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Date Created: 02/14/14
Spring 2011 University of California at Berkeley Suggested Solutions for Problem Set 4 Econ 100A Microeconomic Analysis 144 Suppose you are currently operating a hamburger restaurant that is part of a competitive industry in your city A Your restaurant is identical to others in its homothetic production technology which employs labor l and capital k and has decreasing returns to scale a In addition to paying for labor and capital each week each restaurant also has to pay recurring weekly fees F in order to operate Illustrate the average weekly long run cost curve for your restaurant Answer This is illustrated below where the long run average cost curve for your restaurant is U shaped because of the combination of a recurring xed cost and decreasing returns to scale in production b On a separate graph illustrate the weekly demand curve for hamburgers in your city as well as the short run industry supply curve assuming that the industry is in long run equilibrium How many hamburgers do you sell each week Answer This is illustrated in panel b where the market supply curve SM is simply all short run restaurant supply curves added together This has to intersect demand at p which lies at the lowest point of the AC curve in panel a It is only at that price that long run pro ts for restaurants are zero and thus no incentives for entering or exiting the industry exist At this price you will sell hamburgers so long as p is greater than long run average cost and we know that MC crosses the AC curve at its lowest point Thus you will produce x as indicated in panel a As you are happily producing burgers in this long run equilibrium a representative from the national MacWendy s chain comes to your restaurant and asks you to convert your restaurant to a MacWendy s It turns out this would require no e ort on your part you would simply have to allow the MacWendy s company to install a MacWendy s sign change some of the furniture and provide your employees with new uny orms all of which the MacWendy s parent company is happy to pay for MacWendy s would however charge you a weekly franchise fee of G for the privilege of being the only MacWendy s restaurant in town When you wonder why you would agree to this the MacWendy s representative pulls out his marketing research that convincingly documents that consumers are willing to pay y more per hamburger when it carries the MacWendy s brand name If you accept this deal will the market price for hamburgers in your city change d On your average cost curve graph illustrate how many hamburgers you would produce gc you accepted the MacWendy s deal Answer You would produce where p y intersects your marginal cost curve In the long run we would use the long run marginal cost curve which is illustrated below Output at your restaurant would then increase from x to x If capital is xed in the short run your initial increase in output would be less since the short run MC curve is steeper and you would fully adjust to x only once you can adjust capital e Next for a given y illustrate the largest that G could be in order for you to accept the MacWendy s deal Answer This is done in panel c below where the long run average and marginal cost curves are drawn once again We know that you will be able to sell your MacWendy s hamburgers at the price p y and we know you will sell x That makes your revenue equal to the box p yx We also know you will incur average costs AC or total long run costs AC times x the smaller rectangular box The difference between these two boxes abc is the long run pro t that you can make per time period from being a MacWendy s not counting the franchise fee G Thus a b c is the most you would be willing to pay per time period for the franchise fee f If you accept the deal will you end up hiring more or fewer workers Will you hire more or less capital Answer Since neither the wage nor the rental rate has changed and since the production technology is homothetic we know your labor to capital ratio will not change as you produce more output because all cost minimizing input bundles lie on the same ray from the origin in the isoquant graph We know from what we did above that you will produce more thus you will hire more labor and more capital g Does your decision on how many workers and capital to hire under the MacWendy s deal depend on the size of the franchise fee G Answer No once you accept the Wendy s deal it is a xed cost that has no impact on the MC curve It therefore has no impact on how much you will produce and thus no impact on how many workers and capital you hire i What will happen to the demand for regular hamburgers now that MacWendy s and its huge advertising campaign in uencing consumer preferences is in town Now we must think about just the market demand for regular hamburgers Or the market demand curve without including MacWendy s hamburgers Due to the increased demand for MacWendy s hamburgers the residual remaining demand for regular hamburger demand decreases for all prices all else equal This leads to leftward shift of the demand curve from Dregular to D regu1ar A M rketfor Regri rr Hrrrrrburggersl 1 egu1a1r l39uirge39s I39egiIlar ljurgem j How does this a ect equilibrium price and quantity of regular hamburgers in the short and long run Are rms exiting entering producing more or producing less In the short run regular hamburger firms cannot enter or exit the industry but in the long run under perfect competition there is entry and exit Along with the assumption that all rms are identical this leads to a perfectly elastic long run supply curve Initially the market for regular hamburgers was at a long run equilibrium price P where short run supply and long run supply crossed the demand curve at Dfggulaf This is illustrated below Marrkerfor Regm39ar39 Harnbtirger3 rlegwnll imi 0 139IiquotE111I139 ublwgers is H I iiSRl f E1li IT T1 L 11 gL11t39 Pm Pit Pvsa pU A 139egL1a139 X1Rt P Xi I EETllll I b4l1I El39S i E Due to the leftward shift of demand we see that the short run equilibrium price falls to PSR and the short run quantity falls to XSR The short run supply curve is steeper due to not being able to Vary all inputs of production in the short run e g capital which would make MC steeper in the short run In the long run there is exit out of the market by some firms that are eaming a negative economic profit which further decreases the long run quantity of regular hamburgers to XLR The exit by firms causes the new short run supply S SR to settle or cross at the long run equilibrium For the firms that remain in the industry the long run price PLR equals the original price P k In a torrential downpour the road to your town washes out and you cannot receive more MacWendy s hamburger packaging paper indicating that these hamburgers are the real thing Your supply is sure to run out before the road can be xed How might this change your production decisions over time Thinking in terms of discounting net present value and exhaustible resources some possible plans would be 1 Spread out production and ration the packaging paper so that you spread out the production at a constant quantity per day Pros Expect some business each day while keeping some customers while still employing some of your labor as well Cons The discounted present value of future period pro ts until the bridge is repaired will be less than earlier periods Nonprice rationing mechanisms may kick in if demand exceeds supply e g black markets favoritism etc 2 Produce as normal and then shut down when the packaging paper runs out Pros MacWendy s could take profits eamed at earlier time periods and invest them in an interest bearing asset as opposed to spreading out their pro ts Cons There may be layoffs of labor if other items on the menu do not create sufficient demand Customers could be lost to the regular hamburger market and not retum when the packaging input arrives 3 Incorporate the scarcity costs of the limited packaging Pros MacWendy s would take into account both current marginal costs and the opportunity costs of forgone future production The MacWendy s supply curve would shift above the initial supply curve before the shortage of the input to the extent of those scarcity costs Thus MacWendy s would charge an even higher price and supply in even smaller quantity than before see page 503 of the supplement Cons Consumer would have to be willing to limit their consumption even more Forecasting or estimating the opportunity costs and the length of the time period can be quite complex 189 Suppose the domestic demand and supply for corn intersects at p and suppose further that palso happens to be the world price for corn Since the domestic price is equal to the world price there is no need for this country to either import or export corn Assume throughout that income e ects do not play a significant role in the analysis of the corn market A Suppose the domestic government imposes a price oor 7 that is greater than pand it is able to keep imports of corn from coming into the country a Illustrate the disequilibrium shortage or surplus that results from the imposition of this price oor a V2 On the graph in part a illustrate the deadweight loss in the disequilibrium state P I I l pv N 7 W ml is eq r rrFii Mr l39WlT 1gr Lug Answer This is illustrated in graph a where domestic supply and demand intersect at p and the price oor 7 is imposed above p This results in a disequilibrium surplus with X5 supplied but only XD demanded The greatest possible surplus achievable in this market is abcd e f With just the price oor and no govemment purchasing programwe concluded above that consumer and producer surplus together will be a b c d implying a deadweight loss of e f The deadweight loss is indicated by the two dashed triangles e f from the loss in consumer surplus and the loss in producer surplus relative to the free market equilibrium b In the absence of anything else happening how will an equilibrium be reestablished and what will happen to producer and consumer surplus Note that there could be two methods of reestablishing equilibrium a black market or increased lobbyingadvertising costs Choose one to explain how the equilibrium is reestablished and note the resulting change in consumer surplus in contrast to the scenario in part a Answer Increased AdvertisingLobbying Costs Consumer surplus will fall from abe to a while producer surplus will fall from cd f to d This is because in equilibrium producers will have to exert additional effort ie incur additional costs to compete for the limited number of consumers which will cause the effective price they receive to fall to p The additional marginal cost of effort on the part of producers must be 7 p in order to make point A in graph a the new equilibrium in which the disequilibrium shortage has been eliminated Development of a Black Market An underground economy may result due to the disequilibrium surplus of suppliers willing to sell a quantity that is larger than what is demanded This will most likely result in a price that is cheaper than the legal market price sanctioned by the govemment as corn producers may want to reduce their inventories of corn Many times this black market price or shadow price approaches the equilibrium price and quantity sold in a competitive market p and the respective quantity would be established The deadweight loss may not show up graphically as traditional areas but there is a deadweight loss due to the distributional effects of this rationing mechanism For example there is a probability of getting caught for participating in the black market and expected cost Some consumers and producers may be unwilling to participate and thus the black market does not ensure that consumers with sufficient willingness to pay receive com c Next suppose the government agrees to purchase any corn that domestic producers cannot sell at the price oor The government then plans to turn around and sell the corn it purchases on the world market where its sales are su iciently small to not a ect the world price of corn Illustrate how an equilibrium will now be reestablished and determine the change in domestic consumer and producer surplus from this government program n us E ri1mIm pi urdimsaa olL39sie1 rilihrrLt t in LnT Answer This is illustrated in panel b where the difference between X5 and XD previously labeled a disequilibrium surplus in panel a now becomes the quantity of com purchased by the government In essence the govemment purchasing program causes the equilibrium to settle at B rather than A as in panel a of the graph because producers no longer have an incentive to expend addition effort to attract consumers since the govemment is guaranteeing it will purchase what cannot be sold at the price oor Consumer surplus is then again a since consumers purchase XD at 7 as before producer surplus however now increases to b c d e f g as producers supply X5 at the price 7 d What is the deadweight loss from the price oor with the government purchasing program d V2 If the government sold all the corn on the world market what would have to be true about world price in order to eliminate any deadweight losses Could there be a deadweight surplus Why would this be an unlikely scenario in the real world P F it In n us E ri1mI p uralimsaa olLsleg ri iih i39rM1 in LuT Answer When the price oor is supplemented with the government purchasing program the sum of consumer and producer surplus becomes a b c d e f g However we now need to take into account that the govemment is also having to spend resources in order to buy the surplus at the price oor p and then sell it at a loss at p It will therefore cost e f g h i j to buy the surplus com and when sold at p it will raise revenues of f i j leaving a govemment loss of e g h The total surplus is then the sum of producer and consumer surplus minus the govemment loss which comes to abc d e f ge g habc d f h Compared to the most possible surplus of a bc d e f this implies a deadweight loss of e h indicated by the dashed triangles For the second part of the question to eliminate the deadweight loss from the govemment purchasing program the world price would have to rise suf ciently higher than p such that the extra surplus from the revenues is more than the e h 10 If the world price rises sufficiently high there could be a deadweight surplus where the government buys the com from domestic producers the world price next rises sufficiently high and then they sell it on the world market perhaps eaming a pro t This scenario seems unlikely however because com is a commodity that is traded on many world market exchanges eg Chicago Mercantile Exchange which tend to limit the gains from arbitrage Secondly the situation is also unlikely from the perspective of what the goal of a price oor is to artificially raise prices above a free market equilibrium If the world price rose above the price oor the price oor policy would be nonbinding and there would be no need to continue the price oor policy as domestic producers could receive a higher price from the world market e In implementing the purchasing program the government notices that it is not very good at getting corn to the world market and all of it spoils before it can be sold How does the deadweight loss from the program change depending on how successful the government is at selling the corn on the world market Answer The govemment loss now becomes e f g h i j which gives us total surplus of abc d e f g e f g hi j abc d h i j Compared to the maximum possible surplus of abc d e f this gives us a deadweight loss of e fhi j f Would either consumers or producers favor the price oor on corn without any additional government programs Answer As illustrated in part b of the question both producers and consumers lose surplus under the price oor policy without additional govemment programs Thus neither would favor such a program g Who would favor the price oor combined with the government purchasing program Does their support depend on whether the government succeeds in selling the surplus corn Why might they succeed in the political process Answer As illustrated in part c of the question producers gain substantial amounts of surplus when the govemment program is added to the price oor and the amount of surplus they gain does not depend on what the govemment does with the surplus com that was purchased Thus producers would favor the price oor when combined with the govemment purchasing program and they might succeed in the political process because they are a relatively small group compared to consumers and tax payers experiencing concentrated bene ts ll This gives them an incentive to expend resources to lobby for such a program and the diffuse nature of the costs spread over many consumers and taxpayers makes it unlikely that those who lose from the program will politically organize against it h How does the deadweight loss from the price oor change with the price elasticity of demand Include 2 graphs one where demand is more elastic amp one where supply is more elastic Answer It decreases as demand becomes more inelastic Please see the following graphs Price Flour wit39 E ltttti S ttrJp 1 cl fttmlttstic Dew39rtmrl PTffEFlr 1 FiiJ fIlJ39 fttm39rt3tic t57rtttJ1 amp Elmttic iEtttmrl p7n la5quot F 39 51 0 n m 39t1 t4 m 3 Sumlm K Lonnl 3 psllrljmx frfrn h V2 In which of these scenarios is there likely more support for the price oor From whom There is more support by producers for a price oor for the scenario with elastic supply and inelastic demand Deadweight loss is relatively smaller In addition the deadweight loss falls disproportionately on consumers than on producers In addition producers incur a relatively smaller lobbyingadvertising cost to compete for limited demand i How does this policy a ect the number of firms in the industry and their profits when supply is elastic and demand is inelastic What about when supply is inelastic and demand elastic When supply is elastic and demand is inelastic the number of firms in the industry may be large to begin with and the price oor would increase the number of firms A sizable amount of the consumer surplus is transferred to producer surplus with relatively small lobbyingadvertising costs resulting in increased pro ts 12 For inelastic supply and elastic demand the number of rms would probably decrease due to relatively large lobbying advertising costs and demand having perhaps many close substitutes that consumers could switch to In addition the surplus is relatively smaller and pro ts lower These answers are ampli ed if a govemment purchasing program is in place which would yield higher quantities of revenue to com producers after the govemment purchases the surplus l3
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