eco204_HW_13

# eco204_HW_13 - University of Toronto Department of...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain ECO 204 2008‐2009 Ajaz Hussain HW 13 In the following two questions, you will use the social welfare to evaluate whether a monopoly is “better” than competition. Question 1 Suppose a monopolist has the demand curve P = 100 ‐ 20Q and cost function C(Q) = 10 + 12Q + 2Q2. (a) What is the monopolist’s MC? (b) Solve for the monopolist’s profit maximizing optimal output and price. (c) What is the consumer surplus at the monopolist’s price and output? (d) What is the producer surplus at the monopolist’s price and output? Hint: Use the result for PS in Lecture 15. (e) What is the social welfare of the monopolist? (f) If this firm were to behave as a competitive company, what price would it charge and how much output will it produce? (g) What is the social welfare of the monopolist if it were behave as if it’s competitive? (h) From a social perspective, is monopoly more or less desirable than competition? 1 University of Toronto, Department of Economics, ECO 204 2008‐2009 S. Ajaz Hussain Question 2 Suppose an industry is competitive in which all firms have identical constant marginal cost of \$80. Suppose the industry demand curve is P = 100 ‐ 10Q. (a) Suppose there is a monopolist whose MC ≠ competitive MC. What is the maximum value of the monopolist’s MC for the monopoly price to be less than or equal to the competitive price? Hint: We did this question in HW 12. (b) Assume the monopolist has the MC equal to your answer in part (a). Calculate the monopoly price and output. (c) Show that the monopoly price and output in part (b) are identical to the competitive price and output. (d) Using social welfare = CS + PS criteria, is competition “better” than monopoly? (e) For the prices in parts (b) and (c), is there a scenario in which competition is “as good” as a monopoly? Question 3 (2007‐2008 Test 3 Question) “(B)ro‐gers” is a monopolist with demand P = 120 – 0.5Q and cost equation C = 420 + 60Q. Suggest two regulation prices and discuss any problems associated with these prices. 1 1 In case you need it, the quadratic formula for ax2 + bx + c = 0 is x= {‐b +/‐ square root of(b2 – 4ac)}/2a 2 ...
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