Answer Happy

Question One p" -c'(x(p")) The expression where p" and "(p)are the monopolist's price and 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 pa(qa) = 100-qa, while students have demand function ps(qs) = 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 qs = 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. 1