Introduction to Microeconomics
Introduction to Microeconomics EC 201
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Kareem Larkin PhD
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Date Created: 09/19/15
The Tragedy of the Commons When resources are commonly owned and access is open to all the resulting allocation of resources is inef cient and the outcome is unsatisfactory even tragic A good example is a shery where anyone who chooses can hire and out t a shing vessel take it out on the waters and catch sh The waters and the sh are commonly owned Let s work through a simple example to see how the economy misallocates resources exploiting the shery beyond the ef cient level perhaps even bringing about its destruction Let s say that it takes 410 per day to operate a shing boat The average yield from a day shing depends upon how many vessels are operating The relationship is given below of shing Average catch Vessels per boat AP average product 1 500 2 500 3 500 4 500 5 490 6 480 7 470 8 460 9 450 10 440 11 430 12 420 13 410 14 400 15 390 etc What we see in the table is that the average product is constant when there are less than 4 boats on the waters but that it declines as the number of boats grows to 5 and beyond where the shery becomes congested Now the average product is the private marginal bene t accruing to the shers In deciding whether to sh or not each sher compares the private marginal bene t with the marginal cost The marginal cost includes the rent on the boat and equipment wages for the crew and the costs of raw materials such as bait and fuel What will be the equilibrium allocation of resources Clearly entrepeneurs will enter the shing industry whenever they can make money that is whenever the returns from shing exceed the cost Thus the number of shing vessels will increase until the private marginal bene t average product and marginal cost 410 are equal This occurs at 13 vessels We now turn to the social marginal bene t of a shing vessel on the waters The social marginal bene t is the additional sh harvested It is the marginal product of another vessel To compute the marginal product we must rst nd total product This is simply the average multiplied by the quantity of vessels of shing Average catch Total catch Vessels per boat AP per boat Total product 1 500 500 2 500 1000 3 500 1500 4 500 2000 5 490 2450 6 480 2880 7 470 3290 8 460 3680 9 450 4050 10 440 4440 11 430 4730 12 420 5040 13 410 5330 14 400 5600 15 390 etc 5850 Then we compute the marginal product by taking the change in the total product divided by the change in the quantity of vessels of shing Average catch Total catch Marginal Vessels per boat AP per boat TP Product 1 500 500 2 500 1000 500 3 500 1500 500 4 500 2000 500 5 490 2450 450 6 480 2880 430 7 470 3290 410 8 460 3680 390 9 450 4050 370 10 440 4440 350 11 430 4730 330 12 420 5040 310 13 410 5330 290 14 400 5600 270 15 390 etc 5850 250 Notice the marginalaverage relationship When the average product is constant at 500 it equals the marginal product As the average product starts to fall however the marginal product lies below it In effect the lower marginal product is pulling down the average product But why is the marginal product below the average product For example when the number of vessels increases from 4 to 5 the marginal product is 450 But each boat takes an average catch of 490 Where did the remaining 40 worth of sh go The fth boat reduced the average catch by 10 each for the other 4 boats This reduced catch for the other boats is an external cost The external cost is the difference between average and marginal product and it leads to an inef cient use of the shery Socially ef cient actions have greater bene ts than costs Any boat that increases the value of the total catch by more than its opportunity cost is ef cient The ef cient quantity of shing vessels is 7 where the social marginal bene t marginal product equals the marginal cost 410 As we have seen the equilibrium allocation is 13 boats which exceeds the ef cient allocation of 7 The commonly owned resource is overused To x this inef ciency we must increase the private cost of shing One way to do this is to impose a fee say for a shing license equal to the marginal external cost at the ef cient allocation 7 vessels Checking the table we see that the required fee is 470 410 60 The need to pay 60 for a license before shing would increase the marginal cost to 470 and this changes the equilibrium allocation to 7 vessels where the average product equals the marginal opportunity cost Another approach commonly used in regulating sheries is to auction shing licenses These are called individual transferable quotas The sheries management should put up for auction the ef cient number of licenses In this problem the ef cient number is 7 one license per vessel To sum up i The common ownership makes the private marginal bene t equal to the average product ii When congestion sets in the average product starts to decline as the use of the resource increases iii The equilibrium occurs where the average product equals the marginal opportunity cost iv The marginal product is less than average product whenever the average product is falling This is the marginalaverage relationship v The difference between average and marginal product is an external cost vi The ef cient allocation occurs where the marginal product equals the marginal opportunity cost vii A license fee set equal to the difference between marginal and average product at the ef cient allocation will bring the equilibrium in line with the ef cient allocation Viii An equivalently effective policy sells the ef cient number of licenses Oligopoly In some markets entry barriers limit the number of rms For example there are just ve major producers of breakfast cereal Post Kellogg General Mills Ralston and Quaker and four major producers of tennis balls Penn Wilson Dunlop and Spalding In such markets there may not be enough competition to force price down to near marginal cost or pro ts down to the normal rate Worse a smaller group of rms may be able to collude and x prices at monopoly levels sharing the high pro ts among themselves A group of rms that cooperate in order to limit competition and raise prices is called a cartel When oligopolists are able to push prices above competitive levels they cause a market failure Good economic policies promote competition but before we can design policies to undermine collusion by oligopolists we must rst understand it That is the purpose of this chapter to develop a model that helps us understand when oligopolists can successfully collude and what practices they might employ to foster collusion As usual we begin with a relatively simple model and then add realistic features Pricing Tennis Balls We will work with a model of two rms called a duopoly The rms Bounce and Fuzz produce tennis balls which for now are perfectly homogenous The rms have the same constant marginal cost and there are no xed costs These facts imply that the marginal cost equals the average cost Ifthey could this pair of firms would cooperate and charge the price that maximizes total pro ts Once this socalled joint pro t maximum was achieved they could settle on some convenient way to share the market Figure 1 shows this outcome Price Figure 1 MR Tennis balls 10000 We see that the pro t maximizing price is 3 and the quantity is 10000 or 5000 each Each rm makes 3 1 2 on each can sells 5000 cans and earns apro t or 2 x 5000 10000 This is the maximum total pro t available in this market As a group the rms cannot do better We refer to this outcome as the cooperative outcome So why don t they simply agree to bring about this cooperative outcome The problem is that it is not in the sel sh interest of the individual rm to go along with the agreement Look at the issue from the standpoint of Fuzz Suppose that Fuzz expects Bounce to abide by the agreement and charge 3 What if Fuzz charges say 295 Because the balls are the same all customers will choose Fuzz s cans Fuzz will make 295 100 195 per can and sell a little more than 10000 cans The total will increase due to the decrease in price See Figure 2 Pro ts will be 195 x 10100 19695 almost twice what the company could earn by going along with the plan to share the market In the lingo of game theory cooperating is not the best response for Fuzz price Figure 2 295 Tennis balls 10000 10100 Of course if Bounce were to anticipate Fuzz s price cut it would reduce its price to 290 and capture the entire market for itself And if Fuzz anticipated Bounce s anticipation it would further cut price to 285 This process of undercutting continues until price is driven down to equal marginal cost At this point each rm sets a price equal to 1 which is just suf cient to cover its costs Each rm earns no above normal pro ts Game theorists say that the noncooperative equilibrium involves zero economic pro ts for each rm So we have a situation where the collective interest of the two rms is to set the monopoly price 3 and share monopoly pro ts 10000 each But each rm s individual incentive is to undercut the other and capture the entire market When each follows its own individual incentive however the result is that they each earn zero pro ts They could promise to cooperate but they will always face the temptation to cheat on the cooperative agreement Promises to act against one s own individual incentives are examples of cheap talk They are promises that have no credibility To this point this model is just an example of the prisoner s dilemma Colluding with Trigger Strategies What can the rms do to overcome this dilemma One option involves the use of trigger strategies Here is how they work The managers of the rm meet secretly and make the following agreement First each promises to set their price equal to 3 the monopoly price As times passes each will observe whether its rival has ful lled the promise to cooperate If Fuzz for example observes that Bounce has charged 3 then Fuzz continues with the agreement The duopoly sticks together at a price of 3 sharing the monopoly pro ts 10000 each We have seen that without some other provision these promises will be broken Trigger strategies have a second dimension that deals with the incentive to cheat The second clause in the agreement talks about the trigger itself If Fuzz observes that Bounce has cheated on the agreement and set a lower price then it responds with aggressive pricing of its own Once Fuzz undercuts Bounce s price Bounce will have no alternative but to price aggressively As we have seen two rms competing vigorously with each other result in zero pro ts for each In effect Fuzz punishes Bounce for the cheating The nature of the punishment is to destroy Bounce s agreed upon share of the profits When a firm delivers the promised punishment it is said to pull the trigger We now have to check and see whether the agreement will hold up Are the promises of punishment for cheating credible Does each firm have an individual incentive to keep its promises We will work backwards and consider the second part of the agreement first If Fuzz observes that Bounce has cheated then there is no value in continuing with the agreement Why play the role of a sucker enabling your rival to prosper at your expense By pricing aggressively it will capture a share of the market and earn a normal rate of profit By passively following the agreement it sells no tennis balls and earns nothing Clearly the promise to pull the trigger is a credible threat Now we must return to the first part of the agreement Will the firms abide by their promises to cooperate and charge the monopoly price We have established that a cheater in this market can expect that its rival will pull the trigger once the cheating is observed Before that happens however the cheater temporarily earns more than its share by undercutting its rival and capturing the entire market As we saw above the cheater earns 19695 The question for the potential cheater is whether the extra 9695 is worth breaking up a cooperative relationship and forgoing the steady stream of 10000 each market period thereafter The problem is complicated by the fact that the gains from cheating appear immediately while the punishment comes in the future As we know future dollars are worth less than current dollars they must be discounted We need a way to compare appropriately the present expected value of these two alternatives We will use an idea called the discount factor and represent it by the symbol 5 It means that 1 in the next period is worth only 3 lt 1 in the present Basically 5 depends upon two factors First how stable is the market Suppose for example that there is a probability that the market may be taken over by foreign firms Ifthis event occurs there will be no further profits Suppose that this probability is 12 Thus 5 12 and the expected value ofthe 10000 cooperative profits next period is only 12 x 10000 5000 New innovations the entry of new competitors and changes in consumer demand are all factors that contribute to the instability of a market and reduce the discount factor The second factor is the time that it takes to detect cheating If the detection time is longer then the cooperative profits lie further in the future and due to the time value of money have a lower present value Now we a ready to compute the incentive to cooperate Recall that cheating gives the firm an extra 9 695 in the current period Cooperating on the other hand keeps in place a relationship that earns 10000 next year and 10000 the year after and on into the inde nite future The present value of cooperation is then 10000 0 10000 02 10000 03 10000002 3 10000 01 0 The last step uses a formula derived in the second semester of calculus 1 The agreement to cooperate is credible as long as the present value of cooperation exceeds the extra current pro ts available to the cheater Present value of cooperative pro ts gt Extra current cheating pro ts 10000 l gt 9695 If i 12 for example the condition is satis ed This means that the rms will be able to cooperate The credible threat of aggressive pricing deters each fum from cheating They settle into a stable cooperative relationship effectively conspiring to x prices at the monopoly level Even though there are two rms the rms act as one and the allocation of resources is no different than it would be with a single monopoly rm If i 1A on the other hand the condition is not satis ed and the rms will not be able to cooperate The future rewards from cooperation will have too small a present value to deter cheating The temptation of that extra 9695 will be too great rms will cheat and the cooperation will break down Promoting Collusion What does this little model tell us about where we should expect to see oligopolies exercise market power over price Look at the scale in Figure 3 The left hand side weighs the incentive to cooperate There are two parts how high are the cooperative pro ts and how much must they be discounted On the right we see the incentive to cheat This incentive is the extra pro ts reaped by undercutting rivals and stealing their customers To collude successfully oligopolies need large cooperative pro ts a high discount factor 5 and low cheating pro ts Each of these factors adds weight to the left side of the scale or lightens the right side tipping the balance toward cooperation I If you do not have your calculus book handy here is a derivation of the formula Let S 3 32 33 Then 3 S 32 33 64 Subtracting S 3 S 3 the remaining terms all cancel Finally this can be solved to get S Bli Figure 3 Future cooperative Extra cheating pro ts pro ts To cooperate or not to cooperate Let s start with the discount factor A stable business environment contributes to a high 5 by making the promise of future cooperative pro ts more secure When the same rms return to market year after year when the products do not change a great deal and when consumer demand is constant or easily predicted then the market is stable Barriers to the entry of new rms are an important component of stability New competitors can disturb a comfortable oligopoly They attract customers offer different products and may ght for market share High entry barriers keep out new competition and lead to higher discount factors Industries like breakfast cereal tennis balls cement and oil re ning have stability The second reason for a high 5 concerns the time that it takes to detect cheating Quick detection limits the period of extra cheating pro ts and brings the punishment sooner When the prices charged by competitors are public information it is easy to see when a rival is undercutting the agreedupon price On the other hand an industry characterized by private negotiations and con dential pricing will allow cheating to go undetected for a longer time Also a group of local rms may nd to easier to monitor each other s pricing than a cartel that spreads around the world The next issue is the size of the extra cheating profits The cheater earns more when its price reduction attracts more of its rival s customers Economists use the term switching costs to capture how ready customers are to move from one rm s products to another When the products are homogenous customers look only at price and availability When the products are differentiated then certain characteristics of product may appeal more to some consumers For example if Fuzz s balls are fuzzier then people preferring a slower game of tennis may stick with Fuzz even if Bounce undercuts the price The second component of extra cheating pro ts is the number of rms In the example of the tennis ball oligopoly there were two rms If they share the market equally then the cheater can at most double its pro ts Ifthere are three rms then the cheater can take customers from two rivals and potentially triple its pro ts When there are more rms the rivals have more customers Those customers can be won over by cheating on the pricing agreement Finally some business practices may facilitate collusion These include repeat purchase rewards meet the competition clauses exclusive territories exclusive dealing cooperative arrangements Each of these facilitating practices puts a thumb on the scale favoring cooperation Consider repeat purchase awards such as airline miles Most airlines offer free tickets to customers who accumulate a minimum number of miles traveled with the airline If the threshold for a free ticket is 25000 there is no bene t from ying 5000 on ve different airlines It is obviously better to stick with one airline Thus the mileage award programs stimulate customer loyalty A side effect is that loyal customers are less likely to switch airlines when a rival cheats and cuts prices With fewer switching customers cheating pro ts are lower In this way mileage award programs make cooperation more likely and contribute to higher prices overall for air travel Any type of frequent purchase award like we see now in coffee shops book stores and with credit card companies works similarly to foster collusion When rms promise to sell at the lowest price they sometimes back up their promise with an offer to match any advertised price While this offer seems like a good thing for consumers a closer look reveals that it fosters cooperation among rms If Fuzz makes such a meet the competition commitment then when Buzz cuts its price Fuzz s customers know that their rm will match the low price Why switch if the lowest price is always available for your preferred tennis ball Again fewer customers ready to move in response to price differences mean that cheaters can gain only smaller extra pro ts The scale is tipped toward cooperation Suppose that a cartel could divide the market geographically One rm could take the Detroit market another would take Atlanta and so on Then when the rm controlling the Atlanta market cut price it would not be able to attract many customers from Detroit This is the practice of exclusive territories each rm has exclusive access to customers in one territory The airline industry effectively divides up much of the national market by establishing hubs largely controlled by a single airline Again this practice increases switching costs and reduces cheating pro ts A more cooperative less competitive industry and higher prices follow from exclusive territories Exclusive dealing occurs when say a printing manufacturer requires that its customers purchase exclusively its own ink cartridges service and replacement parts Clearly this practice undermines competition in the market for cartridges And anything that undermines competition promotes cooperation and higher prices 20 ChapterZ travel time for commuters and this is the objective of the transportation department Table 24 gives time savings of each activity as the number of workers assigned to it varies Remember that if a worker is assigned to reprogram lights he cannot x potholes Table 24 Workers Workers assigned to Total assigned to Total reprogramming time saved x potholes time saved 1 100 1 125 2 190 2 225 3 270 3 305 4 340 4 365 5 400 5 415 6 450 6 455 7 490 7 485 8 39 520 8 510 9 540 9 530 10 550 10 540 How should the workers be assigned Hint Let the number of workers assigned to reprogramming be the activity What are the costs of assigning these workers 15 Practice problem marginal costs and marginal bene ts Bugout pesticide kills insects that eat lettuce leaves Currently 11 leaves per head are eaten by the insects In the right concentrations Bugout can be effective On the other hand there are side effects When the concentration is too great leaves fall off the lettuce head Table 25 shows the relationship between concentrations of Bugout leaves eaten and leaves fallen What concentration should the manufacturer recommend Table 25 Concentration Leaves eaten Leaves fallen parts per million per head per head 1 7 0 2 4 l 3 2 3 4 1 6 5 0 10 6 0 15 MARKET DEMAND AND MARKET SUPPLY When the price falls individual demanders want to buy more and individual suppliers want to sell less These individual demand and supply curves are behavioral relationships The market demand and market supply curves are found by adding up all of these individual demands and supplies Tool Kit 24 shows how to do this 16 Worked problem market demand the individual demands of Jason and Kyle for economics tutoring are Tool Kit 24 Calculating Market Demand and Supply The market demand is the sum of the individual de mands The market supply is the sum of the individual supplies This tool kit shows how to add the individual demands and supplies Step one Make two columns Label the left hand column Price and the righthand column Quantity Price Quantity Step two Choose the highest price at which goods are demanded Enter this in the rst row of the price column Price Quantity P1 Step three Find how many goods each individual will purchase Add these quantities Enter the total in the rst row of the quantity column Price Quantity p1 Q1QuQbQ Step four Choose the second highest price and con tinue the process given in Table 26 Calculate the market demand Jason and Kyle are the only two individuals in this market Table 26 Jason Kyle Price Quantity Price Quantity 10 6 10 4 8 8 8 5 6 10 6 6 4 12 4 7 Stepbystep solution Step one Make and label two columns Price Quantity Step two Choose the highest price This is 10 Enter this in the rst row under price Price Quantity 10 Step three Find the market quantity Jason would buy 6 Kyle would buy 4 The total is 6 4 10 Enter 10 in the corresponding quantity column Price Quantity 10 10 Step four Repeat the process The next lower price is 8 Jason would buy 8 Kyle would buy 5 The total is 8 5 13 Enter 8 and 13 in the appropriate columns Price Quantity 10 10 8 13 Continue The entire market demand is given below Price Quantity 10 10 8 13 6 16 4 19 17 Practice problem market demand Gorman s tomatoes are purchased by pizza sauce makers by submarine sandwich shops and by vegetable canners The demands for each are given in Table 27 Find the market demand Table 27 Pizza sauce Submarine shops Vegetable canners Quantity Quantity Quantity Price bushels Price bushels Price bushels 5 25 5 5 5 55 4 35 4 6 4 75 3 40 3 7 3 100 2 50 2 7 2 150 39 1 80 1 7 1 250 18 Practice problem market supply The technique for nding the market supply curve is the same as for the market demand Simply sum the quantities supplied at each price There are three law rms that will draw up partnership contracts in the town of Pullman Their individual supply curves are given in Table 28 Find the market supply curve Table 28 Jones Jones Jones Jones and Jones and Jones Price Quantity Price Quantity Price Quantity 200 0 200 6 200 4 220 0 220 8 220 8 240 0 240 12 240 10 260 8 260 24 260 1 l EQUI Ll B R IUM In equilibrium markets clear The market price will settle where the quantity that demanders would like to purchase exactly equals the quantity that suppliers choose to sell Tool Kit 25 shows how to nd the equilibrium The Price System I 21 Tool Kit 25 Finding the Equilibrium Price and Quantity The equilibrium price in the demand and supply model is the price at which the buyers want to buy exactly the quantity that sellers want to sell In other words the quantity demanded equals the quantity supplied The equilibrium quantity in the market is just this quantity Here is how to nd the equilibrium in a market Step one Choose a price Find the quantity demanded at that price and the quantity supplied Step two If the quantity demanded equals the quantity supplied the price is the equilibrium Stop Step three If the quantity demanded exceeds the quan tity supplied there is a shortage Choose a higher price and repeat step one If the quantity demanded is less than the quantity supplied there is a surplus Choose a lower price and repeat step one Step four Continue until the equilibrium price is found 19 Worked problem equilibrium price and quantity The supply curve and demand curve for cinder blocks are given in Table 29 The quantity column indicates the n mber of blocks sold in one year Table 29 Demand Supply Price Quantity Price Quantity 200 50000 200 200000 150 70000 150 160000 100 100000 100 100000 075 150000 075 50000 050 250000 050 0 a Find the equilibrium price and quantity b If the price is 150 is the market in equilibrium Will there be a surplus or a shortage If so what is the size of the surplus or shortage What will happen to the price Why 0 If the price is 075 is the market in equilibrium Will there be a surplus or a shortage If so what is the size of the surplus or shortage What will happen to the price Why Stepbystep solution Step one a Choose a price At a price of say 200 the quantity demanded is 50000 and the quantity supplied is 200000 Step two The quantities are not equal Step three There is a surplus The equilibrium price will be lower 22 I ChapterZ Step four Continue Try other prices until the quantity sup plied equals the quantity demanded The equilibrium price is 100 where the quantity equals 100000 We can now see the answers to parts b and c Step ve 19 If the price is 150 the quantity demanded is 70000 and it is less than the quantity supplied which is 160000 There is a surplus of 90000 160000 70000 The price will fall because producers will be unable to sell all that they want Step six c If the price is 075 the quantity demanded is 150000 and it is greater than the quantity supplied which is 50000 There is a shortage of 100000 150000 50000 The price will rise because producers will see that buyers are unable to buy all that they want 20 Practice problem equilibrium price and quantity The demand curve and supply curve in the market for billboard space along Interstate 6 are given in Table 210 The price is the monthly rental price The quantity column shows numbers of billboards Table 210 Demand Supply Price Quantity 7 Price Quantity 100 5 100 25 80 8 80 21 60 1 1 60 16 40 14 40 14 20 22 20 3 Q Find the equilibrium price and quantity b If the price is 20 is the market in equilibrium Will there be a surplusor a shortage If so what is the size of the surplus or shortage What will happen to the price Why 0 If the price is 80 is the market in equilibrium Will there be a surplus or a shortage If so what is the size of the surplus or shortage What will happen to the price Why 21 Practice problem equilibrium price and quantity Find the equilibrium price and quantity in each of the following markets a The supply and demand curves for new soles shoe repair are given in Table 211 Table 211 Demand Supply Price Quantity Price Quantity 35 17 35 53 30 21 30 37 25 25 25 25 20 30 20 15 15 35 15 0 b The supply and demand curves for seat cushions are given in Table 212 Table 212 Demand Supply 8 4 8 32 7 8 7 28 6 12 6 22 5 16 5 19 4 17 4 17 SUPPLY AND DEMAND Supply and demand is probably the most useful technique in microeconomics Economists use it to study how markets are affected by changes such as tastes technology government programs and many others Supply and demand offers a wealth of insights into the workings of the economy It is very important to master the procedure spelled out in Tool Kit 26 Tool Kit 26 Using Supply and Demand Supply and demand analysis provides excellent an swers to questions of the following form What is the effect of a change in on the market for You are well on your way to success as a student of economics if you stick closely to this proce dure in answering such questions Step one Begin with equilibrium in the relevant mar ket Label the horizontal axis as the quantity of the good or service and the vertical axis as the price Draw a demand and a supply curve and label them D and S respectively PRICE p Supply curve Demand curve 1 I r I i l l Q1 OUANTlTY 0 Step two Figure out whether the change shifts the sup ply curve the demand curve or neither Step three Shift the appropriate curve PRICE Dz 01 QUANTITY Step four Find the new equilibrium and compare it with the original one PRICE p 8 P2 P1 Dz K 01 01 02 QUANTITY 0 22 Worked problem using supply and demand In response to concern about the fumes emitted by dry cleaning establishments the Environmental Protection Agency has issued regulations requiring expensive ltering systems How will this regulation affect the dry cleaning market Step bystep solution Step one Start with an equilibrium PRICE P Supply curve P1 Demand curve 0 ARTICLES OF CLOTHING 1 DRY CLEANED a The Price System I 23 Step two Figure out which curve shifts The mandated l tering systems increase the dry cleaning rm s costs shifting the supply to the left Step three Shift the curve PRICE 2 31 D ARTICLES OF CLOTHlNG DRY CLEANED Step four Find the new equilibrium and compare The effect of the regulation is to raise price and lower the quantity of clothes dry cleaned PRICE 52 P 31 39 P2 P1 I D 02 01 ARTICLES OF CLOTHING DRY CLEANED O 23 Practice problem using supply and demand As the oil market comes to the realization that Kuwait s production will not return to prewar levels the price of oil has increased by 4 per barrel Explain the effect of this oil price increase on the market for natural gas 24 Practice problem using supply and demand For each of the following show the effects on price and quantity Draw the diagrams and follow the procedure a An increase in income in the market for a normal good A decrease in income in the market for a normal good An increase in the price of a substitute A decrease in the price of a substitute An increase in the price of a complement A decrease in the price of a complement An increase in the price of an input A decrease in the price of an input An improvement in technology 6 aookgman The Price System 25 was a 12 Cost of Cost of LEZES early retirements retaining bureaucrats P d t39 pggsyg ngs Salaries 0 50000 x 8 x 2 curve Fringe bene ts 0 20000 X 8 X 2 Of ce space 10000 20000 for all 8 Pension bene t 20 000 X 8 X Q 0 20900 cmquot BUSHELS Total 330000 1140000 SWEET b ROLLS a Opportunity cost 1140000 330000 2000 810000 17 Sunk cost 330000 14 The marginal bene t of assigning a worker to 0 6 500 DONUTS reprogram the lights is the time saved the marginal cost IS the tlme lost because the worker was not HOUSEWARES c assigned to x potholes 200000 Workers assrgned Marginal Marglnal to reprogramming bene ts costs 1 100 10 2 90 20 3 80 25 v 4 70 30 0 500000 smegma 5 60 40 mg d 6 50 50 z 3 23 9 20 100 10 10 125 Assign 6 to reprogramming and 4 to xing potholes 15 The bene t of recommending higher concentrations of pesticides are the fewer leaves eaten the costs are the I leaves that fall off 0 45500 Concentration Marginal Marginal ARMOHED PERSONNEL CARRIER KILOMETHES of pesticide bene ts costs 1 4 0 2 3 l 11 Cost of Costs of i f g holding canceling 5 1 4 class class 6 0 5 Compensation of instructor 4000 0 Air conditioning and lighting 1000 1000 T111 mainlufacturer should recommend a concentration Custodial services 2000 2000 0 pp 39 Property taxes 2500 2500 17 Price Quantity bushels Rent 0 1200 5 85 Total 9500 4300 4 1 16 3 147 a Opportunity cost 9500 4300 5200 2 207 b Sunk cost 4300 1 337 26 I ChapterZ 18 Price Quantity bushels 17 Demand shifts to the left driving the price down 200 10 and decreasing the quantity 220 16 240 22 PRlCE 260 43 i 20 a Equilibrium price 40 quantity 14 S b If the price is 20 there is a shortage of 22 3 lt 19 The price will be driven up 91 c If the price is 80 there is a surplus of 21 8 13 The price will be driven down p2 21 a Price 25 quantity 25 b Price 4 quantity 1 Di 23 Oil and natural gas are substitutes and therefore the 3 demand curve shifts to the right the price increases 92 and the quantity increases 02 01 GMT 0 quot55 6 Demand shifts to the right driving the price up and increasing the quantity s 1 PRICE I r p s 91 gt gt K p2 02 9 P1 01 a gt Q1 32 NATURAL GAS a De D 24 a Demand shifts to the right driving the price up and 1 increasing the quantity 01 Q2 QUANTITY 0 PRICE cf Demand shifts to the left driving the price down p and decreasing the quantity S gt PRSCE p 32 3 p1 gt p1 02 32 D1 Q1 Q2 ousmm39 a D 02 02 1 QUANTITY 0 Information Problems in the Product Market The Lemons Model Often when we customers go to purchase a good or service we cannot determine its quality For example a haircut may look great when we leave the chair but later we nd that our hair does not lay properly that it takes a lot of effort to fight the hair into place in the morning and that it grows out to a messy mop This perception of quality takes place over some time At the time of purchase the customer is in a position of asymmetric information She does not perceive the quality of the cut but the stylist does know her ability and how diligently she is applying her talents The problem for the customer is How can I know if I will get a good haircut This doubt makes the customer a reluctant purchaser It injects risk into the everyday purchase of a haircut and this risk reduces the reservation pr1ce This asymmetric information also presents a difficulty for the stylist The stylist of course wants the demand to be high Her problem is How can I convince my customer that I will do a good job The buyer and seller stand ready to complete a mutually beneficial exchange but first they must overcome the information problem The stylist might claim that she has been welltaught and works hard Whether such a statement is true or false it conveys no information to the customer It is an example of cheap talk Because it costs nothing to make claims anyone can make them The lazy untrained stylist can say I ll do a great job for you just as easily as the hardworking welltrained one can We need to look elsewhere for a solution Let s see how this situation might play out in a simple example First we strip away any resemblance to the real world and imagine a Stylist s Market similar to farmer s markets that many towns have where local fa1mers peddle their locally grown produce In this imaginary market anonymous stylists offers style cuts to customers Let s say that the value of a good cut is 50 and the value of a bad cut is 10 Further the cost in the stylist s time and effort is 30 for a good cut and 20 for a bad one Now if there were no information problem then customers who were willing to pay 50 for a good cut would transact with stylists willing to sell for 30 The market would bring these demanders and suppliers together and create a surplus of 50 30 for each cut If the price were 40 for example they would split the surplus evenly But any price between 30 and 50 leads to a successful transaction There is no potential market for low quality We will see however that the information asymmetry undermines this transaction and brings about a market failure Let s model this situation as a game between the customer and the stylist The customer has two strategies buy or not buy and the stylist has two high quality or low quality Let P represent the price Then if the customers buys a high quality haircut her payoff is 50 7 P and the corresponding payoff to the stylist is P 30 Their two payoffs sum to 20 which is the surplus when a good cut is purchased Figure 1 represents the payoffs for each combination of strategies Stylist High Low Buy C507P C10P SP30 SP20 Customer Not buy C 0 C 0 S 0 S 0 The Nash equilibrium occurs where each player is choosing the strategy that is the best response to the strategy chosen by the other player Let s nd the equilibrium For a successful transaction the price must be between 30 and 50 We can start in any box but let s start in the lower left That box shows the payoffs 0 if the Stylist were going to do a good cut but the customer had chosen not to buy This choice is not the best response for the customer who could gain 50 7 P gt 0 by choosing Buy as her strategy Thus because one player can improve her situation unilaterally the lower left box is not an equilibrium We move to the upper left Here the Stylist can gain by choosing low quality Her payoffrises from P 30 to P 20 10 Her best response to Buy is to give a low quality cut and her gain is the cost savings Again this box cannot be an equilibrium We move to the upper right Again it is the customer who is not choosing her best response Since the price is above 30 her payoff of 10 7 P is negative and she would to better by choosing Not Buy The final box is the lower right where the customer chooses Not buy which is the best response to low quality The stylist cannot increase her payoffs by choosing high quality because the customer is not buying and the payoffs are zero in any case We say that the equilibrium of this game is no sale The potentially beneficial transaction in which the customer buys a high quality cut is not made There is a market failure In the next section we see how this failure can be remedied through the use of trigger strategies The Reputation Model In the real world we do not buy haircuts at anonymous stylist s markets but rather from the person or shop where we received our previous cut We trust the stylist to continue to provide high quality service Ifwe find that the quality falls below some standard we move on to a different stylist In game theory this sort of approach is called a trigger strategy a concept that we used in our discussion of oligopoly We will use this strategy to nd the equilibrium in this market determine the price and see how the market failure can be overcome We continue with the same example Now suppose that the customer makes the following statement to the stylist I will pay you to cut my hair If over the next few weeks I learn that the quality is high I will return Ifnot I will go elsewhere and never return It is easy to see that this is a credible threat If she learns that the quality is low she has no reason to return But does this trigger strategy give the stylist the right incentives to provide ahigh quality cut In other words does this strategy make high quality the best response when the customer chooses Buy We know that the payoff to choosing low quality is P 20 The payoff to high quality is a stream of payoffs of P 30 First we must compute the present value of this stream Then we must choose a price that is high enough to make the present value of high quality greater than F 20 Because if the price is not high enough the stylist will choose to take the easy money and give a low quality cut First we need a short digression of present value The future revenues that come when the satisfied customer returns must be discounted One reason is that future dollars are worth less than current ones because current dollars can be invested in the interim A discount factor of llr accounts for this difference In situations like these however there is another element in the discount factor The relationship may dissolve for other reasons either player may move away the business may fail for other reasons either party could get sick We use 11 to denote the probability that none of this happens and the relationship continues The product of these two factors is the discount factor nlr which we denote by 5 The stream of payoffs from high quality equals P30 P30 P30 Z P30l 0 32 P30l In the last step we used a property of infinite series Now we only need to figure out the price which must be high enough so that the present value of the stream of payoffs from high quality exceeds 10 P301 gt P 20 Or P gt 30 10 x 1 That is the price must exceed the cost ofhigh quality by 10 x l This difference is called the reputation rent Now we have a complete solution to the incentive problem caused by the information asymmetry Let s review The buyer cannot observe quality at the time of purchase This information problem allows the seller to exploit the situation and seller cheaper low quality goods and services The buyer can put herself in the shoes ofthe seller and anticipate this exploitation The buyer credibly promises to return only if the quality turns out to be high She pays a price above the cost by an amount called the reputation rent The price is just high enough so that the present value of this stream of rents exceeds the cost savings from low quality Problem 1 Restaurants in Vino Valley serve nice dinners to hungry and slightly tipsey tourist who have spent their day visiting the Valley s vineyards The value of a nice dinner with high quality ingredients and skilled preparation is 40 The value of a low quality dinner is 5 The cost of preparing high and low quality meals are 20 and 10 respectively The discount factor for the customers is 08 Customers can choose to buy a meal or not buy Restaurants can choose high or low quality Let P denote the price of a meal a Is there a potential market for high quality meals Is there one for low quality meals b Write down the payoffs in a box the normal form showing the players and their strategies c What is the best response of the customer to the restaurant s choice of high quality d What is the best response of the restaurant to the customer s choice of Buy e What is the best response of the customer to the restaurant s choice of low quality f Explain the equilibrium g What is the minimum price that will eliminate the market failure when the customers use a trigger strategy h Suppose the value of a low quality meal is 15 How does your answer change Solution a There is a potential market for high quality meals because the value to cusomters 40 exceeds the cost 20 There is no potential market for low quality meals 5lt10 b The box is given below Restaurant High Low Buy C407P C5P SP20 SP10 Customer Not buy C 0 C 0 S 0 S 0 c Buy assuming the price is less than 40 because 40 7 P gt 0 d Low quality because P 10 gt P 20 e Not buy because 5 7 P lt 0 f The equilibrium is market failure because Not buy is the best response to low quality for the customer and the restaurant has no option to improve the situation g P 20 10 188 2250 The price covers the cost of high quality ingredients 20 plus a rent of 250 The present value of the stream of 250 payments is just enough to motivate the restaurant to provide a high quality meal h There will be a market for low quality meals Ifthere is free entry in the restaurant market the price for low quality meals will be bid down to the cost which is 10 As in the first case there continues to be a market failure for high quality meals 2 Dave has a housepainting business called Master of Arts Dave has a Masters degree in history hence the name The point of the name is to indicate that Dave provides the highest quality painting Unfortunately the quality of Dave s work only becomes clear as time progresses it cannot be observed at the time he is paid Specifically the value of a room painted by Dave is 1500 The value of a low quality paintjob is 500 The cost ofa high qualityjob is 1000 and the cost of a low quality job is 400 The discount factor is 08 a Is there a potential market for high quality painting Is there one for low quality painting b Write down the payoffs in a box the normal form showing the players and their strategies What is the best response of the customer to Dave s choice of high quality What is the best response of Dave to the customer s choice of Buy What is the best response of the customer to Dave s choice of low quality Explain the equilibrium What is the minimum price that will eliminate the market failure when the customers use a trigger strategy IOH1999
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