Question

26.1 A monopolist produces a good using only one factor, labor. There are constant returns to scale in production, and the demand for the monopolist's product is described by a downward- sloping straight line with slope -1. The monopolist faces a horizontal labor supply curve. If the
monopolist chooses output to maximize profits, then the:
(a) marginal cost of labor to the monopolist exceeds the wage.
(b) marginal product of labor times price of output equals the wage.
(c) marginal product of labor times price of output is less than the wage.
(d) marginal product of labor times price of output exceeds the wage.
(e) marginal revenue product of labor is less than the wage.

The asnwer is d, why?

Answer 1

The Value of Marginal Product f Labor (VMPL) = Marginal Product (MP) * Price (P)
VMPL = MP * P -------------equation 1

However, in a monopoly, we are not interested in VMPL, rather in MRPL which is as follows:

Marginal Revenue Product of Labor (MRPL) = MP*MR (this is the demand curve in the labor market)------- equation2

The monopolist demand curve is determined by MRPL and not by VMPL

Now, in a perfectly competitive set-up, the equilibrium is attained where the MRPL = wage rate

However, under a monopoly, we have the following situation

P > MR   

From equation 1, VMPL = MP * P

From equation 2, MRPL = MP*MR

Since, P > MR, VMPL > MRPL ------------equation 3

and at equilibrium condition for perfect competition, MRPL = w -----------equation 4

Equation 3 and 4 implies that,

VMPL > wage rate

That is, the Marginal Product of labor times the price > wage rate.

So, the answer is d.