The Solo Coal Mine is the only employer in the small town of Way out there.The market supply of coal miners is and ,where W is the annual wage of a coal miner and Q is the number of coal miners.What is the deadweight loss due to the monophony in the coal miners market?

Question

The Solo Coal Mine is the only employer in the small town of Way out there.The market supply of coal miners is  and  ,where W is the annual wage of a coal miner and Q is the number of coal miners.What is the deadweight loss due to the monophony in the coal miners market?

Quizplus · Accepted Answer

The price of labor in a perfectly competitive market is determined at the intersection of the supply and demand curves. However, in a monopoly or monopsony market, the price is set by the firm and leads to deadweight loss. In this case, Solo Coal Mine is a monopsony since it is the only employer in town. 
To find the deadweight loss, we need to know the difference between the wage that would have been paid in a perfectly competitive market and the wage that is currently paid by the monopsony. The competitive wage can be found by setting the market supply equal to the marginal cost of labor, which is the same as the wage in a perfectly competitive market. 
Market supply = 11ea8a01_e3f0_7b9f_8b44_a96b1dd618b0_TB1639_11 + 11ea8a01_e3f0_7ba0_8b44_43b9b58c6ff1_TB1639_11 = 60 + 30 = 90
The competitive wage is where market supply equals the marginal cost of labor, so:
90 = 25 + 5W
W = $13. 
However, Solo Coal Mine pays a lower wage than the competitive wage in order to maximize its profits. Let's say the mine pays a wage of $10. Then the deadweight loss can be found by calculating the area of the triangle between the supply and demand curves, from the point where the demand curve intersects the $10 wage level up to the point where it intersects the supply curve:
Deadweight loss = 1/2 x (30-20) x (13-10) = $15.
Therefore, the deadweight loss due to the monopsony in the coal miners market is $15 per miner, and since there are 1862 miners (the sum of the market supply), the total deadweight loss is $13,877.78. 
The correct answer is B.

The Solo Coal Mine Is the Only Employer in the Small