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ec100_winter2010_ps7 - market demand by altering quantity...

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Problem Set 7 Economics 100, Winter 2010 Due Tuesday, March 2, 2010, 9 am 1. A monopolist faces a demand curve given by: Q = 2000 1/3 P. The monopolist’s cost functions are: MC = 10 + Q ATC = 10 + (1/2)Q + 20/Q a. What is the monopolist’s total cost function? What are total fixed costs? b. Write an equation for the monopolist’s marginal revenue function. c. Find the equilibrium price, quantity and level of profits if the monopolist maximizes profits (but must charge all consumers the same price). d. If a tax of $20 per unit sold is imposed on this monopolist, find the new price charged to consumers and the new output level. 2. The demand curve facing a monopoly is P = 100 Q. The firm’s cost curve is C(Q) = 10 + 5Q. a. What is the profit maximizing P and Q? What are profits at this point. b. How does the answer change if the cost function becomes 100 + 5Q? 3. Show, using a supply and demand curve, how a monopolist can respond to a shift in
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Unformatted text preview: market demand by altering quantity but keeping the same price. 4. A monopolist faces a demand curve given by Q = 10P-3 . Its cost function is C(Q) = 2Q. Find the optimal level of output and price. HINT: Use the fact that this is a constant elasticity demand function, with an elasticity at all points equal to -3. 5. Consider a monopolist with demand given by Qd = 20-.5P and MC = 4 + 2Q. a . Find the equilibrium P & Q. b . Find the equilibrium P & Q when government imposes a price ceiling of $24. c. How does the total surplus (consumer plus producer) compare between the case described in part b (a monopolist subject to a price ceiling of $24) and a perfectly competitive market with the same demand function and a supply curve of P = 4 + 2Q. Explain your answer and illustrate with a graph....
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