Question

Consider a purely competitive firm that has two variable inputs L (labor hour) and K (machine) for production. The price of product is $p. The production function is

Q (K, L) = 4L^1/4 K^1/4 .

Assume that the hourly wage of workers is fixed at $w and the price per machine is $r.

(a) Set up the objective of this firm.

(b) State the first-order necessary conditions for profit maximization.

(c) Write out the optimal inputs quantities, L and K, as a function of parameters, p, w, and r.

(d) Show that this critical point found in (c) is a global maximum.

(e) Show that the demand functions found in (c) are homogeneous of degree zero.

(f) Study the effect of a small change in w and r on the optimal demand for labor and on the optimal demand for capital.

Answer 1