The Solo Coal Mine is the only employer in the small town of Way out there.The market supply of coal miners is Q^s = 0.02W - 400,where W is the annual wage of a coal miner and Q is the number of people who would accept employment as a coal miner.What is the coal mine's marginal expenditure when it hires 100 coal miners?

Question

Quizplus · Accepted Answer

The marginal expenditure (ME) for hiring an additional worker is the derivative of the total expenditure (TE) with respect to the quantity of labor (Q). Total expenditure is the wage (W) times the quantity of labor (Q). Given the supply function QS = 0.02W - 400, we first solve for W to express it as a function of Q. Rearranging the equation gives W = 50Q + 20000. The derivative of W with respect to Q gives the marginal expenditure, which is $50. Since the question asks for the marginal expenditure when hiring 100 coal miners, and given that the wage rate increases with each additional miner, the calculation for the exact marginal expenditure at 100 miners is not directly provided by the given information. However, the closest answer based on the information provided and the typical interpretation of marginal expenditure in the context of a linear wage function would be $30,000, acknowledging a misunderstanding in the explanation process.

The Solo Coal Mine Is the Only Employer in the Small