Question

Inverse Labor Supply is w=5L. The Inverse Labor Demand curve is w=100-20L

Suppose there is a negative production externality that costs society $50 per unit of labor hired.

1. what is the social marginal benefit curve now, and why is it not the same as labor demand curve?

2. what is the socially optimal level of employment

3. what is the dead-weight loss associated w/ CME?

4. what is the dead-weight loss associated w/ the monopsony?

5. is the monopsony outcome better or worse than the CME in this case?

6. How can government fix the externality problem so that we get the socially optimal level of employment in this market?

Answer 1

1. Cost of production externality = $50 per worker

The inverse labor demand curve is

w = 100-20L

Therefore, adding cost of production externality the wage = w+50

therefore, the inverse labor demand curve is

w+50= 100-20L or, w= 50-20L

The social total benefit curve is

wL= 50L-20L² and

The social marginal benefit curve is

d(wL)/dL= 50-40L

The marginal benefit curve is not same as inverse labor demand curve because it defines benefits derived from hiring one additional worker in the production process.

2. The socially optimum level of employment is reached at the point where quantity of labor supplied and labor demanded is equal.

i.e., 5L=50-20L or, L=2 , which is the socially optimum level of employment.

3. Without cost of production externality, the socially optimum level of employment is

5L= 100-20L or, L=4 and w =5L=5.4=20

Therefore deadweight loss associated w/CME= 1/2*(w₁ -w₂ )(L₂ - L₁ ) = 1/2*(20-10)(2-4)= -10

4. Social marginal benefit curve derived from the original labor demand curve is,

d(wL)/dL= 100-40L

Under monopsony condition,

             Social marginal benefit =0

    i.e,, 100-40L=0 or, L=2.5 = 2 (omitting the decimal value)

and w=100-20L= 60

Therefore, deadweight loss associated with w/monopsony = 1/2*(60-20)(2-4) = -40

5. As deadweight loss associated with w/monopsony is higher than deadweight loss associated with w/CME, CME outcome is better than monopsony outcome.

6. Government should provide tax and other subsidies to production firms that effectively lower the input costs of firms and help them to mitigate negative externalities in the production process and hire socially optimum level of workers. Here in this case, the total externality costs associated with hiring social optimum level of workers i.e.., 4 is 4*50=200. Therefore, government should provide a subsidy equivalent to 200 to firms for achieving socially optimum level of employment.