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Unformatted text preview: Economics 101 Fall 2007 Answers to Homework #5 Directions: The homework will be collected in a box before the lecture. Please place your name , TA name and section number on top of the homework (legibly). Make sure you write your name as it appears on your ID so that you can receive the correct grade. Please remember the section number for the section you are registered, because you will need that number when you submit exams and homework. Late homework will not be accepted so make plans ahead of time. Good luck! 1.Suppose that the popcorn market is currently a monopoly. In this market, the monopolists marginal cost curve is given by the equation MC=2Q+8. The monopolists demand curve is given by the equation P=56-3Q. a) If this monopolist acted as if it were a perfectly competitive firm in a perfectly competitive industry, what would the market price and quantity equal? What would the value of consumer surplus equal if this firm acted as if this was a perfectly competitive industry? What would the value of producer surplus equal if this firm acted as if this was a perfectly competitive industry? [Hint: the numbers for this problem are a bit challengingyou may want to pull out your calculator for this one!] In the competitive equilibrium, MC=P. Therefore, 2Q+8=56-3Q. So Q=9.6, P=27.2. CS=(56-27.2)*9.6/2=138.24; PS=(27.2-8)*9.6/2=92.16. b) Suppose this monopolist acts as a monopolist. What is the monopolistic price and quantity in the popcorn market? Calculate the value of consumer surplus, producer surplus and dead weight loss for this monopoly. The optimal quantity of the monopolist satisfies MC=MR. Here, MR=56-6Q. Therefore 2Q+8=56-6Q. So Q=6, P=38. DWL=(9.6-6)*(38-20)/2=32.4(calculate the area of the triangle directly). c) Suppose this monopolist knows what the maximum price each consumer of popcorn is willing to pay for popcorn and is therefore able to practice first degree price discrimination. What is the monopolists profit equal to when it practices first degree price discrimination. The profit is the total surplus of the society in part (a) which is 138.24+92.16=230.4. 2. Suppose a market has a single producer and that this producer is able to distinguish two types of customers, Group A and Group B (such as men and women, or young and adult). Group As demand curve is P = 16 3Q, and Group Bs demand curve is P = 10 Q. In both markets, MC=ATC=4. a) If the monopolist is required to charge the same price to the two groups of people, what is the best output level and price? What is the profit for this single price monopolist? [Hint: to find these answers you will need to find the market demand curve: this will entail the horizontal summation of the demand curves for the two groups.] The coordinates of the kink is P=10, Q=2, that of the lower ending point is P=0, Q=46/3....
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