Question

You are a labor economist trying to evaluate whether the labor market for computer scientists is competitive or monopsonistic. Based on previous research, you know that the production function for computers depends only on labor input: Y = -0.5L² + 10L; where Y is the output of computers and L is the quantity of labor used. The price of a computer is p = 2. You also know that the labor supply, as a function of the wage, for computer scientists is the following, where w is the wage per unit of labor: L = -10 + w.

a. Find the equilibrium wages and employment (wc; Lc) that would prevail if the market for computer scientists were competitive. [Remember that a competitive firm takes the wage as given : that is, it assumes that the quantity of workers that it hires has no effect on the price of the next worker. (Of course, the equilibrium wage must equate demand and supply)].

Answer 1

In a perfectly competitive labor market, the equilibrium wage and employment level are determined where the market demand for labor equals the market supply of labor. For a competitive labor market for computer scientists, the equilibrium wages and employment can be found by equating the supply and demand for labor, resulting in wc = 20/a and Lc = -10 + (20/a).

Step-by-step explanation:

In a perfectly competitive labor market, firms can hire all the labor they wish at the going market wage. The equilibrium wage and employment level are determined where the market demand for labor equals the market supply of labor.

For a competitive labor market for computer scientists, we can find the equilibrium wages and employment by equating the supply and demand for labor. The labor supply function is given as L = -10 + wa, and the demand for labor can be derived from the production function Y = -0.5L² + 10L. To find the competitive equilibrium, we set the wage equal to the value of the marginal product of labor (VMPL). In this case, it is the derivative of the production function with respect to labor, which is -L + 10. Setting this equal to the wage, we get -L + 10 = w.

Substituting the labor supply function into the equation, we have -(-10 + wa) + 10 = w. Simplifying, we get 10 - wa + 10 = w, which gives us wa = 20. Rearranging, we find that w = 20/a. Plugging this back into the labor supply equation, we get L = -10 + (20/a). Thus, the equilibrium wages and employment that would prevail in a competitive market for computer scientists are wc = 20/a and Lc = -10 + (20/a).