state This agency is able to impose a herd size limit of 10 animals per person and is capable of enforcing this Finally consider the state charging a user fee of 50 cents per animal in addition to the one dollar per animal labor cost The following payoff matrix results O 5 10 15 O O O O 25 O 5 O 75 5 25 O 25 25 25 5 15 45 10 5 O 5 25 3 3 l l5 15 75 O 45 15 15 l O5 O5 This also takes us to the socially eff1cient stocking level of 10 10 Now the state gets 10 in tax revenue as well localized degradation paper Responses to the commons 1 Land tenure reform assign rights think Coase 2 Limit use restrict quantity think emissions standard 3 Charge fee that intemalizes the negative externality think emissions fee McPeak Lecture 7 PPA 723 Firms and Production Firms Three main kinds 1S ole proprietorships 2Partnerships 3Corporations Limited Liability Objective of the rm make decisions so as to maximize pro t Pro t is de ned as revenue What it earns from selling the good minus costs What it costs to produce the good TC 2 R C or in slightly different form TEpfX WX Necessary vs sufficient conditions A necessary condition is in the nature of a prerequisite Statement A is true only if another statement B is true then A only ifB or If A then B B is a necessary condition for establishing the truth of A If a person is a father A then they are a male B Being male B is a necessary condition for being a father A If Felix is a cat A then Felix hates baths B Felix is a cat only if he hates baths If A cat then B hates baths Can we turn it around If B hates baths then A cat If Felix hates baths can we assume Felix is a cat No Felix might be a four year old boy for example Felix hating baths is a necessary condition for Felix to be a cat but it is not sufficient It is one characteristic of being a cat but this characteristic is shared by noncats as well Consider the situation Where A is true if B is true but A can be true when B is not true B is a suf cient condition for A but B is not a necessary condition for A A ifB IfB then A A is one can get to Chicago from Syracuse B is There is a plane that ies to Chicago from Syracuse then the truth of B suf ces for the establishment of the truth of A but is not a necessary condition for A to be true B is a suf cient condition for A but not a necessary one Consider where A and B imply each other A is it is the month of February B is there are less than 30 days in the mont A is a necessary and sufficient condition for B and Vice versa A if and only if B There is no way for A to be true without B being true There is no way for B to be true without A also being true IfA is false there is no way B is true IfB is false there is no way A is true It is a definition Back to economics A The point X1 X2 is the optimal bundle B The point X1 X2 is on the budget line Necessary If A then B Suf cient If B then A B is a necessary but not suf cient condition for A Yes it has to be on the budget line but other conditions need to be met as well A lot of nonoptimal bundle points are on the budget line as well We need to get a condition that takes care of these The reverse statement is a suf cient but not necessary condition The point X1X2 is the optimal bundle therefore it lies on the budget line but there are other ways of being on the budget line besides being at the optimal bundle The point XlX2 is the point where MRSMRT implies the point Xlx2 the optimal bundle for an interior solution Optimal bundle for an interior solution iff MRSMRT MRSMRT implies optimal bundle and optimal bundle implies MRSMRT Technologically ef cient production is a necessary but not suf cient condition for pro t maximization Pro t maximization is a suf cient but not necessary condition to know we are using technologically ef cient production Pro t max implies we are technologically ef cient but being technologically ef cient is not enough to know we are producing at a pro t maximizing level Technologically ef cient production the rm can not produce more output given the amount of inputs it is using and the rm cannot produce the amount of output it is producing by using fewer inputs Show sets Production function A rm gathers together inputs or factors of production The rm then applies a technology or production process to these inputs The result is an output can be a good or a service No costs of input are involved yet No selling of the product is going on yet Just boring old production l De ne a production function QfKLEM Q is output of the good in many studies people use Y rather than Q means the same thing K is capital L is labor E is energy M is materials f de nes the relationship between the quantities of inputs used and the maximum quantity of output that can be produced given current knowledge about technology and organization What is the nature of the f It can take on lots of different forms An important part of econometric work is to estimate the nature of the production function We can treat inputs in the production function as xed or variable inputs In the short run factors of production that can not easily be varied are viewed as xed inputs A factor for Which it is relatively easy to adjust the quantity quickly is a variable input The long run is the time span required to adjust all inputs There is no precise definition of time period applied to these terms It is a relative relationship All inputs are variable in the long run there are no fixed inputs in the long run An example A commonly made assumption is that labor is the most variable of inputs so we de ne it to be the variable input hold the others constant in the analysis No law here but convention Q REL in K bar E bar M bar mean xed in short run Holding xed inputs constant in the book Perloff de nes a labor output table ll in units and total rst then revisit marginal and average Labor units Total Marginal Average Output product product 0 0 NA NA 1 5 5 5 2 18 13 9 3 36 18 12 4 5 6 20 14 5 75 19 1 5 6 90 1 5 1 5 7 98 8 14 8 104 6 13 9 108 4 12 Marginal product of Labor the change in total output resulting from the use of an additional unit of labor all else constant A Note that this contrasts With the average product of labor the ratio of the output to the number of workers used to produce this labor Note further that there is also a marginal product of capital of materials of energy We are focusing on labor but other inputs also have marginal and average measures as we have just de ned for labor ll these in on chart Production Function Total N 100 I Marginal Average 80 60 40 20 u 39 0 m 39 I I I I I I I I l I 012345678910111213 Outputs Labor Units We can draw a graph of this information Why these shapes At low levels of labor workers help each other do tasks that are hard for one person to do or conversely they specialize This gives us initially a convex function Then after we reach some critical level of labor They have to wait for each other to nish at a machine or they get in each other s way then we get a concave function If MP curve is above AP curve then AP is upward sloping If MP below AP then AP downward sloping Think of heights for the intuition Geometrically if you draw a ray from the origin to any point on the Total Product curve you nd the average product at that point If you identify the slope of the total product curve at this point you nd the marginal product If AP steeper than MP then AP gt MP If AP atter than MP then AP lt MP At some point APMP The law of diminishing marginal returns If a rm keeps increasing an input holding all other inputs and technology constant the corresponding increases in output will become smaller eventually Not diminishing returns but diminishing marginal returns Long run production That was a discussion of variation in output due to different levels of labor holding other things K E M constant Now we are in the long run so all inputs are variable Note that the short run implies that at least one input is being held fixed Do not come away from this with the impression that the difference between the short run and the long run is one versus two inputs That is not right In the short run at least one input and potentially more than one input is held constant while one or more other inputs are allowed to vary In the long run all inputs are allowed to vary However to keep things simple we are going to assume there are only two inputs used in production of our good We will call them capital and labor More than two are possible likely in reality We focus on two because it is easier to draw and the logic carries through to higher dimensions We can combine different quantities of these inputs in a variety of ways to produce a given level of output De ne a curve that traces out the minimum combinations of inputs required to produce a given level of output This is an isoquant Again if you want to think of this as a contour line it is a contour line on the production function in 3D space Properties 1 The farther an isoquant is from the origin the greater is the level of output remember more is better than less 2 Isoquants do not cross as that would imply inef ciency remember transitivity 3 Isoquants slope downward as they are ef cient levels of production remember there are tradeoffs Draw an isoquant What will in uence the shape of the isoquant How substitutable are inputs Production function of processed pork Processed Pork pigs bought in New York pigs bought in Pennsylvania Straight line graph Production function of peanut butter sandwiches Peanut butter sandwiches minimum dollops of peanut butter slices of bread 2 I have 10 dollops of peanut butter and 4 slices of bread I can only make 2 sandwiches Leontief graph Most lie intermediary to these two extreme cases Show contrast on single graph note nature of subs connect at upper and lower extreme The slope of the isoquant is called the marginal rate of technical substitution This tells us the trade off between inputs in production It is measured as the number of units of one input that have to be given up While increasing the other input to continue to produce a given level of output The MRTS like the MRS is a negative number since it is implicitly a tradeoff Here we define it for the capital to labor MRTS change capital amp MRT SKL change labor AL Unless goods are perfect substitutes MRTSl for example or perfect complements MRTSoo undefined or 0 the MRTS varies as different points are considered on the isoquant Remember we are on an isoquant The quantity of output stays the same Therefore we know that if we change labor and change capital on a given isoquant the total output should not change ATP Recall that AK and a s1milar express1on eX1sts for the marginal product of labor So if we know the change in total product is zero by de nition and we know the de nition of the marginal product is what we just saw we can add zero plus zero to nd the following AK1IPKAL1IPL ATP0 Show math note connection to calculus and answer zero minus zero question if it comes up Also note connection back to MRS and the Marginal Utility equations developed earlier While not overwhelming exciting this allows us to gain the insight that the marginal rate of technical substitution is equal to the negative of the ratio of the marginal products important note the numerator denominator relationship AK lP MRT sKL L AL lPK From an intuitive point of view the movement along an isoquant is related to marginal changes I am getting this level of output using a speci c mix of inputs now I want to move over there to another mix of inputs holding output constant That is a marginal change Returns to scale Up until now we have been considering adjustments to our input bundles holding output constant That is how we have de ned an isoquant Or we have been changing one input at a time holding others constant That is how we thought about a production function Now however we want to turn to the question of how changes in the total input bundle are related to changes in output What can we learn by comparing different isoquants rather than looking at movement along a given isoquant We are going to look at a specific type of change to the input bundle blowups Equal percentage change applied to all inputs I use labor and capital to produce my good Let s say we can continue to ignore other inputs like materials and energy for production of our good What are the implications of different production functions for changing input levels Say I use 2 units of labor and 3 units of capital to produce 6 problem sets In this case assume the production function is de ned by capital times labor If I double both units 4 units of labor and 6 units of capital I get 24 units of problem sets 236 new output 22324234624 Doubling inputs gives a fourfold increase in output 2464 Increasing Returns to scale Doubling inputs leads to a more than double increase in outputs f2K2L gt 2fKL Say instead that the production function is capital plus labor perfect substitutes in production 235 new output2223223 10 Doubling inputs gives a doubling of output 1052 Constant returns to scale Case two additive production function Doubling inputs leads to a doubling of output f2K2L 2fKL Finally assume we have a production function that de nes output as the natural log of capital times labor ln23l79 New output ln2223ln463 18 Doubling inputs increases output by 78 318l79l78 Decreasing returns to scale Doubling inputs leads to a less than double increase in output f2K2L lt 2fKL Technical note CobbDouglas production function is useful as it embeds these three cases FYL KB IfaBgt1IRS IfaB1 CRS If O Blt1DRS While this defines the relationship between scale and the production function as either one or the other it is important to note that there can be variation over the scale of production in the returns to scale In other words returns to scale can depend on where you are in the production function A common pattern is IRS over low levels of input CRS over moderate levels and DRS with high levels of input If we think of isoquants as contour lines they are close together near the origin and spread further apart as we move away from the origin Show graph from book that illustrates IRS over low ranges CRS mid range and DRS higher range Innovations Technological progress is one of the main driving factors of economic growth Different types Neutral technological progress All inputs are equally affected Allows same input bundle to be used but generates more output Nonneutral technological progress The innovation affects inputs unequally This alters the proportions of the input bundles when generating more output Show progress on a single input production function show on an isoquant neutral technological progress McPeak Lecture 2 PPA 723 A market is in equilibrium at the point where the demand and supply curves cross The equilibrium price is the market price at which consumers can buy as much as they want and sellers can sell as much as they want The equilibrium quantity is the quantity demanded quantity sold at the equilibrium price The equilibrium price quantity pair p q is the price and quantity at which neither buyers nor sellers have an incentive to change their behavior Finding it on a graph A O 0 Demand D Supply 5 9 8 7 6 5 4 3 2 1 O 100 120 140 160 180 200 220 240 260 280 Quantity The price quantity pair where the supply curve crosses the demand curve Finding it by algebra Qd28620p QS884Op At what price does QdQS QdQS Where 28620p8840p7 198260ka pz330 What is the implied quantity 28620330 8840330220 Derive inverse show p28620 l20Qd p 8840 l40Qs is an equivalent statement of the relationship and is easier to graph yfx issue here What happens if we deviate from this equilibrium Price above equilibrium 4 We will have excess supply the amount by which the quantity supplied is greater than the quantity demanded The quantity demanded is 206 286204 The quantity supplied is 248 88404 Producers have oversupplied 42 units excess supply These can either be wasted or stored As there are costs to storage why not lower the price on the excess supply Say for simplicity that each rm produces one unit The rst 220 rms to gure out they can lower the price to 330 the equilibrium price and not have to store the pork do so That leaves 28 rms that moved too slowly They have pork at a price that nobody wants to buy 4 They close down their operations and give away the excess pork as a severance package The market has moved to its equilibrium Or alternatively each rm decides to produce slightly less Price below equilibrium 2 We will have excess demand the amount by which quantity demanded exceeds quantity supplied at a given price The quantity demanded is 246 286202 The quantity supplied is 168 88402 Consumers want to buy 78 units more at the price of 2 but are not able to get it at the prevailing market price Potential producers notice this and rush to open factories Again assuming each rm produces one unit 52 rms open and start selling driving the price up to 330 and the quantity up to 220 Why is the price going to go up from 2 to 330 when there is more being produced What is to be made of the statement supply demand By de nition they are equal in equilibrium However this is only in equilibrium In our rst example we had the observed price 4 and the corresponding consumer demand of 206 If we see a 4 price and observe that 206 units were sold does this tell us supply demand No recall this was a case of excess supply Supply gt Demand at going market price Likewise when we had 2 and 168 units supplied This was a case of excess demand Demand gt Supply at going market price In economic terms supply demand only at the equilibrium point How do we know we are at equilibrium and not in a situation of excess supply or demand No rms entering or leaving the market expanding or contracting production No shortage of the good no unsold surplus of the good Price of the good is stable Arriving at the equilibrium is an example of moving along a supply curve and along a demand curve to arrive at a stable point How do policies in uence the intersection of supply and demand Return to the idea of supply and demand curves shifting as introduced in an earlier lecture Now we want to think about what happens to the market equilibrium when all else constant that is in the background experiences a change Recall that there are things like prices of complements prices of inputs rules and regulations that can lead to shifts in supply or demand curves Let s move some supply and demand graphs around 1 What happens if new environmental regulation is introduced relaxing the restrictions on the disposal of pig waste thus lowering the cost of production for hog producers 10 o Demand 9 8 D 7 Supply 6 5 4 3 2 1 0 Price 100 120 140 160 180 200 220 240 260 280 Quantity Supply gt 2 What happens if new regulations on pork processing hygiene that are more stringent are introduced thus increasing the costs of producing processed pork 10 o Demand 9 8 D 7 Supply 6 5 4 3 2 1 0 Price 100 120 140 160 180 200 220 240 260 280 Quantity Supply lt 3 What happens if the government funds an advertising campaign Pork it whitens teeth and freshens breath and consumers believe it 10 9 o Demand 8 n Supply 7 6 3 5 A n 4 A A X 3 an 2 X D 1 u 0 fry 100 120 140 160 180 200 220 240 260 280 Quantity Demand gt 4 What happens if the price of chicken decreases dramatically in response to a new veterinary innovation at Cornell funded by USDA money 10 9 o Demand 8 D Supply 7 6 3 5 E I 4 A 3 2 2y quot3 1 y n Ir 0 I I I I I I I I 100 120 140 160 180 200 220 240 260 280 Quantity Demand lt How do policies in uence the intersection of supply and demand 1 Price Floor There is a minimum price legally enforced below which a commodity can not be purchased Price OANWLLDCDVOJCOO 0 Demand Ii Supply price oor 100 120 140 160 180 200 220 240 260 280 Quantity Excess supply agricultural surplus unemployment What if the price oor is set at 2 Price OANWLLDCDVOJCOO 0 Demand n Supply price oor 100 120 140 160 180 200 220 240 260 280 Quantity The price oor is nonbinding It is there but has no effect on the market equilibrium 2 Price Ceiling There is a maximum price legally enforced above which a commodity can not be sold Price OANWLLDCDVOJCOO 0 Demand Ii Supply price ceiling 100 120 140 160 180 200 220 240 260 280 Quantity Nonbinding What if the price ceiling is set at 2 Price OANWLLDCDVOJCOO 0 Demand D Supply price ceiling 100 120 140 160 180 200 220 240 260 280 Quantity There is excess demand Waiting in line black market exchange