Answer to Question #215657 in Microeconomics for fafa

Question #215657

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



1
Expert's answer
2021-07-12T11:49:57-0400

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\u00d72,500 = 75."

"TP = TR - C = 75\u00d72,500 - (50\u00d72,500 + 10,000) = 52,500."


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