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Suppose that a price-searcher monopolist had a total cost function given by: TC= 20 + 0.5Q...

Suppose that a price-searcher monopolist had a total cost function given by: TC= 20 + 0.5Q +0.2Q2. The demand for the price searcher's product is given by: QD= 100 -20P. Calculate the monopolist's profit.

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Answer #1

MC=0.5Q+0.4Q

MR=100-2Q/20

MC=MR

0.5+0.4Q=100-2Q/20

10Q=90

Q=9

P=100-9/20 = 4.55

TR=P*Q = 4.55*9 = 40.95

TC=20+0.5(9)+0.2Q^2 = 40.7

Profit = TR-TC = 40.95-40.7 = 0.25

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