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 inverse demand function for 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 is the inverse demand function for coal miners?

Quizplus · Accepted Answer

The inverse demand function for coal miners is given by the market demand equation, which is the sum of individual demand functions. In this case, the market supply of coal miners is given by Qs = W/1000 - 8, so the individual demand function for coal miners is Qd = 22 - W/1000. Thus, the market demand function is Q = 22 - (W/1000) * (Q1 + Q2), where Q1 and Q2 are the quantities supplied by the two types of coal miners. Substituting the market supply functions for Q1 and Q2, we get Q = 22 - (W/1000) * (11W/8000 - W/1000 - 8). Simplifying this expression, we get Q = 22 - (11W^2/8) + (33W/2000), which can be rewritten as W = (73000/33) - (8000/33)Q + (2000/33)Q^2. This is the inverse demand function for coal miners. Therefore, the correct answer is (C).

The Solo Coal Mine Is the Only Employer in the Small