Consider a monopolist selling a product with inverse demand of Pp-12-Q. The firmcurrently has production costs of C(q)=5+6Q. The firm has the option of attemptingto develop a new technology that would lower production costs to C(q)=5+2Q.Research and development costs are $4 if undertaken and must be incurredregardless of whether or not the new technology is "successful" or a "failure." Thismeans that in case of failure, the firm still needs to produce with C(q)=5+6Q butincurs $4 in sunk costs. If the firm attempts to develop the new technology, theinnovation will be successful with probability p=3/8. Throughout your analysis,restrict attention to the profit/loss of the firm in only the current period (i.e., assumethat the firm will not be operating in any future period).Assume that the monopolist is risk averse, what would be the expected utility ofperfect information [assuming that U(Payoff)=sqrt(Payoff)]?2.753.03.253.5O O O

The profit of the firm if it new technology is a failure is, ?0 = TR - TC = PD*Q - (C(q) + sunk…

Answered: Assume that the monopolist is risk…

Assume that the monopolist is risk averse, what would be the expected utility of perfect information [assuming that U(Payoff)=sqrt(Payoff)]? O 2.75 3.0 3.25 3.5

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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P, = 100-Q1 - BQ2 P2= 100- BQ1-Q2 Q1 Q, 5-40. BR;: = 25– BR2: Q2 = 25– 4 (Product Differentiation Problem) In the case when beta=1, solve for Nash equilibrium and profits. O Q', = 100, Firm 1 profits = 2800 Q'2 = 100, Firm 2 profits = 2800 O Q, = 100, Firm 1 profits = 0 Q'2 = 100, Firm 2 profits = 0 O Q', = 50, Firm 1 profits = 280 Q2= 50, Firm 2 profits = 280 O Q', = 25, Firm 1 profits = 1200 Q'2= 25, Firm 2 profits = 1200
1. For what range of interest rates could the collusive outcome be supported if the following game is infinitely repeated? A C X 0,110 y 50, 50 a) r > 50% b) r > 10% c) none of the above d) r < 20% e) r < 500% B d 60, 60 110,0
4. An auctioneer holds a second-price auction for two bidders, Ann (A) and Bonnie (B), who have independent private values of the good 0, and 0g If a bidder wins, her payoff is her value 0 minus the price she pays, and if she loses, her payoff is 0. The values are independently and identically distributed, but otherwise you don't need to know the specific distributions to solve the problem. Ann and Bonnie's respective strategies are to bid some value b0), that is, bid given their privately-known value (type). e. Suppose the good had one true value for both bidders equal to the average of 0, and e, (signals that are still i.i.d.); hence, the good's true value has a common component. Suppose Ann knows Bonnie is going to bid her own evaluation 0, no matter what, but like normal, Ann doesn't know 0g. Explain why bidding 0, is now a strictly dominated strategy for Ann.
4. An auctioneer holds a second-price auction for two bidders, Ann (A) and Bonnie (B), who have independent private values of the good 0, and e, If a bidder wins, her payoff is her value 0 minus the price she pays, and if she loses, her payoff is 0. The values are independently and identically distributed, but otherwise you don't need to know the specific distributions to solve the problem. Ann and Bonnie's respective strategies are to bid some value b (0.). that is, bid given their privately-known value (type). a. Explain what a second price auction is, who wins given some pair of bids b, and bg. and what the winner pays. b. Why is a strategy where Ann bids above her own value 0, weakly dominated by a strategy where she bids her value? c. Why is a strategy where Ann bids below her own value e, weakly dominated by a A strategy where she bids her value? d. Applying the ideas from (b) and (c) to both Ann and Bonnie, what is the Weakly Dominant Strategy Equilibrium for this game?
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For the infinitely repeated game based on the stage game as shown, consider a symmetric strategy profile in which a player initially chooses x and continues to choose x as long as no player has ever chosen y; if y is ever chosen, then a player chooses z thereafter. Derive a condition on the discount factor for this strategy profile to be a SPNE.
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Repeated Game Consider the game below, which is infinitely repeated at t = 1,2, .... Both players discount the future at rate d E (0, 1). The stage game is C C 5,5 0,6 D 6,0 1,1 1. The following three questions are about "Grim Trigger" strategies. (a) Describe the "Grim Trigger" strategy profile of this game. (b) Draw the finite automata representation of this strategy profile. (c) Find the lowest value of 8 for this strategy profile to form a subgame perfect equilibrium. 2. Suppose that the players play (C,C) in period t = 1, 3, 5, ... and plays (D,D) in period t = 2,4, 6, ... Compute the discounted payoff of each player. 3. Find a subgame perfect equilibrium such that, on the equilibrium path, (D,D) is played at periods t = 1, 3, 5, ..., and (C,C) is played at periods t = 2, 4, 6, ... Write down the finite automata representation for the strategy profile you proposed. Find the lowest value of d for the profile to form a subgame perfect equilibrium.
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H10.
3. Repeated Game Consider the game in which the stage game depicted below is infinitely repeated and in which both players discount future payoffs with discount factor 6 € [0, 1]. Player 1 E S Player 2 E 3,3 4, -1 S -1.4 1,1 (a) Suppose that both players play the tit-for-tat strategy. This strategy is characterized by exerting effort (playing E) in the first round. Then in future rounds, a player copies the action chosen by his opponent in the previous period (i.e if Player 2 shirks (plays S) in period 2, then Player 1 plays S in period 3). Then, for what values of d can tit-for-tat be supported on the equilibrium path of play? (b) Suppose that both players play the perfect tit-for-tat strategy. This strategy is characterized by exerting effort (playing E) in the first round. Then in future rounds, a player plays E unless the actions are disagreed in the previous period. Then, for what values of d can perfect tit-for-tat be supported on the equilibrium path of play?