Question One The expression -c'(x(p")) where p" and x" (p) are the monopolist's price and DM output level, respectively,

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Question One The Expression C X P Where P And X P Are The Monopolist S Price And Dm Output Level Respectively 1 (254.76 KiB) Viewed 22 times

Question One The expression -c'(x(p")) where p" and x" (p) are the monopolist's price and DM output level, respectively, is known as the price-cost margin. It measures the distortion of the monopolist's price above its marginal cost as a proportion of its price. (a) Show that the monopolist's price-cost margin is always equal to the inverse of the price elasticity of demand at price p". (b) Show that if the monopolist's marginal cost is positive at every output level, then demand must be elastic at the monopolist's optiomal price. Question Two Consider the case of pricing for the UNZA Basketball games at the University of Zambia Sport Hall. The freedom fighters have a demand function given as p(q) = 100-qa, while students have demand function ps(q) = 20-qs/10. The analysis in the notes concludes that if MC = 0, the profit maximizing quantity (i.e. stadium capacity) is 150, with q'a = 50 and q's= 100. Suppose that the capacity of the Sport Hall is equal to Q < 150. (a) For what values of Q is it profit maximizing to sell only to students? (HINT: It may be helpful to solve this question: For what values of qa is MR(alumni) > 20?) (b) Assume that it is profit maximizing to sell to both groups. Solve for profit- maximizing prices and quantities as a function of Q. Question Three Suppose that there are two consumers in an exchange economy with two goods. There are total of ten units of each good. The initial endowments for these consumers are (e₁x, ey) for consumer 1 and (e2x, ezy) for consumer 2, where ex = 10-e₁x and e2y = 10-e₁y. Consumer 1 has utility function u(x1, y₁) = x₁¹/3 y₁2/3, while consumer 2 has utility function given as v(y₁, y2) = x22/3 y2¹/3 (a) Normalize the price of good 1 to 1 and denote the price of good 2 by p. Write the budget constraints for each consumer. (b) Solve for each consumer's optimal consumption bundle as a function of price P. (c) Is each person's consumption of good x increasing or decreasing as a function of p? Explain the meaning of this result in words. (d) What is the equilibrium price for the initial allocation of (6, 2) to consumer 1 and (4, 8) to consumer 2? What are the resulting equilibrium bundles?