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Unformatted text preview: Problem Set #2 Micro II – Spring Term 2010 SUGGESTED SOLUTIONS 1. (Third Degree Price Discrimination) Suppose that for some good, the marginal cost of production is $5. Demand comes from two sources, senior citizens and the rest of the population. Senior citizen demand is given by the inverse demand function P seniors = 15 – Q/500. Demand by the rest of the population is given by the inverse demand function P rest = 20 – Q/2000. a. If a monopolist facing these two demands must set a single price for the good, what price would it optimally set? What would be its profit? For setting single price, total demand curve has to be derived. Q = Q s + Q R Q s = (15 – P s )500 Q s = 7500 – 500P s Q R = 40000 – 2000P R Since Q = Q S + Q R and P s = P R Q = 7500 – 500P + 40000 – 2000P Q = 47500 – 2500P P as a function of Q P = 47500/2500 – Q/2500 = 19 – Q/2500 MR = 19 – 2Q/2500 = MC = 5 Q = 17500 and putting this in P = 19 – 17500/2500 = $12 Profits = (P – MC) * Q = (12 – 5)*17500 = $1,22,500 b. Suppose this monopolist could set two prices, one for seniors and another for regulars. What prices maximize profit and what is that level of profit? The monopolist can set different prices by engaging in third-degree price discrimination. MR S = 15 – Q s /250 and MR R = 20 – Q R /1000 and MC = 5 1. Total output should be divided between groups so that MR for each group is equal 2. Total output is chosen so that MR for each group of consumers is equal to the MC of production MR for each group will be equated to MC 15 – Q s /250 = 5 or Q S = 2500 20 – Q R /1000 = 5 or Q R = 15000 P S = 15 – 2500/500 = $20 P R = 20 – 15000/2000 = $12.5 Profits = 20 * 2500 + 12.5 * 15000 – 17500 * 5 = $1,50,000 NOTE: DO CHECK IF THE TWO CONDITIONS ARE BEING FOLLOWED 2. (Third Degree Price Discrimination) Suppose a firm sells to students and others at a single price of $10 per unit. At this price, it sells 10,000 units in total; 2,000 to students and 8,000 to the others (non-students). At the price of $10, demand by students has elasticity -3, while demand by the others has elasticity -1.5. a. Suppose the firm decided to raise the price it charges non-students by $0.10. At the same time, it will lower the price facing students. If it wants to lower the price charged to students so that it sells (approximately) the same 10,000 units (so that the decrease in demand by non-students is balanced by an increase in demand by students), by how much...
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This note was uploaded on 04/19/2011 for the course ECON 101 taught by Professor Gul during the Spring '11 term at Lahore School of Economics.
- Spring '11