In equilibrium, the firms will produce outputs such that the market price is equal to the marginal cost of production. The market price is given by the inverse demand function, P = 40 - (1/3)Q. The marginal cost of production for the first firm is MC1 = 20 and for the second firm is MC2 = 5 + 2y2.
Setting MC1 = MC2 = P, we get:
20 = 5 + 2y2
y2 = 7.5
Substituting this value of y2 into the demand function, we get:
Q = 120 - 3(40 - (1/3)Q)
Q = 90
Therefore, the output of the first firm is y1 = 45 and the output of the second firm is y2 = 7.5.
An industry has only two firms producing outputs y1 and y2, respectively. The first firm has a
cost function of TC(y1) = 20 + 20y1 and the second has a cost function TC(y2) = 10 + 5y2 + y22. The demand function for the product these firms make is Q = 120 - 3P, where Q is the
total output of the two firms. What are the firms' outputs in equilibrium?
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