Econ805midans00

Econ805midans00 - The Ohio State University Department of...

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The Ohio State University Department of Economics Econ. 805 Prof. James Peck Winter 2000 Midterm Questions and Answers (1) 25 points A monopolist has many potential customers, represented by the interval, [0,1]. For customer x ! [0,1], consuming one unit of the product provides a benefit of v, but the customer must pay a transportation cost of tx to purchase the product, where t is a positive parameter. The monopolist has a constant marginal cost, c, and no fixed costs. Assume that customers are uniformly distributed across the interval, [0,1], according to the density function, f(x) = 1. In other words, if everyone in the interval [0,x] purchases, the monopolist sells x units of the product. Also assume the following: assumption 1: (v-c)/2 " t " (v-c). (A) Suppose that the monopolist must charge a constant price, p, but that it can also offer to pay a “transportation subsidy” to its customers, as a function of their location, denoted by s(x). That is, a customer at “location” x that pays the price, p, and incurs the transportation cost, tx, also receives a payment from the monopolist, s(x). Therefore, her utility would be (v - p - tx + s(x)) if she purchases the product, and zero if she does not purchase. What are the profit maximizing values of p, s(x), and monopoly profits? (Hint: think of price discrimination) (B) Suppose that the monopolist must charge a constant price, p, with no transportation subsidy. Therefore, a customer at location x would receive utility of (v - p - tx) if she purchases the product, and zero if she does not purchase. Calculate the profit maximizing value of p, the total quantity sold, and monopoly profits. ANSWER: (A) The monopolist can perfectly price discriminate, charging everyone their full willingness to pay. The highest net payment, p - s(x), that consumer x is willing to make is v - tx. The monopolist can extract this payment by setting p - s(x) = v - tx. The simplest way is to set p=v and s(x) = tx. The additional profits received from consumer x is: v - tx - c. Since v - c > t
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Econ805midans00 - The Ohio State University Department of...

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