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Homework answers / question archive / Problem Set #3 – ECON 100B, Spring Quarter 2021 Name:_____________________ Due: May 5, 2021 at 11:59pm
Problem Set #3 – ECON 100B, Spring Quarter 2021 Name:_____________________ Due: May 5, 2021 at 11:59pm. ------------------------------------------------------------------------------------------------------------------------------Note: In order to receive credit, you must show your work. 1. Suppose there are two players in a game, Player A can choose top or bottom and player B can choose left or right. If the players play simultaneously in this game, is there a Nash equilibrium? If so, what is it? Player B Player A Top Bottom Left 0,0 1,0 Right 0,-1 -1,3 2. Suppose there is a monopolist in a market (incumbent). A competitor is considering entering the market (entrant). The incumbent has an opportunity to fight (compete) or not fight (share the market). The payoffs are given in the following diagram: What is the Nash equilibrium in this situation? 1 3. Alice and Betsy are playing a game in which each can play either of two strategies, leave or stay, simultaneously. Betsy Leave Stay Leave $300 , $??? $D , $C Alice Stay $C , $D $600 , $600 If you know that a Nash equilibrium exists where both players play ‘leave’, which of the following statements is correct? Briefly explain. a. b. c. d. Never, since $600 > $300. Whenever D < $600. When D > C and C > $300. Whenever $300 > C. 4. Fred’s utility function is u(I) = I (where I represents income). Suppose Fred’s discount rate is δ = 0.95. If Fred considers $773.78 today the same as $1000 five years from now, are his preferences consistent with exponential discounting, hyperbolic discounting, or neither? Briefly explain. 5. Suppose you and a complete stranger must split $100 in even dollar increments. You propose a split (you must propose at least $1), and the stranger with whom you are splitting the $100 either accepts or rejects. If she rejects, you both receive nothing. a. What is the Nash equilibrium for this game? b. The Nash equilibrium solution is not frequently observed in practice. Explain why. 2 Problem Set #1 – ECON 100B, Spring Quarter 2021 Name:__ANSWER KEY___________ Due: April 14, 2021 at 11:00pm ------------------------------------------------------------------------------------------------------------------------------Note: In order to receive credit, you must show your work. 1) A monopolist has the total cost function c(y) = 8y + F. The inverse demand function is p(y) = 80 – 6y. If the firm is losing $800 when it is required to sell the quantity demanded at a price that is equal to its marginal costs, what are its fixed costs, F? 2) Suppose a firm in a perfectly competitive environment has the following cost function: ?(?) = ??? + ? a) If profits are 200 when price is 60, what is F equal to? b) What are the firm’s profits as a function of only p and F? 1 3) In a market where there is one firm (a monopoly) the inverse demand function is given by: p(y) = 240 – y The cost function for this monopolist is: ?(?) = ???? + ?. ??? a) What is the monopolist’s profit maximizing level of output? What price will the monopolist charge for this output? What are the monopolist’s profits at this point? Explain your answer numerically and with the aid of a graph. b) Suppose the government wants to decrease the deadweight loss in this market and makes the monopolist set price equal to marginal cost. How much will the monopolist produce in this case? What will the monopolist’s profits be? 2 4) Suppose Ford sells cars in Canada and the US. The inverse demand for cars in Canada is: p1(y1) = 20,000 – 20y1 The inverse demand for cars in the US is: p2(y2) = 25,000 – 10y2 The cost for Ford of producing cars is given by: ?(?) = ???, ??? + ???? a) How many cars will Ford sell in Canada and at what price? How many cars will Ford sell in the US and at what price? b) What will Ford’s profits be? 3
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