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# Intermed Microecon ECON 4010

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This 33 page Class Notes was uploaded by Chelsie Cronin on Monday October 26, 2015. The Class Notes belongs to ECON 4010 at University of Utah taught by Staff in Fall. Since its upload, it has received 51 views. For similar materials see /class/230030/econ-4010-university-of-utah in Economcs at University of Utah.

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Date Created: 10/26/15

ltLecture 13gt 7 The Cost of Production In the last two classes we examined the film39s production technology 7 the relationship that shows how factor inputs can be transformed into outputs Now we will see how the production technology together with the prices of factor inputs determines the firm39s cost of production Opportunity Cost is the cost associated with opportunities that are forgone when a firm39s resources are not put to their best alternative use For example consider a firm that owns a building and therefore pays no rent for office space Does this mean that the cost of office space is zero Economists would note that the firm could have earned rent on the office space by leasing it to another company This forgone rent is the opportunity cost of utilizing the office space Sunk Cost is an expenditure that has been made and cannot be recovered For example consider the purchase of specialized equipment for a plant Suppose the equipment can be used to do only what it was originally designed for and cannot be converted for alternative use The expenditure on this equipment is a sunk cost Because it has no alternative use its opportunity cost is zero Total Cost TC or C is divided into two components Fixed Cost and Variable Cost Fixed Cost FC is a cost that does not vary with the level of output and that can be eliminated only by going out of business It may include expenditures for plant maintenance insurance and perhaps a minimal number of employees Variable Cost V C is a cost that varies as output varies Which costs are variable and which are fixed depends on the time horizon that we are considering Over a very short time horizon 7 say one or two months 7 most costs are fixed Over such a short period a firm is typically obligated to receive and pay for contracted shipments of materials and cannot easily lay off workers On the other hand over a long time horizon 7 say two or three years 7 many costs become variable Over this time horizon if the firm wants to reduce its output it can reduce its workforce purchase fewer raw materials and perhaps even sell off some of its capital People often confuse fixed and sunk costs Fixed costs can be avoided if the firm goes out of business Sunk costs on the other hand are costs that have been incurred and can not be recovered Marginal Cost MC is the increase in cost that results from producing one extra unit of output MC tells us how much it will cost to expand output by one unit MCAVCAQATCAQ Average Cost AC or ATC is the firm39s total cost divided by its level of output TC Q Average Fixed Cost AFC is FC Q Average Variable Cost is VC Q Short Run Cost Q1 upp Ltmtmu tr nr Wh martnatcostofproductton The rnargrnal product of labor rnustbe rncreasrng MC measures the extra cost of producrng one more unrt of output If Lhts cost rs drrnrnrshrng then rt rnust be ta mg fewer unrts o 1abor to produce the extra unrt of output smce the extra cost refers to the extra cost ofthe 1abor If fewer unrts of labor are requrred to produce a unrt of output then the rnargrnal product extra output produced by an extra unrt of labor rnust be rncreasrng VCwLLhusAVCwALl MPLAQAL2 From 1 and 20 MC AVC AQ WAL AQ w mm When there rs on1y one Vanable rnput the rnargrnal cost rs equa1 to the prrce of the tnput dmded by us margmal product Whenever the rnargrnal product of 1abor decreases the rnargrnal cost of productron rncrease and vtce versa Drrntntshtng rnargrnal returns means that the rnargrnal product of labor dechnes as the quanttty of labor mot d m ea As aresulg mar mat costwtll tncrease as output tncreases Cost Curves p 222 Mm LuluHan m mm mn MN I t r39ni m Hmpulum xlmr IL 4rd M minim t tn t7 rhupn Hun m FC does not vary with output 7 a horizontal line at 50 VC is zero when output is zero and then increases as output increases TC is the vertical sum of FC and VC Because FC is 50 AFC falls continuously from 50 when output is 1 toward zero for large output Whenever MC lies below AC AC falls Whenever MC lies above AC AC rises Thus MC crosses AC AVC and ATC at their minimum points ATC is the sum of AVC and AFC In a the slope of the dashed line drawn from origin to point A measures AVC The slope of VC is MC Therefore at A MC is equal to AVC Q2Assume the marginal cost of production is greater than the average variable cost Can you determine whether the average variable cost is increasing or decreasing If MC is greater than AVC then each additional unit is adding more to TC than previous units added to TC which implies that the AVC increases Q3 If the firm39s AC curves are Ushaped why does its AVC curve achieve its minimum at a lower level of output than the ATC curve TC is equal to FC VC Since AFC continues to fall as more output is produced ATC will continue to fall even after AVC has reached its minimum because the drop in AFC exceeds the increase in AVC Q4 The shortrun cost function of a company is given by the equation TC 200 55q where TC is the total cost and q is the total quantity of output both measured in thousands a What is the company39s fixed cost When q 0 TC 200 so FC is equal to 200 or 200000 b If the company produced 100000 units of goods what is its average variable cost With 100000 units q 100 VC is 55q 55100 5500 AVC is TVCq 5500100 55 or 55000 c What is its marginal cost per unit produced What is its average fixed cost With constant AVC MC is equal to AVC 55 At q 100 AFC is TFCq 200100 2 or 2000 d Suppose the company borrows money and expands its factory Its fixed cost rises by 50000 but its variable cost falls to 45000 per 1000 units The cost of interest 139 also enters into the equation Each one point increase in the interest rate raises costs by 3000 Write the new cost equation TC 250 45q 3139 Long Run Cost In the long run the firm can change all of its inputs Cost of Capital r Depreciation rate Interest rate The cost of capital ie the annual cost of owning and using a capital asset is given by the sum of the economic depreciation and the interest that could have been earned had the money been invested elsewhere Isncnsl Line and Isoquam Curve p 228 Capital per year Ilt2 H A KI K3 t t t t i t Lh Cr C1 L2 L L1 Labor per yun39 Isooost Line rs a gaph showrhg all possrble oorhbrhatrohs of 1abor and oaprtal that oar be purchased for a goveh total cost r r r rK Ifwe rewrrte the above equataoh we get K Gr 7 wrL 1ope A wr rs the ratao ofthe wage rateto the rental oost ofcaphtal Ifthefum gave up auhrt otho buy wruhrts ofC at a oost ofrper umt rts TC wouldremam the same 5 Q5 Why are rsooost hhes strmght hhesv The slope ofthehsocostlme rs the ratao of the rhout phoes oflabor and oaprtal Ifmputpnces are f1xedthen the ratro ofthese prroes rs o1ear1y rxeo anothe rsooost hhe rs strmght Cast Minimizatinn The Problem 15 to choose the pomt oh the rsoquant that mrmrmzes total cost Mm CwLrK st QFKrL However o can be aohreveowrth c2 erther by usrhg K2 and L2 or by usrhg K3 ahoLs But c2 rs hot the mum Cost qr can be producedmore oheaply at a oost ofcr by usmg Kr andLl E a The point of tangency of the isoquant ql and the isocost line C1 at point A gives use the cost minimizing choice of inputs L1 and K1 At this point the slopes of the isoquant and the isocost line are equal MRTSMPLMPKwr gtMPLwMPKr Q6 Suppose a chair manufacturer finds that the marginal rate of technical substitutions of capital for labor in the production process is substantially greater that the ratio of the rental rate on machinery to the wage rate for assemblyline labor How should she alter herhis use of capital and labor to minimize the cost of production The manufacturer would be better off if she increased herhis use of capital and decreased herhis use of labor decreasing the marginal rate of technical substitution MRTS She should continue this substitution until herhis MRTS equals the ratio of the rental rate to the wage rate Q7 A chair manufacturer hires its assemblyline labor for 30 per hour and calculates that the rental cost of its machinery is 15 per hour Suppose that a chair can be produced using 4 hours of labor or machinery in any combination If the firm is currently using 3 hours of labor for each hour of machine time is it minimizing its costs of production If not how can it improve the situation Graphically illustrate the isoquant and the two isocost lines for the current combination of labor and capital and the optimal combination In this case isoquant is a straight line with a slope of 1 and intercept at K4 and L4 The isocost line C 30L 15K has a slope of 3015 2 and has intercepts at KC15 and LC30 The cost minimizing point is a corner solution where L0 and K4 At that point total cost is 60 Capital isocost lines isoquant Q8 The production function for a product is given by q 100KL If the price of capital is 120per day and the price of labor 30 per day what is the minimum cost of producing 1000 units of output At the point of cost minimizing combination of C and L MRTS MPL MPK wr MPL is dq dL 100K MPK is dq dK 100L Therefore MRTS is KL KL 30120 gt L K Substitute for L in the production function and solve where K yields an output of 1000 units 1000 100K4K gt K 158 L 632 Thus total cost is C wL rK 30632 120158 37920 Q9 You manage a plant that produces engines by teams of workers using assembly machines The technology is summarized by the production function q 5KL where q is the number of engines per week K is the number of assembly machines and L is the number of labor teams Each assembly machine rents for r 10000 per week and each team costs w 5000 per week Engine costs are given by the cost of labor teams and machines plus 2000 per engine for raw materials Your plant has a fixed installation of 5 assembly machines as part of its design a What is the cost function for your plant namely how much would it cost to produce q engines What are average and marginal costs for producing q engines How do average costs vary with output K is fixed at 5 The shortrun production function then becomes q 25L That is for any level of output q the number of labor teams hired will be L q25 Cq rK wL 2000q 100005 5000q25 2000q 50000 2200q AC Cq 50000q 2200 MC 6Cq6q 2200 MC is constant and AC will decrease as quantity increases b How many teams are required to produce 250 engines What is the average cost per engine To produce 250 engines we need labor teams L 25025 10 AC 50000250 2200 2400 c You are asked to make recommendations for the design of a new production facility What capitallabor ratio should the new plant accommodate if it wants to minimize the total cost of producing any level of output q We no longer assume that K is fixed at 5 We need to find the combination of K and L that minimizes costs at any level of output q The costminimization rule is given by MPKr MPLw Since MPK 6Q 6K 5L and MPL 6Q 6L 5K we obtain 5Lr 5Kw gt KL wr 500010000 l2 Duality Cost Minimization Products Maximization with Lagrangian Method Min CwLrK Max QFL K St Q FL K St C wL rK 1LwLrK7tFLKQ LFLK77twLrKC 2FOC 6L6L wikMPL 0 6L6L MPLikw 0 6L6K rikMPK 0 6L6K MPKikr 0 16 FLK7Q 0 16 wLrKC 0 3MPLMPKwr ltLecture 2gt 3 Consumer Behavior Maximizing Utility Two components in consumer behaviour Preferences indifference curve amp Constraints budget line Indifference curves represent the quotwillingnessquot aspect of consumer demand while the budget line captures the quotabilityquot Budget Line A u L L L 3911 an L l r a given consumer budget The amount of a good that a consumer can afford will depend on the consumer39s income and the price ofthe goods AD Consumer39s Income I 80 Price ofFood PF 1 Price of Clothing Pc 2 Budget line PFF PcC 1 0 2 gt F 2C m It can be rewritten C PFPcF IPc gt 12F 40 12 U 2n AD F ED an The slope of the budget line is the negative ofthe relative price oftwo goods the ratio ofthe prices Let39s think about how the change in the determinants will affect the budget line A change in consumer income causes the budget line to shift parallel to the original line i An increase in consumer income 80 gt 160 an If consumer income increases then the consumer will be able to purchase higher combinations ofgoods Hence an increase in consumer income will result in an outward shift in the budget line F2C80gtF2C160 F ii A decrease in consumer income 80 gt 40 m If consumer income fell then the potential combinations ofthe two goods that can be purchased also fell 0 2D There would be a corresponding parallel shift to the left to represent a decrease in the potential combinations of m the two goods that can be purchased F2C80gtF2C40 U 2n AD F ED an Ifincome is held constant andthe price of one of the goods changes then the slope of the curve will change In other words the curve will prvot i A decrease of price offend 1 gt 12 The reduction of the price of food from 1 to 50 cents means that on a xed budget of80 the consumer could purchase a maximum of 160 units as opposedto 80 3D 0 Note that the price of clothing has remained xed hence 20 the maximum point for clothing will remain xed Because the price of food falls with respect to clothing if one gives up a unit of clothing one can now get more offood than before Therefore the slope is now atter U 20 AU EU EU WU 120 MB WED F 2C 80 gt 12F 2C 80 ii An increase in price offend 1 gt 2 The budget line would be steeper than the original 3n budget line re ecting the rise of the price of food from 2 F2C80gt2F2C80 U 2n Am F ED an r A change in price of clothing a2gt1FC80 b2gt4F4C80 Au an an Eu 0 0 2n Au m 2n U 2n 4n ED an E 2n Am F ED an F w m in fat mm m cmnpmmx ufcmlmmxhzhawmx Cmmxhehmm mm mm m ammyu ildi wuu ulvu ardlndya lira Gwznpxzfmmrs amhudgetcmummn autumn chm gm m rmxmm mummy Mnimin39r39lmhy Irdx 39nzm Cum mayme m m mpovm mmDu mmammm mamkhmmu nth M ughufhbndgathr N pm A m a u budg unruth Kam zdhm hum 4007 1 mm hng 1m nfuolny mm A cmmxwm mgumh hghznmdm mm ma mdahlz andduwmlzadhmmwmc nu 9mm st mm are mm AH nmrmmamnhlz 1m n mmy ah ylz mm budg ard mum pm c 39 m xlupeuf nhudyllim mmummuhdam n yeuf nhdmumuemm Q1 Explmnwhyanmshmeenwn gunk mm qua m m mi ufdnp e um sad mm mmmlzxm aahlm rmxmnmxamfacnnn MRS describes m m mth cmm mm ma m gmdfmamhnn rmmmm a 5m lzvzlnfxamfzom u monufpnar mm m hadwfmmh mkztuwllhrg mmhmeenh samvm u targmq fth magma mmwnhthz budg m mm m pm atwl39nchd39lz m7 n 39 an qualmd mmmna xfzmu rmxxmmsi KhMRS hemenwngmk 1 minimum monufpnmx mu cmmxcmldmd m 931 fax mum at mkztpnnex m taml39nghxlzvzk ufxamfacnnn For example if the slope of the budget line the ratio of the prices is 4 then the consumer can trade 4 units on for one unit of X If the MRS at the current bundle is 6 then the consumer is willing to trade 6 units on for one unit ofX The consumer is willing to trade 6 but only has to trade 4 so she shouldmake the trade This trading continues until the highest level of satisfaction is achieved As tIades are made the MRS will change and become equal to the price ratio Corner Solutions A comer solution exists if a consumer buys in extremes and buys all of one category ofgood and none of another Q2 Jon is willing to trade one can of coke for one can of sprite or one can of sprite for one can of coke a What can you say about Jon39s marginal rate of substitution MRS Jon39s MRS can be de ned as the number of cans of coke he would be willing to give up in 1 exchange for a can of sprite Since he is willing to trade one for one his MRS is b Draw a set ofindifference curves for Jon His indifference curves are linear with a slope ofl U coke sprite coke sprite dead omit U 1 2 3 5 E 7 E 4 5pm Draw two budget lines with different slopes and illustIate the satisfaction maximizing choice What conclusion can you aw If Jon39s budget line is steeper than his indifference curves en he will choose to consume only the good on the vertical axis Indifference curve S C 6 Budget Line ZS C 6 MRS lt Ps Pc Jon consumes only coke If Jon39s budget line is atter than his 5 indifference curves then he will choose to 7 consume only the good on the horizontal axis Indifference curve S C 6 Budget Line S 2C 6 CUR 3 MRS gt PgPc 2 If the consumer could give up more clothing 1 for food he would do so But there is no more D 1 2 3 A 5 E 7 E clothing to give up Sum L L solution L quai the price ratio Maximizing Utility The consumer39s objective is to maximize the utility received from the consumption of a market bundle of MM i mL Max UF C st PFFPCCI Now we will learn how to solve this maximizing problem with the Lagrangian Method The Lagrangian method uses a method of modifying the objective function being maximized to account for c L n i Transform all of the constraints into a form that equals zero PFFPCCI gt PFFPcCI0 ii Create a new olj ective function called Lagrangian by multiplying each constraint in its zero form by a Lagrangian multiplier 9t and adding the results to the olj ective function L UF c MPFFPCC 1 iii Differentiate the Lagrangian with respect to all the control Varzable and the Lagrangian multipliers In the example the control variables are F C and it The consumer does not control the other parameters of the optimization pro lem e prices of the goods and the wealth are generally assumedto be exogenous at the level of the consumer 8L8F8U8F71PF0 8L8C8U8C71Pc0 8L3LPFFPCC710 iv At the constrained maximum all of these partial derivatives will equal zero These rst order conditions can be algebraically manipulated to deduce properties of the constrained optimum That is to say 39 39 39 the mzminzl rate of substitution 39 39 39 MRS 8U8F aUac PF Pc Given the problem ofmaximizing U FC subject to the constraint F 2C 80 let us write the Lagrangian function as follows L FC 2 80 F 2C Fistorder condition 8L 8F C 7 9t 0 gt C 9t 1 8L8CF72t0 gtF2t 2 8L82F2C800 3 Combining 1 and 2 we get MRS 8U8F3U8C MUF MUc CF 12 PF Pc 4 Substituting 4 into 3 we get 2F 80 0 gt F 40 C 20 9t 20 Marginal Utility the additional utility that a consumer derives from an additional unit ofa good Diminishing Marginal Utility MU is inversely relatedto the number of units already consumed or owned For example the marginal utility of one slice of bread offered to a consumer that has ve slices will be great since the consumer will be less hungry and the difference between ve and six is proportionally signi cant An extIa slice offered to a consumer that has 30 slices will have less marginal utility to the consumer since the difference between 30 and 31 is proportionally smaller and the consumer39s appetite may be satis ed by what she already had Diminishing MU Diminishing MRS Because of diminishing marginal utility less of a good must be given up to gain an additional unit of some An other good 3 A A F c 20 30 Czn B F c 60 10 a Agt BMU ofFi MU ych 1 Therefore MRS MUFMUc i U 2n Am F ED an Q3 Consumers in Georgia pay twice as much for avocados as they do for peaches However avocados and peaches are equally priced in California If consumers in both states maximize utility will the marginal rate of substitution of peaches for avocados be the same for consumers in both states If not which will be higher The marginal rate of substitution of peaches for avocados is the amount of avocados that a consumer is willing to give up to obtain one additional peach When consumers maximize utility they set their MRS equal to the price ratio which in this case is Pp PA In Georgia PA 2Pp which means that when consumers are maximizing utility MRS 12 In California PA Pp which means that MRS 1 The MRS is therefore not the same in both states and will be higher in California ltLecture 15gt 8 Pro t Maximizatjon and Competitive Supply A fundamental problem faced by every rm How much should be produced Pro t Maximizatjon Pro t Difference between total revenue and total cost Short Run Pro t Maximizatjon p265 Short Run Pro t Maximization p268 m mupm mum par yuan Lost pmm fur I t lt 739 Pro t is maximized at the oint at which an itional increment to output leaves pro t unchanged ied1rdq 0 dndqdR dqrdCdq0 gtMRqMCq Thus pro t is maximized when marginal revenue is equal to marginal cost TR W gt Competitive Market gt MR p gt MR p MCq MC I Lost pmmf a gt 39139 R x 9 Ill 1 I w Uulput ShutDown Rule The rm should shut down ifthe price of the product is less than the average economic m of production at the pro t rmaximizing output Suppose that the rm has incurred a large sunk cost which it treats as an ongoing xed cost and suppose that there are no other xed costs In this case the rm39s average variable cost is now the appropriate measure of the rm39s average economic cost ofproduction ATC r AVCq cannot be avoided even ifthe rm shuts down Average economic cost is equal to average total cost when there are no sunk costs but equal to average variable cost when costs treated as xed are actually sunk costs Short Run Supply Curve p273 a n l I Output A supply curve for a rm tells us how much output it will produce at every possible price The rm39s supply curve is the portion of the marginal cost curve for which marginal cost is greater than average economic cost In the case in which all xed costs are sunk costs the shortrun supply curve is given by the crosshatchedponion ofthe MC curve Q1 The data in the following table give information about the price for which a nn can sell aunit ofoutput and the total cost ofproduction In the table P is assumedto be 60 a Fill in the blanks in the table b Show What happens to the firm39s output choice and profit if the price of the product falls from 60 to 50 Q 1 2 TR 50 100 TC 150 178 n 100 78 5 8 400 310 90 9 450 355 95 10 500 410 90 1 1 550 475 75 At a price of 60 the firm should produce 10 units of output to maximize profit because this is the point closes to Where price equals marginal cost Without having marginal cost exceed price At a price of 50 the film should produce 9 units to maximize profit When price falls from 60 to 50 profit falls from 190 to 95 c Show What happens to the firm39s output choice and profit if the fixed cost of production increases from 100 to 150 and then to 200 Assume that the price of the output remains at 60 per unit 1 1 50 Q 1 2 TR 60 120 TC 200 228 n 140 108 2 200 8 9 10 1 1 480 540 600 660 360 405 460 525 1 20 1 35 1 40 1 35 In all of the given cases With fixed cost equal to 100 then 150 and then 200 the firm Will produce 10 units of output because this is the point closes to Where price equals marginal cost Without having marginal cost exceed price In general fixed costs do not in uence the optimal quantity because they do not influence marginal cost Higher fixed costs also result in lower profits d Derive the firm39s shortrun supply curve Q 0 1 2 3 4 5 6 7 8 9 10 11 TC 100 150 178 198 212 230 250 272 310 355 410 475 MC 50 28 20 14 18 20 22 38 45 55 65 TVC 0 50 78 98 112 130 150 172 210 255 310 375 AVC 500 390 327 280 260 250 246 263 283 310 341 P The firm39s shortrun supply curve is its marginal cost curve above average variable cost The firm Will produce 8 or more units depending on the market price and Will not produce in the 0 7 7 units of output range because in this range AVC is greater than MC Q2 Suppvse the cast fuhc hh 1s Cq4q 16 a Fmdvanable cast xed cast average custmargmal cast average vanable cast and average xed cast VC degmds 1m qahdrc duesmtdepmd mq VC4q FC 16 AC4q 16q MC8q AVC4q AFC 16q 1 mm mat 1 t Cost Curves c Fmdthe uutgut that mrmmrzes average cast The mrmmum average cast quan ty 15 where MC 15 equa1 tn AC 4q16q Sq gt 11 At what range Dfpnces wr11 the rm pmduce apnsmve uutputv r p MC gt AVC r r h the abhve case L L AVC 5D the rm W111 supply pusmve uutput at any pusmve ane The rmwr11 H r e Atwhatrarge nfpncesw l the rm eam ahegatrve grg tv The rm wr11 M lt AC T e mrmmum average cast quah ty 15 q z Atthrs1eve1 AC 15 16 The rm W111 therefme eam hega vegrh t 1fpnce 1s beluw 16 f 1deh fy the rms supply curve 1m yum graph The rm supply curve 15 the MC curve abuvethe gmht where MC AVC Q3 Suppose that a rm39s production function is q 9x Z in the short run Where there are xed costs of 1000 and x is the variable input Whose cost is 4000 per unit a What is the total cost of producing a level of output q Identify the total cost function TC Cx Fixed Cost Variable Cost 1000 4000x Express x in terms ofq so that x qZ81 Substitute this into the above cost function to nd Cq Cq 1000 4000qZ81 b Write doWn the equation for the supply curve The rm supplies output Where p MC so MC curve is the supply curve P 8000q81 c lfprice is 1000 hoW many units Will the rm produce What is the level ofpro t Illustrate on a cost curve grap Cast Curves HUD The rm Will produce q 10125 Since P 8000q81 120D WW 7 100010125 7 1000 BUD 400010125Z81 40625 c 5039 Graphically the rm produces Where the ma horizontal price line hits the upward sloping MC curve 200 Pro t is the difference between the revenue D 2 4 E a 2 4 IS a 20 1q 1 i 1 1 boxpqandthecostboxACq The shortrun Market Industry supply curve is the sum ofthe supply curves ofthe individual rms The price elasticity of market supply Es AQQ APP The producer surplus of a rm is the sum over all units produced of the differences between the market price of the good and the marginal cost of production Just as consumer surplus measures the area beloW an individual s demand curve and above the market price of the product producer surplus measures the area above a producer39s supply curve and beloW the market price Q4 Suppose that a competitive rm39s marginal cost of producing output q is given by MCq 3 2q Assume that the market price ofthe rm39s product is 9 a What level of output Will the rm produce To maximize pro ts the rm should set P MR MC 9 3 2q or q 3 b What is the rm39s producer surplus Producer surplus is equal to the area beloW the market price Pme MCq ie 9 and above the marginal cost curve ie 3 2q P Because MC is linear producer surplus is a triangle With a base pmduce of 6 and a height of 3 Therefore producer surplus is 9 Surplus 3 3 Quantity c Suppose that the average Variable cost of the firm is glvm by AVCq 3 q Suppose that the film s A n ati RTC TRpq9327 TCZTVCFC TVCZAVC q3qq6318 ThusTC18321 1T 27 7 2l 6 Therefore the firm is eamlng positive economic profits LongRun Pro t Maximizmjon In the short run Tn mtm t in th lm min a Firm an alt rall its inputs including plant size it can decide to shut down i e to eXit the industry or to begin producing a product for the first time i e to enter an industry 7tRrCRerrK Long Run Proiit Minimization p 282 Mill n H l ll untin 1 L39 39h The longrun output of a pro tmaximizing cornpetitiye firm is the point at which longrun marginal cost equals the price If 40 LMC P at qg Total profit is EFGD Longrun competition cquilitiriuni A11 films in an industry are maximizing profit No firm has an incentive either to enter or eXit the industry The price is such that supply quantity equals dernand quantity Q5 A firm produces a product in a competitive industry and has a total cost function TC 50 4q 2q2 At the given market price of 20 the firm is producing 5 units of output Is the firm maximizing profit What quantity of output should the firm produce in the long run If the firm is maximizing profit then price will be equal to marginal cost MC44qPMCresultsinP2044qMCorq4lt5 The firm is not maximizing profit At the level of profitmaximizing output profit is 204 7 50 44 242 80 7 98 l 8 The film should produce q 0 units of output in the long run since at the quantity where price is equal to marginal cost economic profit is negative The firm should exit the industry Q6 A number of stores offer film developing as a service to their customers Suppose that each store that offers this service has a cost function Cq 50 05q 008q a If the going rate for developing a roll of film is 850 is the industry in long run equilibrium If not find the price associated with long run equilibrium First find the profit maximizing quantity associated with a price of 850 by setting price equal to marginal cost so that P 85 MC 05 016q or q 50 Profit is then 8550 7 50 0550 008502 150 This industry is not in the long run equilibrium because profit is greater than zero In the long run equilibrium firms produce where P is equal to minimum AC and there is no incentive for entry or exit To find the minimum average cost point set MC AC and solve for q MC 05016q AC 50q 05 008q gt q25 To find the long run price in the market substitute q25 into either MC or AC to get P 450 b Suppose now that a new technology is developed which will reduce the cost film developing by 25 Assuming that the industry is in long run equilibrium how much would any one store be willing to pay to purchase this new technology The new total cost function can be found by multiplying the old function by 075 or 75 Cq 7 7550 05q 008q2 7 375 0375q 006q2 The firm will set MC P450 in the long run equilibrium MCq 0375 012q P 450 gt q 34375 The firm will develop approximately 34 rolls rounding down If q 34 then profit is 3339 which the most the firm would be willing to pay for the new technology ltLecture 5gt 4 Individual and Market Demand Substitutes and Complements Prices of related goods also in uence how much of a product people buy Goods that are substitutes satisfy the same set of preferences An example of a substitute for hamburger is pork If pork prices are high people are tempted to shift away from pork to hamburger and if pork prices are low people are tempted to shift from hamburger to pork The opposite of a substitute is a complement a good that helps complete another in some way Ketchup and hamburger buns are complements to hamburger and if they are priced low enough consumption of hamburger may rise Sometimes goods are such good complements that they are sold together and we think of them as a single item Left shoes and right shoes are an example Q1 Suppose that a consumer spends a fixed amount of income per month on the following pairs of goods If the price of the first goods increases explain the effect on the demand quantity of each of the goods In each pair which are likely to be complements and which are likely to be substitutes a Tortilla chips and salsa If the price of tortilla chips increases the demand for both goods will fall assuming they are complements b Tortilla chips and potato chips If the price of tortilla chips increases the demand for tortilla chips will fall and the demand for potato chips will rise assuming they substitutes c Movie tickets and gourmet coffee If the price of movie tickets increases the demand for movie tickets will fall and the demand for coffee is unchanged assuming they are unrelated d Travel by bus and travel by subway If the price of bus travel increases the demand for bus tickets will fall and the demand for subway tickets will rise assuming they are substitutes Income and Substitution Effects p116 A fall in the price of a good has two effects 1 Consumers will tend to buy more of the good that has become cheaper and less of those goods that are now relatively more expensive 2 Because one of the goods is now cheaper consumers enjoy an increase in real purchasing power Q2 Explain the difference between an income effect and a substitution effect The substitution effect measures the effect of a change in the price of a good on the consumption of the good utility held constant The income effect measures the effect of a change in purchasing power caused by a change in the price of a good on the consumption of the good relative prices held constant IncomeEffect real Income fall as pnces nse For example assume someone has a xedmcome of120 dollars a week Ifthe pnce ofabottle ofwme ts 10 dollars they cm buy 12 bottles Ifthe pnce doubles to 20 dollars now they cm only afford 5 bottles Ifthe p A o asthepnceofvw th mmtoafford them falls Nohce that Income m the example ts xed tt does not change Substitution Effect As the pnce of goods moreases people are hkely to purchase other products mstead Subststutes are goods thatare mxlar For example L p Pepsl Coke md buy Pepst mstead Income and Subs m nn Effects Nnrmal Gnnd p117 1 th ihmmv nmlm month L tfect Enact 39rnta Hfuct A m t t t t 55m t at A on the budgethne RS When the pnce offoodfalls consumption tncneoses by we as the consumer moves The subsmuhm effect 171E changes the nelotsve pnces of food and clothmg but keeps real mcome sausfactton constant The subsututton effect tsolates the pure effect from changtng the relatnve pnces It mustbe negatwe thatts quanuty moves oppostte the derectnon of pnce 4 1m an mm ormfenor good For whrch cf the followlng goods ls a prrce rhcrease llkely to lead to a substautral rhccrhe as well as substltutlon effch a Salt effect The amount of rhccrhe that ls spent on salt ls l crhe effect srhall substrtutrch relauvely small but srhce there are few away from rt As the phce of salt hses real declrhe u cchsurhptrch subsututes for salt cchsurhers wlll hct readlly subsutute rhccrhe wlll fall only slrghtly thus leadmg to a small b Housmg Large rhccrhe effect we subsutuuch effect The amount cfrhccrhe spent on housmg ls relatwely large for most consumers If the phce cf housmg were to rrse real rhccrh ould be reduced v w w v l uh Mum c Theaternckets ll FF ub tub u e fect u it ls relauvely small but consumers can subsutute away from the theater uckets by choosmg cther hrheht Ast e p ce oftheatertlckets rlses real rhccrhe wlll fall chly slrghtly but ffect cau belarge enough to reduce cchsurhptrch y alarge arhcuht forms of entertal the substltutlon e Income and SubsLimLion Effects Inferior Good p118 39l I Food 4 truutspr Eubthlmn nmnim um Imiwm Ellwl Tum ul Wrth a decrease m the phce cffccd the Consumermoves frcrh Ato B The resuluhg change rh fccd purchased can be broken down rhtc a substrtutrch effect m and au rhccrhe effect EFz In thrs case foodls au rhfehcr good because the rhccrhe effect ls hegatwe However because the substitution T L H quahuty of food derhahded Income and Substjmtjon Effects The Giffen Good p119 7 Fond lllnlts 7 Subsmulil n mm WWWquot lt7 7 lncoxxwli ecl lt Total Et39lecl food 15 an lnfenor good and when the lncome effect 15 large enough to domlnate the substltutloh effect the demand curve will be upwardslopmg hut l m n t t t t F W e t t t m 4 leads to alower quahhty of food demanded Speclflc Examples Perfect Complements Indltfe39ence nurves Final budget line fem a Income effect owl effect What about Perfect Substltutes7 Checkthls case for yourself An algehnic Inalmenl ufincume and sullsn39lu un ems Tumchmgemnemmd Substmmne ect Immee ect AQAP AQUA muAP 04 Sara 11mm fullwmgunhty funmm 1107 c PC a Asmemahexmmmsxo DmveSarisdemmdfmmnnsbyunngLaganganmem Laganganl unmm LFc4prpncxo FOC BLBF 4PM gtcchF eLe inks eLexwmncixow gtPr PcPr PEF80ZPEF800 Thus qedemmdfumhmfmfwdxs Ham and the demandfmmmfm mum s c 40m fund and Elman wmm pm mm 5 changed mszv 42 F1oczo A Fr Pt 32 32 F 20c 20 C Fmdthe amuum nfsubsmunm 8381 andmmme ed MA Sma smhtystFC 1020200 Keep nsm ymn m AHhe newpure uffwdaz the budget msummszp no 1 Undzx ms mum we have m Emith uhhtymmrmzmgpmm atwhmh MmMUHMUEslwpeuf hebudgahmmc CFmusF1m Thesubsnmum fm ErA MW 414 Themmme fm C43 201mm 535 Market Demand p113 Elf Mnlkel Dcmmlll 1 L71 r2L L a J L W 111 t 30 3 3 Quanlllv The market demand curve 15 obtaned by summmg out Consumers demand curves Elasticity Pnce Elastlclty ofDemand an t t t t t quotA change In demand afgoom quotA change In pnce afgoom Q5 t t H t t t t 10to11 Pnee s 8 9 10 11 12 Quanuty Demanded 170 130 100 80 55 To calculate the pnce elastlclty we needto know what the percentage change The formula used to calculate the percentage change 15 New Value 7 Q1gmal Value Ongnal Value quotnchangemdemandls seem100 change In pnee 15 1110 Pnce elastlclty of demand 0 2012 when we analyze the pnce elasuclty we are concerned wlth the absolute value so we Ignore the negauve value So when the pnce Increases from 10 to 11 the prlce elasuclty ofdemandls 2 Genml Funnula m a Pride Elasticin umemand MADAW p we Demand AQAP PQ slope A7 151WE PQ p Elammy nfa1mem demand curve A p Q 12 s1npe Elamcny 10 40 72 11 38 e2 71727 12 36 e2 715 13 34 72 013077 14 32 e2 71142 15 30 72 1 a 1 16 28 72 008750 0 Q m 0 quotW TypanfElzslici zs e If L112 nnee elasumy m demand 15 P 9 PM 1 gen une gnnd 1spnc2 e1asue Demands Pgn gcdylilasm peneeuyxnenene 1e 1 a Chang 1n a n D 71 1m mnennee 219111 m demand 15 m m lessthanmeth enndm Q y Q y me1asde Demand 15 ml v y 125 n e in In nEE PM mm 1111 7 mt Elasunty If39he y nnee elasumy m demand w 1 1eeua1 nne e nnd hasumtzlasumy c mges pmpnmnnately in a nnee change Quanmy anmy 7 Perfecdy me1asue If me nnee 213mm m demand 15 equal in 22m L112 end 15 perfectly me1asue A vzmcal e Perfecdy e1asue mne nnee 213mm m dznand1s1n mty me gnndlsperfec y e1asde Any change m d nnee W111 see quanmy demm ed fall in zem Th1 demand cuxve 1s assncmed w1th11ms nperaung m pzxfecdy campeuuve markets Factors that determine the value of price elasticity of demand Number of close substitutes within the market The more and closer substitutes available in the market the more elastic demand will be in response to a change in price Luxuries and necessities Necessities tend to have a more inelastic demand curve whereas luxury goods tend to be more elastic Percentage of income spent on a good It may be the case that the smaller the proportion of income spent taken up with purchasing the good the more inelastic demand will be Habit forming goods Goods such as cigarettes and drugs tend to be inelastic in demand Price points Decreasing the price from 2 to 199 may result in greater increase in quantity demanded than decreasing it from 1 99 to 198 Q6 Explain which of the following items in each pair is more price elastic a The demand for a specific brand of toothpaste and the demand for toothpaste in general The demand for a specific brand is more elastic since the consumer can easily switch to another brand if the price goes up b The demand for gasoline in the short run and the demand for gasoline in the long run The demand in the long run is more elastic since consumers have had more time to adjust to the change in price Q7 You run a small business While you do not know the exact demand curve for your product you do know that in the first year you charged a price of 45 and sold 1200 units and in the second year you charged a price of 30 and sold 1800 units a If you plan to raise your price by 10 what would be a reasonable estimate of what might happen to the quantity demanded in percentage terms You can estimate the slope of the demand curve in the following way 6Q6P AQAP 120018004530 60015 40 You can now use the elasticity formula PQXSQAPH to calculate elasticity at each data point as well as the average point P45 Q1200 gt Elasticity 45120040 15 P30 Q1800 gt Elasticity 30180040 067 P375 Q1500 gt Elasticity 375150040 1 Given you are coming up with an estimate based on only two data point it may be best to go with the average point If elasticity is 1 then a 10 increase in price will cause quantity demanded to fall by 10 b If you raise your price by 10 will revenue increase or decrease If the elasticity is 1 the revenue will be unchanged when price is increased If elasticity is actually closer to 067 inelastic then revenue will rise when price is increased because the effect of the increase in price will outweigh the effect of the decrease in quantity If elasticity is closer to 15 elastic then revenue will fall when price is increased Relationship between elasticity and expenditure rable 4 3p125 Dernand Inelastic Unit Elastic Elastic KPnce Increases Expenditures Increase Are Unchanged Decrease KPn ce Decrease Expenditures Decrease Are Unchanged Increase Cunsuniei Surplus a Marke t Price Rock concert akes thousands ltLecture 14gt 7 The Cost of Production Ql Suppose that a firm39s production function is q lOLIZKlZ The cost of a unit of labor is 20 and the cost of a unit of capital is 80 a The firm is currently producing 100 units of output and has determined that the costminimizing quantities of labor and capital are 20 and 5 respectively Graphically illustrate this situation on a graph using isoquants and isocost lines The isoquant is convex 100 lOLIZKlZ TC 2020 805 800 so the isocost line is 20L 80K 800 At the optimal quantities of L and K the isocost line is tangent to the isoquant Capital optimal point isoquant line isocost line L abor b The firm now wants to increase output to 140 units If capital is fixed in the short run how much labor will the firm require Illustrate this point on your graph and find the new cost Capital The new level oflabor is L 392 q 140 10 L V5 c Graphically identify the costminimizing level of capital and labor in the long run if the firm wants to produce 140 units d If the marginal rate of technical substitution is KL find the optimal level of capital and labor required to produce the 140 units of output Set the MRTS the ratio of the input costs KL 2080 Now substitute this into the production function set q equal to 140 and solve 140 10LL4 then L28 K7 Expansion Path and LongeRun Total Cost p 233 Expanslon Path The curve passng through the polnts of tangency between the flrm lsocost hnes and lts lsoquants IS lts expansion path The expanlerl path descrlbes the cornblnatlons of L and K that the fum wlll choose to mlmmlze costs at each output level As long as the use of both L and K lncreases wlth output the expanslon path curve wlll be upward slopng The slope ofthe expanslon path As output lncreases 100 to 200 unlts K lncreases from 25 to so unlts whlle labor lncreases from so to 100 unlts Therefore the expanslon path 15 a stralght hne wlth a slope equal to AKAL50251005012 LongRun Total Cost curve Cq Q2 How A a a t t h m ratlo also changes For example lf the pnce of an lnput lncreases the ntercept ofthe lsocost hne on that lnputs axls moves closer to the Orlgln Thus the expanslon path bends toward the axls of the now cheaper nput Q3 h t fall by at that level for a long tlrne Show graphlcally how thls change In the relatwe pnce of labor and capltal affects the fllm s expanlerl pa Capltal Expanslunpath Let us assume that the productlon functlon exhlblts hefurewageml constant remms to scale resultlng ln llnear expmslon aths If the prlce of L decreases whlle the prlce of K IS constant the lsocost curve pwots outward around lts lntersectlon wth the capltal axls As the lsocost curves pwot outward the expanslon path pwots toward the labor axls As the prlce of labor falls relatwe to capltal the fum u es rnore abor as output lncreases Ecnunmies nl39 Scale Q4 Whatls the dlfference between ecummles nfscale anllletlllnstn 523157 l llnes cast llnllhle less than llnllhle nlnnnle than llnllhle e tn scalemeasures what happens tn nutnllt when all lnnllts ae llnllhlell LaugrRun Average and Marginal Cast n 236 Cosl dullals LMC per lull nlourpult LAC A l l l l l 1 Output lee the shunrmn average cast curve a typlcal lnugrmn avaage cost mm LAC ls Unshaped but the m u Df pmductmn The LAC Eihlblts rst lncleasmg letums 7 scale and than Dunstant letums 7 scale and eventually decreasing letlllns tn scale 39 h l LAC ls nsmg The twn curves lntelseet at A whele LAC achleveslts mnmum ACTCq gt AACAqATCAqquCqz ATCAQrTCq q MC V ACq when AC ls decleaslng AAC Aq ls negatwe and MC lt AC when AC ls lncleaslng AAC Aq lsnnslhve and MC gt AC l Elmstant mm 27 ml Q5 Wlth nutnllt what can ynu say ahnut the shape nfthe lungrmn average cast curvev l lts LAC falls then becames hmzuntal Q639Ihe Longheel Press produces memo pads in its local shop The company can rent its equipment and hire workers at competitive rates Equipment needed for this operation can be rented at 36 per hour and labor can be hired at 12 per workerhour The company has allocated 960 for the initial run ofmemo pads The production function using available technology can be expressed as 4K075L025 where Q represents memo pads boxes per hour K denotes capital input units per hour and L denotes labor input units of worker time per hour a Find the marginal products oflabor and capital MPL K075L7075 y MPK 3K7025 L025 b Construct the isocost equation C L W r 960 12L 36K c Determine the appropriate input mix to get the greatest output for an outlay of 960 for aproduction run ofmemo pads Also compute the level of output MPK PL PK K3L 1236 gtLK 96048L48K gtLK20 Q420075200254 2080 d Explain what would happen in the short run to the appropriate input mix ifthe output were changed to 160 boxes per hour Would the input combination be different in the long run If so how would it change short run K is fixed to 20 Q 160 4 200 75L0 25 Thus L 320 C 12L 36K12320 3620 4560 In the long run MPL MPK PL PK thus L K So we get 604K4L thusLK40 C12L36K4840 1920 The level ofproduction in the short run would be more expensive than producing this rate of output in the long run because both L and K could be adjusted in the long run for the most e icient input combination The Relationship between ShortiRun and LongiRun Cost p239 41 4 1 4 Onrpm There are three possible plant sizes SAC1 SACZ and SAC3 If the firm expects to produce qo then it should build the smallest plant SACI AC would be 8 If it then decides to produce ql SAC would still be 8 If it expects to produce q the middlesize plant SACZ is best If it expects to produce q3 the largestsize plant SAC3 is best LAC curve is given by the crosshatched portions of the SAC curves because these show the minimum cost of production for any output level LAC is the envelope of the SAC curves Because there are economies and diseconomies of scale in the longrun the minimum points of SAC1 and SAC3 are not efficient and do not lie on the LAC For the case of plant 1 larger plant can take advantage of increasing returns to scale to produce at a lower AC LMC is not the envelope of SMC curves SMC curves intersect LMC at the output level at which SAC is tangent to LAC ie the most costefficient level Economies of Scope Many firms produce more than one product In this case a firm is likely to enjoy production or cost advantage when it produces two or more products These advantages could result from the joint use of inputs or production facilities joint marketing programs or possibly the cost savings of a common administration Economies of Scope are present when the joint output of a single firm is greater than the output that could be achieved by two different firms each producing a single product

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