# Question 5 a monopolist sells a product that is

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QUESTION 5: A monopolist sells a product that is demanded by two kinds of consumers. The demand by each consumer of type A is given by the demand curve: P = 10 – 2q . The demand by each consumer of type B is given by the demand curve: P = 12 – 2q There are 30 consumers of type A and 10 consumers of type B. There is no resale possible for this product among consumers. The monopolist cannot identify the type of any consumer. The monopolist produces at a constant cost per unit of 4 dollars. Suppose that the monopolist engages in two-part pricing. As part of an optimal two-part price, the monopolist chooses a variable price of 4.50 dollars per unit. (7 points) (a) How much profit does this monopolist earn? Demand by each of type A: qA = 5 – (1/2)P Demand by each of type B: qB = 6 – (1/2)P Total demand in market At prices below 10: Q = 210 – 20P Total Demand curve P = 10.5 – (0.05)Q [2points] The optimal fixed fee, T, is the consumer surplus of a type A consumer, which is given by ½ *(10 – v)*(5 – v/2) where v = 4.50. [2 points] This equals 7.563. The profit is then 40(7.563) + .5*(210 – 90) = 362.52. [3 points] (2 points) (b) What is the consumer surplus earned by each consumer of type A? zero (2 points) (c) What is the consumer surplus earned by each consumer of type B? . 5(12 – 4.50)(6 – ½ *4.50) - T = 6.50 (2 points) (d) The demand curves of the two groups of consumers differ only by the vertical intercept, and with these demand curves the profit-maximizing variable fee is \$4.50. 13

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Without doing any calculations, answer the following: what would happen to the profit-maximizing variable fee if the two demands changed to become very similar (i.e. the intercepts moved very close together)? The optimal variable fee would decrease. Intuitively, as the demands become identical, the optimal variable fee approaches marginal cost. (2 points) (e) What impact would a resale market for the product have on the monopolist’s attempt to engage in two-part pricing? The monopolist would not be able to engage in two-part pricing, as 1 or 2 consumers could purchase the entire quantity at his announced two-part price and then re-sell the amount to other consumers. 14
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