Consider two firms who are engaged in a Research and Development (R&D) "con-test". Both firms simultaneously expend resources to try to win the contest (whichmay mean developing a superior product or developing a product before the com-petitor). If the two firms expend bị and b2, respectively, on R&D, the probabilitythat firm 1 wins the contest isif b1 = b2 =0BE otherwiseP1(b1, b2) =where r is some exogenous constant, r E (0, 0). If firm 1 wins the contest, it willsubsequently earn revenue of 1 (not including the cost of R&D, b1). If firm 1loses the contest, it will earn zero revenue, and thus lose bj in total. Hence, firml's expected profit is n'(b1,b2) = p1(b1,b2) - b1. Everything is symmetric forfirm 2.i. How does p1(b1,0) depend on b1? Is it an equilibrium for both firms tospend nothing on R&D (b1 = b2 = 0)? Prove and explain your answer. Forwhich values of r is n' (b,b2) concave in b1 when b2 > 0?ii. Consider the possibility of a symmetric pure-strategy equilibrium. Assum-ing such an equilibrium exists, derive it and prove it is unique. Is the equi-librium efficient? Under what conditions onr do a symmetric pure-strategyequilibrium exists? Prove and explain your answers.iii. Assume r = 1 and that firm 2 observes firm 1's expenditures before it hasto make its own investment. Derive the subgame perfect Nash equilibrium.How does it differ from the equilibrium in the simultaneous-move game? Isthere a first-mover advantage in this game? Does firm 2 prefer the sequentialgame or the simultaneous game?iv. Assume r = 2. Does firm 2 have a unique best response to all bi E (0, 00)?Is there an equilibrium of the sequential game in which firm 1 invests morethan in the simultaneous-move game? If firm 1 invests less than insimultaneous game, does firm 2 invest more or less than firm 1? Describean equilibrium of the sequantial game and compare it to the equilibriumof the simultanous game. Does firm 1 prefer the sequential game or thesimultaneous game? How about firm 2? Prove and explain your answers.

When the equilibrium state of the perfect competition is being considered, it is not applicable in…

Answered: equilibrium

Business

Economics

equilibrium

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Ana and Ivan each individually and simultaneously decide whether to spend the evening at a play or a concert. Ana prefers to attend the concert twice as much without Ivan than to attend the play without him, and she prefers this three times more than being in the same place with Ivan (and at that point, she doesn't care where they are). Ivan prefers being in the same place with Ana twice as much as being at the play without her, and he prefers this four times more than being without Ana at the concert. Both have von Neumann-Morgenstern (vNM) preferences. With what probability will Ivan choose to attend the concert in Nashe's equilibrium?
Suppose you observe a person's answer to two decision problems. Problem 1: You are offered $40 today. What is the minimum amount x you demand one month from today in order to be willing to give up the $40 now? Answer: x = 52. Problem 2: Your are offered $40 today. What is the minimum amount x you demand one year from today in order to be willing to give up the $40 now? Answer: $60. 1. Demonstrate that the rational model of time preferences is violated for this choice pattern. 2. Derive this individual's B and d for the hyperbolic time discounting model. 3. Suppose the utility you get from eating ice cream now is 10 utils. But you pay a cost of -4 utils per hour for the next 4 hours, because it gives you indigestion and makes you feel lethargic. If your hourly B and d for this problem are B = .6 and d = .9, ... 1. What is the total discounted utility of eating ice cream now? 2. What is your total discounted utility now of planning to eat ice cream after lunch tomorrow? 3. Do you eat ice…
Tom, Dick, and Harry live in the same apartment building in downtown Los Angeles. Tom and Dick work at local auto parts stores, and each of them has an income of y dollars per week. Harry is less fortunate. He used to have a good job at the LAPD, but his penchant for firing large caliber weapons in crowded public places led to his dismissal. He currently has no income. Tom and Dick (who are originally from Texas) firmly believe in a man’s right to draw his gun in the defence of just about anything, and are happy to financially support Harry. Tom gives Harry zT dollars each week, and Dick gives Harry zD dollars each week Tom’s utility UT depends upon the dollar value of his own weekly consumption, cT , and of Harry’s weekly consumption, cH : Likewise, Dick’s utility UD depends upon the dollar value of his own weekly consumption, cD, and of Harry’s weekly consumption: Harry spends all of the money that he receives from Tom and Dick. Tom and Dick spend…
In an eight-hour day, Andy can produce either 8 loaves of bread or 24 kilograms of butter. In an eight-hour day, Rolfe can produce either 8 loaves of bread or 8 kilograms of butter. At what price will trade happen?
On Sundays, people in Los Angeles consider a boat to Catalina Island to spend the day on the beach there. The utility that a person gets from visiting Catalina is 1-[n/10] – p , where n is the number of visitors on the island and p is the price of round-trip transportation (by boat). (Note that a visitor obtains more satisfaction if there are fewer other visitors on the island). The utility of staying home is zero. In equilibrium, how many people visit the island on a given Sunday? ( Your answer should depend on p.)
Jia is considering whether to go out to dinner at a restaurant with her friend. The meal is expected to cost $40, Jia typically leaves a 20% tip, and an Uber will cost $5 each way. Jia values the restaurant meal at $25. Jia enjoys her friend s company and is willing to pay $30 just to spend an evening with her.
Consider the problem of an individual that has Y dollars to spend on consuming over two periods. Let c, denote the amount of consumption that the individual would like to purchase in period 1 and c2 denote the amount of consumption that the individual would like to consume in period 2. The individual begins period 1 with Y dollars and can purchase c1 units of the consumption good at a price P and can save any unspent wealth. Use sı to denote the amount of savings the individual chooses to hold at the end of period 1. Any wealth that is saved earns interest at rate r so that the amount of wealth the individual has at his/her disposal to purchase consumption goods in period 2 is (1+r)s1. This principal and interest on savings is used to finance period 2 consumption. Again, for simplicity, we can assume that it costs P2 dollars to buy a unit of the consumption good in period 2. 2 The individual's total happiness is measured by the sum of period utility across time, u(cı) + u(c2). Let u(c)…
Van has plans to go to an opera and already has a $100 nonrefundable, nonexchangeable, and nontransferable ticket. Now Amy, whom Van has wanted to date for a long time, asks him to a party. Van would prefer to go to the party with Amy and forgo the opera, but he doesn't want to waste the $100 he spent on the opera ticket. From the perspective of an economist, if Van decides to go to the party with Amy, what has he just done? 1. Incorrectly allowed a sunk cost to influence his decision 2. Made a choice that was not optimal 3 Correctly ignored a sunk cost Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
social preferences are not really preferences, and unselfish behavior is really motivated by the desire to follow rules and conventions with respect to what is fair. Is this interpretation correct?
Uncertain what would be the correct answer
Smith and Jones are stranded on a desert island. Each has in her possession some slices of ham (H) and cheese (C). Smith prefers to consume ham and cheese in the fixed proportion of 2 slices of cheese to each slice of ham. Her utility function is given by Us = min(10H, 5C). Jones, on the other hand, regards ham and cheese as substitutes – she is always willing to trade 3 slices of ham for 4 slices of cheese, and her utility function is given by UJ = 4H + 3C. Total endowments are 100 slices of ham and 200 slices of cheese. a. Draw the Edgeworth Box diagram for all possible exchanges in this situation. What is the contract curve for this exchange economy? b. Suppose Smith’s initial endowment is 40 slices of ham and 80 slices of cheese (Jones has the remaining ham and cheese as her initial endowment). What mutually beneficial trades are possible in this economy and what utility levels will Smith and Jones enjoy from such trades? c. Now imagine a new endowment in which Smith has 60 slices…
Several local golf tournaments are coming up and Tommy needs to purchase golf balls in preparation. He has set a $150 budget and will choose golf balls that will give him as much utility as possible. A local sporting goods store sells a box of golf balls at a retail price of $30 and Tommy purchases 2 boxes. A few buddies tell Tommy about an online store that offers boxes of golf balls at a discounted price of $21, while all other prices remain the same, and Tommy decides to purchase 3 additional boxes of golf balls to keep on hand. Given this information, plot Tommy's demand curve for golf balls. Provide your answer below: Price of Golf Ball Boxes Online Store (4,$22) 20 Local Store (1,$10) —101 Quantity of Golf Ball Boxes