Question

There is a monopsonist employer in a labor market. Value of the monopsonist’s marginal product=240-0.5E. Labor supply facing this monopsonist is given by Es=2ws. w is in dollars per week and E is number of workers. Suppose that the monopsonist is a perfectly wage discriminating monopsonist.
a)   Draw the labor demand, labor supply curves and find the number of workers that the monopsonist will hire. What is worker surplus and deadweight loss? Explain.
b)   Now suppose that a minimum wage is set at $100 per week, how will this affect worker surplus and deadweight loss compared to part a? Explain.

Answer 1

There is a monopsonist employer in a labor market.

The value of the marginal product of labor is given by, MRPL=240-0.5E. This is the labor demand here.

Also given the labor supply Es=2Ws, where W is in dollars per week and E is number of workers.

Now the total cost of labor is given by

TCL=Es×Ws=Es×0.5.Es

Now, The marginal cost of labor is given by

MCL=d(TCL)/d(ES)=Es.

(a) The labor demand(MRPL), Labor supply(Es) and marginal cost of labor(MCL) is drawn in the following diagram.

From the above diagram, we can see the monopsonist will hire labor where

MCL=MRPL

or, E=240-0.5E

or, E* = 160

Hence, the monopsonist will hire 160 labors.

Now we can see from the diagram, the deadweight loss and worker surplus is shaded in the graph. We will find the area of the triangles.

Worker Surplus: The area of the triangle ∆OCW* is given as the Worker Surplus.

Hence, ∆OCW*=(1/2)×80×160=$6400

Hence worker surplus is $6400.

Deadweight Loss: The area of the triangle ∆ABC is given as the Deadweight Loss.

Hence, ∆ABC=(1/2)×(120-80)×(240-160)+(1/2)×(160-120)×(240-160)=$3200

Hence deadweight loss is $3200.

(b) If the minimum wage is set at $100 per week then we will draw the diagram from this case. The following be the diagram.

From the diagram, we can see the labor hired at minimum wage $100 is 200 workers. We get this by putting the minimum wage at the labor supply curve.

Now, the deadweight loss and worker surplus is shaded. We have to find the area of the triangles.

Worker Surplus: The area of the triangle ∆ODWm gives the worker surplus.

Hence, ∆ODWm=(1/2)×100×200=$10000

Hence worker surplus is $10000.

Deadweight Loss: The area of the triangle ∆FBD gives the deadweight loss.

Hence, ∆FBD=(1/2)×(120-100)×(240-200)+(1/2)×(140-120)×(240-200)=$800.

Hence deadweight loss is $800.

From our analysis we can see the Worker Surplus has increased by $(10000-6400)=$3600.

And, the deadweight loss is decreased by $(3200-800)=$2400.

Hence, the overall welfare of the economy increased.

Hope the solution is clear to you my friend.