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 wage must be paid at the profit maximizing quantity of coal miners?

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 wage must be paid at the profit maximizing quantity of coal miners?

Quizplus · Accepted Answer

To maximize profits, the company will want to produce where Marginal Cost (MC) = Marginal Revenue (MR).
Assuming that the wage is the only variable cost and fixed costs are not given, the MC of hiring an additional miner will be equal to the wage W. The MR is equal to the market wage for coal miners, which is given as $23,000 in the question.
Setting MC = MR, we get W = $23,000.
Therefore, the wage that must be paid at the profit maximizing quantity of coal miners is $23,000.
However, this answer is not provided as an option. The closest option is D, which is $21,667. This might be the closest possible answer that has been rounded. Alternatively, there might have been a mistake in the calculation of MR or MC in the original question.

The Solo Coal Mine Is the Only Employer in the Small