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 function?

Question

Quizplus · Accepted Answer

The marginal expenditure (ME) function is derived from the market supply function by taking its inverse and then differentiating it with respect to Q. Given the supply function QS = 0.02W - 200, solving for W gives W = 50Q + 10,000. Differentiating W with respect to Q gives the marginal expenditure function, which is ME = 50, indicating a constant marginal expenditure. However, since the original function includes a -200 which when solved for W gives a +10,000 (to balance the equation), the correct interpretation of the differentiation process was misunderstood in the explanation. The correct approach should involve recognizing that the supply function's structure implies a direct relationship between wage (W) and quantity (Q), but the differentiation step described does not accurately reflect the process for finding the ME function from the given supply function. The correct ME function should reflect the change in total expenditure with respect to a change in quantity, which typically involves the wage rate and possibly additional factors from the original equation. The error in explanation suggests a misunderstanding of the differentiation process in this context.

The Solo Coal Mine Is the Only Employer in the Small