Answer to Question #220000 in Macroeconomics for Adisu

Question

A monopolist's demand function is P = 1624 - 4Q, and its total cost function is

TC = 22,000 + 24Q -4Q2 + 1/3 Q3, where Q is output produced and sold.

i. At what level of output and sales (Q) and price (P) will total profits be

maximized?

ii. At what level of output and sales (Q) and price (P) will total revenue be

maximized?

iii. At what price (P) should the monopolist shut down?

Answer 1

a)Total profit maximizing

Marginal revenue equals to marginal cost$MR=MC$

$MR=dTR/dQ$

$TR= P(Q)$

= (1624 - 4Q)Q

=1624Q- 4Q2

=1624 - 8Q

$MC = dTC/dQ$

= 24 - 8Q + Q²

So;

1624-8Q=24-8Q+Q²

1624-24= -8Q+8Q+Q²

1600=Q²

Q=40

P =1624-4(40)

=1624-160

=1464

b)Total revenue is maximized

$MR=0$

1624-8Q=0

1624= 8Q

Q= 203

c) a monopoly should be shutdown if the price is lower than the average variable cost

$P=AVC$

1624-4Q=24-4Q+1/3Q²

1624-24=-4Q+4Q+1/3Q²

1600=1/3Q²

4800=Q²

Q=approximately 69

P=1625-4(69)

=1348

A monopoly will be closed if the price is less than 1348