Question

Suppose that the demand equation for a monopolist is

P= 100 - 0.01x

 and the cost function is

C(x) = 50x + 10 000

Find the value of x that maximizes the profit and determine the corresponding price and total profit for this level of production

Answer 1

The value of x that maximizes the profit is:

MR = MC,

$MR = TR'(x) = 100 - 0.02x,$

$MC = C'(x) = 50,$

100 - 0.02x = 50,

0.02x = 50,

x = 2,500 units.

$P = 100 - 0.01×2,500 = 75.$

$TP = TR - C = 75×2,500 - (50×2,500 + 10,000) = 52,500.$