Question

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

Answer 1

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:

$TP = TR - TC = 32×4 - (4×4^2 - 8×4 + 15) = 81.$

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.