Question

Suppose that the firm’s production function is given by q = 10kl^3. The firm’s capital is fixed at k. What amount of labor will the firm hire to solve its short-run cost-minimization problem?

a) The firm will hire an infinite amount of labor.

b) The firm will hire zero labor.

c) The firm will hire labor until the marginal cost equals the wage rate.

d) Labor hiring is not influenced by the fixed capital.

Answer 1

The firm will hire labor until the marginal cost equals the wage rate. (option c)

Step-by-step explanation:

In the short-run cost-minimization problem, the firm seeks to minimize its costs by determining the optimal amount of labor to hire while keeping capital fixed. The production function is given by q = 10k*l³, where q is the quantity of output, k is the fixed capital, and l is the amount of labor employed.

The marginal cost (MC) can be calculated by taking the partial derivative of the production function with respect to labor:

MC = 30k*l²

To minimize costs, the firm will hire labor until the marginal cost equals the wage rate (w). Mathematically, this condition can be expressed as:

MC = w

Substituting the expression for marginal cost, we get:

30k*l² = w

Now, the firm will hire labor l until this equation holds true. The amount of labor hired is determined by the equilibrium between the marginal cost of labor and the wage rate, ensuring the firm minimizes costs in the short run. Therefore, option c) is the correct answer.(option c)