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
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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