Consider a quantity-setting duopoly. The two firms are Alpha, Ltd. and Beta, Inc. The demand schedule in this market is: p Qd 180 150 155 175 130 200 Each firm has a constant marginal cost of 30 per unit. Suppose each firm can choose to produce either 75 units or 100 units. Firms make their quantity choices simultaneously and the market price is whatever it needs to be to sell the total output in the market. (a) Draw up the normal form game matrix, showing the players, strategies, and payoffs. Show your work determining the profits in each box in the matrix. (b) Determine the Nash equilibrium of this game. (c) Suppose the firms were able to come to an agreement to make more profit. What would this agreement be?
Consider a quantity-setting duopoly. The two firms are Alpha, Ltd. and Beta, Inc. The demand schedule in this market is: p Qd 180 150 155 175 130 200 Each firm has a constant marginal cost of 30 per unit. Suppose each firm can choose to produce either 75 units or 100 units. Firms make their quantity choices simultaneously and the market price is whatever it needs to be to sell the total output in the market. (a) Draw up the normal form game matrix, showing the players, strategies, and payoffs. Show your work determining the profits in each box in the matrix. (b) Determine the Nash equilibrium of this game. (c) Suppose the firms were able to come to an agreement to make more profit. What would this agreement be?
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.3P
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Consider a quantity-setting duopoly. The two firms are Alpha, Ltd. and Beta, Inc. The demand schedule
in this market is:
p Qd
180 150
155 175
130 200
Each firm has a constant marginal cost of 30 per unit. Suppose each firm can choose to produce either 75
units or 100 units. Firms make their quantity choices simultaneously and the market price is whatever it
needs to be to sell the total output in the market.
(a) Draw up the normal form game matrix, showing the players, strategies, and payoffs. Show your work
determining the profits in each box in the matrix.
(b) Determine the Nash equilibrium of this game.
(c) Suppose the firms were able to come to an agreement to make more profit. What would this agreement
be?
(d) Explain how the government might respond to such an agreement and why.
in this market is:
p Qd
180 150
155 175
130 200
Each firm has a constant marginal cost of 30 per unit. Suppose each firm can choose to produce either 75
units or 100 units. Firms make their quantity choices simultaneously and the market price is whatever it
needs to be to sell the total output in the market.
(a) Draw up the normal form game matrix, showing the players, strategies, and payoffs. Show your work
determining the profits in each box in the matrix.
(b) Determine the Nash equilibrium of this game.
(c) Suppose the firms were able to come to an agreement to make more profit. What would this agreement
be?
(d) Explain how the government might respond to such an agreement and why.
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