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Unformatted text preview: Micro 3101 Solution to Homework Assignment 4 Monopoly 1. (a) To find the Marginal Revenue, we first have to ”invert” the demand function to the inverse demand function as P = 100 Q. The total revenue is then TR ( Q ) = P × Q = 100 Q Q 2 . Differentiating TR with respect to Q , we have MR ( Q ) = 100 2 Q. Marginal cost is the derivative of TC with respect to Q , which is MC ( Q ) = Q + 10 . Average cost is just total cost divided by Q , which is AC ( Q ) = Q 2 + 10 + 20 Q (b) For perfect competition, we have P ( Q ) = MC ( Q ) 100 Q = Q + 10 Q = 45 P = 100 45 = 55 Profit is then defined as π ( Q ) = TR ( Q ) TC ( Q ) = 100 Q Q 2 Q 2 2 10 Q 20 = 90 Q 3 2 Q 2 20 = 992 . 5 (c) For monopolist, we have MR ( Q ) = MC ( Q ) 100 2 Q = Q + 10 Q = 30 P = 100 30 = 70 Profit is then π ( Q ) = 90 Q 3 2 Q 2 20 = 1330 . 2. (a) The monopolist problem is maximizing profit, which is total revenue minus total cost....
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 Spring '10
 ECON
 Economics, Microeconomics, Monopoly, Supply And Demand, Harshad number, order condition

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