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Monopoly- output, price and profits

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(Demand) P=$85Q-$0.2Q
(Marginal Reveune) MR=$85-$0.4Q
(Total Cost) TC=$900+$20Q+$0.8Q2
(Marginal Cost) MC=$20+$1.6Q

where P is price (in dollars), Q is output (in thousands of megawatt hours) and TC is total cost (in thousands of dollars).

a) if the firm were operating as a pure monopolist, what would be its optimal price/output solution and level of economic profits?

The way I worked it out:

MR = MC
$85-0.4Q = $20+1.6
65 = 2.0Q
32.5 = Q

P = 85Q-0.2Q2
= 85(32.5)-0.2(32.5)2
= 276.25-0.2(1056.25)
= 276.25-211.25
= $65.00

Could someone look over this to make sure that I am right.

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Solution Summary

The solution calculates equilibrium quantity equilibrium price and profits for a monopoly. Pure monopolists for operating firms are discussed.

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There appears to be some mix up in the equations that you have written
as
P = 85Q-0.2Q2
= 85(32.5)-0.2(32.5)2
= 2762.50-0.2(1056.25) { as 85 x 32.5 is 2762.50 and not 276.25 as you have written)
= 2762.50-211.25
= $2511.25
which is wrong

The ...

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