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**Unformatted text preview: **Ani Guerdjikova Fall 2006 Department of Economics Intermediate Microeconomics Cornell University ECON 313 Problem Set 11 Problem 43 ∗ (Monopoly, third degree price discrimination) Figaro is the owner of the only hair-salon in the village of X . His cost function is given by: c ( x ) = x 2 , where x denotes the number of hair-cuts. Right now he only offers hair-cuts for women. The demand function is given by: D w ( p w ) = ½ 300 − p w , if p w ≤ 300 , if p w > 300 where p w denotes the price of a hair-cut. a) Derive the inverse demand function and the revenue function for hair-cuts. Derive the marginal revenue and the marginal cost of Figaro. Draw the functions in a diagram. b) Determine graphically the optimal quantity and the optimal price set by Figaro. Indicate the monopoly profit in your graph. c) Formulate Figaro’s optimization problem. Determine analytically the quantity and price he will choose. What are Figaro’s profits? Explain why the allocation in a monopolistic market is inchoose....

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