Question

The marginal revenue product of labour is given by MRPₙ= 60−0.03N, where w is the wage rate ($/hr) and N is the number of workers the firm want to employ. The market supply of labour is given by w=4+0.01N, where w is the wage rate ($/hr) and N is the number of workers who want to work. The firm is a monopsonist in the labour market.

a. What are the equilibrium wage rate and employment? Show your work.

Answer 1

The equilibrium wage rate and employment for a monopsonist can be determined by setting the marginal revenue product (MRP) equation equal to the wage rate equation, solving for the number of workers (N), and then substituting N into the wage rate equation to find the wage (w).

Step-by-step explanation:

The equilibrium wage rate and employment level for a monopsonist firm in the labor market are found at the point where the marginal revenue product (MRP) is equal to the marginal cost of labor (MCL). From the given MRP function MRPN = 60 - 0.03N and the supply function w = 4 + 0.01N, we need to find the point where MRP equals the wage rate w, since the monopsonist's MCL is the market wage rate.

To find the equilibrium employment level (N), set MRP equal to the wage equation: 60 - 0.03N = 4 + 0.01N. Solving this for N gives the equilibrium number of workers. To then find the equilibrium wage rate (w), substitute the value of N into either equation. Consequently, the monopsonist will hire N workers and pay them a wage of w dollars per hour, which maximizes their profits.

Example: If we find that N = 1000 workers from solving the equation, the wage would be w = 4 + 0.01(1000) = $14 per hour as the equilibrium wage rate.