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Economics 1480 Answer key #4 Question 1: Rosen, chapter 6, problem 1 C wins in every pairwise vote. Thus, there is a stable majority outcome, despite the fact that persons 1, 2, and 3 have double-peaked preferences. This demonstrates that although multi-peaked preferences may lead to voting inconsistencies, this is not necessarily the case.

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a. With the demand curve of Q = 100-10P and a perfectly elastic supply curve at P = 2, then the milk is sold at a price of \$2, and a quantity of 80 units is sold. b. The marginal revenue curve associated with the inverse demand curve P = 10-(1/10)Q is MR = 10-(1/5)Q, while the marginal cost curve is MC = 2. The cartel would ideally produce a quantity where MR = MC, or 10-(1/5)Q = 2, or Q = 40. The price associated with a cartel quantity of 40 units is P = 10-(1/10)*40, or P = 6. c. The rent associated with the cartel is the product of the marginal profit per unit and the number of units produced. The marginal profit per unit of milk is \$4 (=\$6 price - \$2 marginal cost), while 40 units are produced. Thus, the rents equal \$160. d. The most the cartel would be willing to contribute to politicians is the full economic rent of \$160. The cartel situation, the quantity of milk produced is too low from society’s point of view. The deadweight loss triangle (area 1) is computed using the difference between the cartel output and competitive output as the “base” of the triangle, and the difference between the cartel price and competitive price as the “height.” Thus, the triangle is equal to (1/2)*(80-40)*(\$6-\$2) = \$80. 10
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