Consider a market with an Incumbent firm, Firm I, and a potential entrant, Firm E. Firm...
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Consider a market with an Incumbent firm, Firm I, and a potential entrant, Firm E. Firm I's cost function is Cr(Q) = cr* Q where c1 € {4, 32} and Firm E's cost function is CE(Q) = 8* Q. Values of c, are equally likely and cost functions, possible values of cy and probabilities are common knowledge. In the market, price is determined by the price function P=64 - Q where Q the total supply in the market. They play a two-period game. In the first period, nature picks a marginal cost for Incumbent firm, Firm I observes that value cy and chooses a quantity supply Q {16, 30} and make some profit. At the end of this period Firm E observes chosen quantity but not the marginal cost and decides either to enter or to stay out. If Firm E chooses to enter the market then pays the cost of $1000, enters the market and learns the true value of cj. In the second period if there are two firms in the market, first Firm I chooses its quantity supply, Q7, next Firm E observes that and chooses its quantity Q (they play a Stackelberg Game), otherwise Firm I chooses a quantity supply Q and make some profit. The payoffs are total net profits they earn at the end of the second period, i.e. up = T (C₁, Q) + (C1, Q7, QE), UE(In) = T² (Q, QE) - 200, up (Out) = 0. (a) What would Firm I choose as Q if Firm E stays out? Find two values for Firm I (one for high cost and one for low cost). (b) What would be the best response function of Firm E, Q (Q) if Firm E enters? 1 (c) What would Firm I choose as Q2 in subgames where Firm E enters (Backward induction strategy)? What about Firm E? Find two values for each firm (one for high cost Firm I and one for low cost Firm I). (d) Given that they choose Q1,Q you found in part a,b and c in the second period, draw a reduced game for the first period. (e) Find the set of pure strategy Perfect Bayesian Equilibrium such that they choose Q1, Q you found in part a,b and c in the second period. Consider a market with an Incumbent firm, Firm I, and a potential entrant, Firm E. Firm I's cost function is Cr(Q) = cr* Q where c1 € {4, 32} and Firm E's cost function is CE(Q) = 8* Q. Values of c, are equally likely and cost functions, possible values of cy and probabilities are common knowledge. In the market, price is determined by the price function P=64 - Q where Q the total supply in the market. They play a two-period game. In the first period, nature picks a marginal cost for Incumbent firm, Firm I observes that value cy and chooses a quantity supply Q {16, 30} and make some profit. At the end of this period Firm E observes chosen quantity but not the marginal cost and decides either to enter or to stay out. If Firm E chooses to enter the market then pays the cost of $1000, enters the market and learns the true value of cj. In the second period if there are two firms in the market, first Firm I chooses its quantity supply, Q7, next Firm E observes that and chooses its quantity Q (they play a Stackelberg Game), otherwise Firm I chooses a quantity supply Q and make some profit. The payoffs are total net profits they earn at the end of the second period, i.e. up = T (C₁, Q) + (C1, Q7, QE), UE(In) = T² (Q, QE) - 200, up (Out) = 0. (a) What would Firm I choose as Q if Firm E stays out? Find two values for Firm I (one for high cost and one for low cost). (b) What would be the best response function of Firm E, Q (Q) if Firm E enters? 1 (c) What would Firm I choose as Q2 in subgames where Firm E enters (Backward induction strategy)? What about Firm E? Find two values for each firm (one for high cost Firm I and one for low cost Firm I). (d) Given that they choose Q1,Q you found in part a,b and c in the second period, draw a reduced game for the first period. (e) Find the set of pure strategy Perfect Bayesian Equilibrium such that they choose Q1, Q you found in part a,b and c in the second period.
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Answer rating: 100% (QA)
a If Firm E stays out then Firm I will choose the quantity Q that maximizes its profit Firm Is profit function is given by IQ P CIQ where P 64 Q is the price in the market Substituting P into the prof... View the full answer
Related Book For
Managerial Economics and Strategy
ISBN: 978-0321566447
1st edition
Authors: Jeffrey M. Perloff, James A. Brander
Posted Date:
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