In: Economics
Workers for a firm have the following marginal productivity of labor: M P subscript L equals 50 minus L Suppose the firm sells its output for $2 per unit. The firm is a nondiscriminating monopsonist and faces the following labor supply curve: L equals W Determine the number of workers employed and the wage that the workers are paid.
In order to maximize profit a non discriminating monopolist that amount of L where MRP = wage rate(W)
where MRP = Marginal Revenue Product = Price of Output * MPL = 2(50 - L)
So, MRP = W => 2(50 - L) = W => L = 50 - W/2 --------labor demand equation
It is given that, L = W--------------------Labor supply equation.
Equilibrium occus when Labor demand and Labor supply intersects
=> 50 - W/2 = W => W = 100/3 = 33.33
=> L = W = 33.33
Thus, Number of workers employed(L) = 33.33 and Wage that workers are paid(W) = 33.33