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 - 200,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 150 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). The total expenditure is the wage (W) times the quantity of labor (Q). Given the supply function QS = 0.02W - 200, we first solve for W in terms of Q: Q = 0.02W - 200 => Q + 200 = 0.02W => W = 50Q + 10,000. The derivative of W with respect to Q gives the marginal expenditure, which is 50. Therefore, for each additional coal miner hired, the marginal expenditure is $50. For 150 coal miners, the marginal expenditure remains $50 per additional coal miner, not the total cost, making the correct answer based on the interpretation of marginal expenditure as the cost of hiring an additional worker, not the total expenditure for all workers.

The Solo Coal Mine Is the Only Employer in the Small