Suppose in the short run, the firm can adjust the amount of labor L, and the amount of capital, K*, is fixed. The production function is ?(?, ?) = ?1/3? 1/3 . The price of output is p, the rent of capital is r, and the wage of labor is w.
a. Write down the profit of the firm in terms of K*, L, p, r, and w.
b. Suppose now ? ∗ = 125, ? = 27, ? = 2, and ? = 5. Write down the isoprofit equation when the profit is 0. (Hint: the quantity of output q, is a function of labor L)
c. ? ∗ = 125, ? = 27, ? = 2, and ? = 5. The firm is trying to maximize the profit in short run. Write down the first order condition and find how much labor the firm would like to hire.
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