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A profit-maximizing firm manufactures widgets (output is denoted by q) using machines (K) and full-time employees...

A profit-maximizing firm manufactures widgets (output is denoted by q) using machines (K) and full-time employees (E). In any given week, its output is given by the production functionq = f(E,K) = 1200K + 700E + 2EK – E2 -2K2

The marginal product of labor (MPE) is: 700 + 2K – 2E

Consider the long-run factor demand problem.

a. Suppose that the price of labor is again $400 per week. What is the firm’s long-run demand for labor? What is the firm’s long-run demand for capital? Compute the firm’s level of output and profits per week in this long-run equilibrium.

b. What will the firm’s long-run labor demand be when the weekly wage decreases to $380 per full-time worker? Compute the firm’s demand for capital, level of output and profits in this new long-run equilibrium.

c. What is the firm’s long-run elasticity of labor demand as the wage falls from $400 to $380? Is this an elastic or inelastic response?

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