A monopolistic market (or industry) demand curve is described by Q = 50 – 0.5P The firm’s cost function is T?
A monopolistic market (or industry) demand curve is described by
Q = 50 – 0.5P
The firm’s cost function is
TC = 10 + 2Q
a. Find the profit-maximizing quantity and price.
b. If the industry is regulated in a way that requires it to set P = AC, how much will be sold and what will the price be?
c. If the industry is regulated in a way that requires it to set P = MC, how much will be sold and what will the price be?
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Profit is revenue-total cost. Revenue R=PQ, so profit p=PQ-10-2Q. P=100-2Q, so p=100Q-2Q-2Q^2-10=98Q-2Q^2-10. p'=98-4Q, so Q=98/4 maximizes profit. Since half units don't make sense in this context, profit is maximized at 24 units, with P=52.
b. AC=2+10/Q. At this price, R=2Q+10 and p=2Q+10-(2Q+10) thus profit is 0 at any level of production greater than 0, so one unit should be produced at P=12, which will allow recovery of fixed costs.
c. Since MC=2 for all Q>0, and this is less than AC, the only reasonable solution is to produce as much as possible and sell nothing. The following year(s), when production is 0, MC=12 and 44 units can be sold.