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In: Economics

An industry contains two firms, one whose cost function is C(y) = 30y and another whose...

An industry contains two firms, one whose cost function is C(y) = 30y and another whose cost function is C(y) = y2. The inverse demand function for the firms' output is p = 120 -Q, where Q is the total output. What are the firms' outputs in a Nash equilibrium of Cournot's model? Graph the best response functions for Firm 1 and Firm 2.

Solutions

Expert Solution

The inverse demand is given to be , and for , we have , where q1 and q2 are quantities of the respective firms.

Firm 1 have the cost function , and its marginal cost would be . The total revenue of firm 1 would be , and the marginal revenue would be . The profit maximization would occur where the MC is equal to MR, ie or or . This is the BR function of firm 1.

Firm 2 have the cost function , and its marginal cost would be . The total revenue of firm 2 would be . and the marginal revenue would be . The profit maximization would occur where the MC is equal to MR, ie or or .

The cournout (nash) equilibrium would occur where the BR function intersects. Putting the first BR function into the second one, we have or or or , and since , we have . These are the required equilibrium output.

The graph is as below.

Rahul Sunny answered 2 years ago
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