solve final questions
Microsoft Word - final.136.2021.docx Economics136 Name FinalExam Spring2021 FinalExam:Answers 120pointspossible.Eachquestionisweightedequally. Choose5outof7questions. 1.LyingandTruthTelling Thegovernmentiscontemplatingpavingaroadthatleadstotwofarmsoutinthe countryside.Mr.HatfieldownsthefirstfarmandMr.McCoyownsthesecondfarm alongtheroad.(Allfiguresbelowareinhundredsofthousandsofdollars.)Thecost ofpavingtheroadis$200,andthegovernmentwilldecidetopavetheroadonlyif thetotalstatedwillingnesstopayofbothindividuals, ,isatleast$200.The valuetoHatfieldofpavingtheroadis andthevaluetoMcCoyis . Beingsimplefolk,HatfieldandMcCoywilleacheitherlieandstateawillingnessto payofzeroortellthetruth,whichforHatfieldinvolves andforMcCoymeans .Thegovernmentinsiststhatiftheroadispaved,eachofthemmustpay one-halfofhisstatedwillingnesstopay(tohelpfinancetheproject).Assumethe twopartiessimultaneouslystatetheirwillingnesstopayinseparatesealed envelopes. A.Writedownthestrategic-formmatrixandthemonetarypayoffsinthematrix cells. B.Findanyandallpure-strategyNashequilibriatothisgame.IsthereaPrisoner’s Dilemmaproblem?Pleaseexplain.Isthereanydifficultythepartieswillhavein achievingaNashequilibrium?Pleaseexplain. C.SupposeMcCoybelievesthatHatfieldgenerallyliesabouteverything,except whenofferedabribethatmakestruth-tellingmorelucrative.Howmuchwould McCoyneedtopayHatfieldtotellthetruth?Canthebribemakebothpartiesbetter off?Pleaseexplain. w 1 + w 2 v 1 =160 v 2 = 240 w 1 = v 1 w 2 = v 2 2 2.RiskAnalysis Aninvestorcomestoyouforsomeadvice.Shehastheutilityfunction , whereyisincomeandisconsideringachoicebetweentwoinvestments:1year TreasuryBillsorthepurchaseofTeslastock,averyriskyinvestmentindeed! TheT-Billgeneratesacertainreturnof$3,600whilethepurchaseofTeslastockwill return$10,000withprobability.5and$0withprobability.5. A.Whichinvestmentshouldshetake?Pleaseexplain. B.WhatisthecertaintyequivalentreturnforthisinvestorifshebuystheTesla stock?Inwordsandagraph,interpretyouranswer. U = y 1/2 3 3.InputChoiceandProductivity Afirmproducescoffeepotsaccordingtotheproductionfunction whereKandLrepresentthedailyamountsofcapitalandlaboremployedbythe firm.Thedailyrentalrateforaunitofcapitalis$625,andthewagerateforlabor perdayis$100. A.Ifthefirmwishestominimizethetotalcostofproducing800coffeepotsperday, howmuchlaborandcapitalshoulditemploydaily?Whatistheminimumdaily totalcostforproducing800coffeepots?Whatistheaveragecostofproducinga coffeepot?Pleaseexplain. B.Computethefirm'saverageproductoflaboratthesolutionyouobtainedinpart (A)anditsmarginalproductoflabor.Whichisgreater?Explainintuitively. Q = 2KL 4 4. Entry Game An entrepreneur is trying to decide whether to start a dry cleaning store (firm #1) in a town already served by a single dry cleaner (firm #2). Firm #1 is uncertain about whether the economy will be in recession or not, which will affect the demand for dry cleaning services and hence its profits from entering the market. Firm #1 is also concerned about whether firm #2 will respond to entry with a price war or by maintaining its high price. Both firms believe that the probability of recession is .3 and the probability of no recession is .7. The timing of their interactions is as follows: Firm #1 first decides whether or not to enter the market. Then, the state of the economy is revealed to be either in recession or not in recession. Finally, firm #2 responds with either high price or low price. Under the circumstances of recession and no recession, the payoffs for firms 1 & 2 are in $ millions: Recession Firm #2 High Price Low Price Firm #1 Enter 30, 40 -120, 50 No Enter 0, 240 0, -10 No Recession Firm #2 High Price Low Price Firm #1 Enter 80, 100 -80, 80 No Enter 0, 300 0, 50 A. On the next page, sketch the game tree showing decision nodes, chance nodes, and the final payoffs for both firms. Find the Subgame Perfect Nash Equilibrium. What are each firm’s strategies in this equilibrium? What are the expected profits of both firms in the equilibrium? Please show and explain. B. What is the value of perfect information to firm #1 concerning whether or not a recession will occur? Please compute. What is the value of perfect information to firm #2? Please explain. 5 6 5. Bankruptcy Game Suppose Leveraged Enterprises has assets valued at $16 million. It also has two creditors, Sympathy Inc. & Empathy Ltd.; and Leveraged owes $10 million to each creditor. (Notice that Leveraged is insolvent because its assets are valued at less than its liabilities.) If the company declares bankruptcy, then its assets are liquidated; and Sympathy & Empathy each get only partial repayment. Hence, each creditor has an incentive to try to recover its own loan by conducting a “fire sale” of Leveraged assets that will yield $12 million. (Call this action the “grab.”) Suppose that each creditor moves simultaneously in deciding whether to “grab” (i.e., try to recover its loan immediately) or to “refrain” (i.e., wait until later to recover its loan). If both creditors grab, then the company goes into immediate bankruptcy and the proceeds of the fire sale are split between the two creditors, each receiving $6 million. If only one creditor tries to grab the firm’s assets, then it is successful in recovering its entire loan; and the remaining $2 million is given to the other creditor. If both creditors refrain, then the insolvent company is sold at a later date for $15 million, and each creditor gets $7.5 million. A. Place the creditors’ payoffs in a strategic-form matrix showing how the payoffs vary with the strategies chosen. Find the Nash equilibrium in pure strategies. Please explain. Is this Nash Equilibrium best described as arising from a coordination problem or a Prisoner’s Dilemma? Please explain. EmpathyLtd. Strategy grab refrain SympathyInc. grab refrain B. Now suppose that it costs a creditor $3 million to grab. Find the Nash Equilibria in pure strategies. Please explain. Are these Nash equilibria best described as arising from a coordination problem or a Prisoner’s Dilemma? Please explain. C. Now instead of moving simultaneously in part B suppose that Sympathy Inc. moves first by announcing its intention either to grab or to refrain. What is the Nash equilibrium in this case? Please explain. 7 6. Two-Part Tariff Suppose Tiger Woods’ annual demand for playing rounds of golf at the Sandstorm Golf Club (SGC) is . The marginal cost of having him play a round of golf is $2. A. First, assume that the SGC charges a uniform price per round of golf. What is the profit- maximizing price for SGC to charge Tiger Woods? How many rounds of golf will he play annually? Please show and explain. B. Now suppose that SGC offers Tiger a pricing schedule called a two-part tariff whereby Tiger pays an annual membership fee E and a price per unit P such that his total payment is T = E + P Q, if Q > 0 and zero otherwise. Compute SGC’s profit-maximizing output Q, membership fee E, and price per unit P. C. Which scheme (A) or (B), will Tiger prefer? Which scheme will SGC prefer? Show and explain. Q = 200 − P 8 7. Regression Analysis The director of marketing at Vanguard Corporation believes that sales of the company’s Bright Side laundry detergent are related to Vanguard’s advertising expenditures and the advertising expenditures of the three biggest rival detergents . Using data from 36 quarters, the following regression estimates were obtained: where standard errors are shown in parentheses, and . A. Do Vanguard’s advertising expenditures have a statistically significant effect on its sales? What about the advertising expenditures of rivals? Please explain. B. What fraction of the total variation in sales of Bright Side remains unexplained by the regression? What other explanatory variable might be added to this equation? Please justify. C. What is the expected level of sales if Vanguard spends $40,000 on advertising in a quarter while its three rivals spend $100,000 over the same time period? Please explain. D. Suppose the Durbin-Watson statistic is 0.5, indicating positive serial correlation. What sort of problem does this indicate with the regression estimates? How would you alter your answer to part (A)? What modifications would you try to correct the problem? (S) (A) (B) Ŝ = 175086 (63821) + .855 (.325) A − .284 (.247) B R 2 = .26