Consider a market dominated by two firms with identical cost functions C(q) = c*q for some constant “c”, both facing inverse demand function P(Q) = a – b*Q. Firms are in Bertrand competition by simultaneously setting prices (i.e., static, one-shot, simultaneous move game). If prices offers are equal, the two firms split the market.Suppose firms can pick only one of two prices: a high price or a low price. Construct an example with a 2 X 2 Normal Form payoff matrix using the profit functions of each firm as payoffs, and show that the low price is the Nash equilibrium.Now suppose firms can pick any price. Construct an argument to show that any pair of prices offered by the firms in which p>c is NOT a Nash equilibrium.Suppose again that firms can pick only one of two prices: high or low, but now suppose they have committed to a price-match guarantee. Construct another 2 X 2 Normal Form payoff matrix using the profit functions of each firm, and show whether high or low price (or both) is an equilibrium. (Hint: this is slightly tricky. Keep in mind the actions are now (high or match, low or match) rather than simply (high or low). So if Firm 1 chooses high and the other chooses low, Firm 1’s payoff is the low price payoff.Now suppose firms can pick any price. Can any pair of price offers from the two firms be a Nash equilibrium as long as the price offers are equal to each other? Construct an argument for yes or no.

In Bertrand competition firms compete in prices rather than quantities . Cost function : C(q) = c*q…

Answered: Consider a market dominated by two…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.5P

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Consider a market dominated by two firms with identical cost functions C(q) = c*q for some constant “c”, both facing inverse demand function P(Q) = a – b*Q. Firms are in Bertrand competition by simultaneously setting prices (i.e., static, one-shot, simultaneous move game). If prices offers are equal, the two firms split the market.
1. Suppose firms can pick only one of two prices: a high price or a low price. Construct an example with a 2 X 2 Normal Form payoff matrix using the profit functions of each firm as payoffs, and show that the low price is the Nash equilibrium.
2. Now suppose firms can pick any price. Construct an argument to show that any pair of prices offered by the firms in which p>c is NOT a Nash equilibrium.
3. Suppose again that firms can pick only one of two prices: high or low, but now suppose they have committed to a price-match guarantee. Construct another 2 X 2 Normal Form payoff matrix using the profit functions of each firm, and show whether high or low price (or both) is an equilibrium. (Hint: this is slightly tricky. Keep in mind the actions are now (high or match, low or match) rather than simply (high or low). So if Firm 1 chooses high and the other chooses low, Firm 1’s payoff is the low price payoff.
4. Now suppose firms can pick any price. Can any pair of price offers from the two firms be a Nash equilibrium as long as the price offers are equal to each other? Construct an argument for yes or no.

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