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6. The demand function for a good supplied by a monopolistis: (500-P)/p=x, 0<p<500 The cost of producing x units of output is 2x, for all x20. Show that the monopolists profit may be expressed as a concave function of output, and find the output and price that maximize profit.
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Answer #1

Answer:

Given

Demand function

x=(500-P)

x=500-x

P=500-x

TR=x*P=x*(500-x)=500x-x^2

TC=2x

So profit=TR-TC=500x-x^2-2x

profit =498x-x^2

Profit 70000 60000 50000 40000 30000 20000 10000 10 30 50 70 90 110 130 150 170 190 210 230

For maximum profit

dProfit/dx=0

498-2x=0

x=249 units

P=500-x=500-249=251

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