For a monopolist firm the demand and the total cost functions are given as Q = 20-
0.5P and TC= 4Q2-8Q+15, respectively.
Find
a) the optimum quantity and the optimum price level
b) the profit/loss on these levels
c) at what price should the monopolist shut down?
d) Show the economic profit (loss) of the firm in a graphic representation
a) The optimum quantity and the optimum price level occur at MR = MC.
Q = 20 - 0.5P, P = 40 - 2Q,
"MR = TR'(Q) = 40 - 4Q,"
"MC = TC'(Q) = 8Q - 8,"
40 - 4Q = 8Q - 8,
12Q = 48,
Q = 4 units,
P = 40 - 2×4 = 32.
b) The profit/loss on this level is:
"TP = TR - TC = 32\u00d74 - (4\u00d74^2 - 8\u00d74 + 15) = 81."
c) The monopolist should shut down if P < AVC.
At Q = 4 units AVC = VC/Q = 4×4 - 8 = 8, so he should shut down at P < 8.
d) The economic profit occurs when the price level P is above the ATC curve at optimal level of Q.
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