5. There exists two types of workers in the market, distinguished by some charac

Question

5. There exists two types of workers in the market, distinguished by some charac- teristic that has no relationship to labor market productivity. There are 100 type 1 workers and 100 type 2 workers. The productivity of per hour worked of each type is equal to 2. The product price is fixed at p 2. Each type of worker has the same labor supply function as in the previous problem, that is hi 1wi 1. Assume that the labor market is inhabited by a monopsonist. The monop- sonist's production function is q-H+H2. The objective of the monopsonist is to maximize his utility, which is given by where H 100(1w). The term -H2 in the utility function of the monopsonist reflects a distaste for having employees of type 2. What are the monopsonist's utility-maximizing choices of wi and w2? 2. Say that the labor market becomes competitive in the following sense. Other firms enter the market that are simply profit-maximizers, that is, they have no distaste for hiring type 2 workers. What happens to the wage of type 1 and type 2 workers? What happens to the welfare of the (former) discriminatory monopsonist if he is obligated to offer employment to any individual willing to supply hours to the firm (that is, whether they are type 1 or type 2) at the competitive wage rates prevailing in the labor market?

Explanation / Answer

Answer:-

1) Assume that the labor market is inhabited by a monopsonist.

The monopsonist’s production function is q = H1 + H2.

The objective of the monopsonist is to maximize his utility, which is given by u = p(H1 + H2) H2 w1H1 w2H2,

Note that H1= 100(1 + w1) and that H2= 100(1 + w2)

The utility function becomes:

u = p(H1 + H2) H2 w1H1 w2H2

u = 2H1 + 2H2 H2 w1H1 w2H2

u = 2H1 + H2 w1H1 w2H2

u = H1(2 – w1) + H2(1 w2)

u = (100 + 100w1)(2 – w1) + (100 + 100w2)(1 – w2)

u = 200 + 200w1 – 100w1 – 100w12 + 100 – 100w2– 100w2 – 100w22

u = 300 + 100w1 – 100w12 – 100w22

Maximize this utility function by finding the first order conditions

u'(w1) = 0

100 – 200w1 = 0

u'(w2) = 0

–200w2 = 0

w2 = 0

This suggests that the monopsonist will pay a wage rate of 2 to type 1 worker and 0 to type 2 worker.

2) Labor market becomes competitive when firms enter the market that are simply profit-maximizers, that is, they have no distaste for hiring type 2 workers. In that sense they will hire equal amount of both type of workers.

The wage of type 1 will fall and type 2 workers will rise. The welfare of the (former) discriminatory monopsonist will fall,when he is obligated to offer employment to any individual willing to supply hours to the firm at the competitive wage rates prevailing in the labor market.

This is true since the labor supply function is hi =1 + wi and when type 2 worker will experience a rise in their wage rate w2,the monopsonist has to pay a higher wage cost.

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