Imagine there are 100 firms in a perfectly competitive industry. Each produces an output, q, using labour L and capital K according to the following short-run production function:
q = 5 + 4L - .25L2 + K
Each firm currently has five units of K. The price of each worker is $50 per day. The price of capital, K, is $100 per day. Suppose the industry is in long and short-run equilibrium.
a. How much output does each individual firm produce?
b. How much output does the entire industry produce?
c. What is the price of output in this industry?

Solution Preview

a.
Each firm will produce an output where its marginal cost or total cost is minimized. This will happen where marginal product of labor per dollar of labor equals marginal product of capital per dollar of capital.
MPL/Labor wage = ...

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