3. Consider a monopolist with cost function c(y) = cy. with e > 0, facing demand function x(p) = ap-, where c> 0. a. Show that if & $ 1. then the monopolist's optimal price is not well defined. b. Assume that &> 1. Derive the monopolist's optimal price, quantity, and price-cost margin (p" -c)/p" . Calculate the resulting deadweight welfare loss. 4. Consider the jewelry market. The total demand by men is given by D_(p) =100-2p. and the total demand by women is given by D_(p)= 200-p. The cost of production is c per unit. a. Suppose the jewelry market is competitive. Find the equilibrium price and quantity sold. b. Suppose, instead, that the firm A is a monopolist of jewelry. If firm A is prohibited from discriminating (i.c. charging different prices to men and women), what is the profit-maximizing price and quantity. For what values of c will it choose to sell to both men and women? c. Suppose that firm A is allowed to discriminate. What prices does it charge? Does aggregate welfare rise or fall relative to the nondiscrimination regime? 5. One common way to price discriminate is to charge a lump sum fee to have the right to purchase a good, and then charge a per-unit cost for consumption of the good after that. The standard example is an amusement park where the firm charges an entry fee and a charge for the rides inside the park. Such a pricing policy is known as a two part tariff. Suppose that the cost of providing the service is c(x). If the monopolist sets a two part tariff, will it produce more or less than the efficient level of output?(b) Assume these firms behave like price takers, how much will they produce and what price will they charge? Draw the outcome on a graph. What is the individual firms producer surplus? What is the total producer surplus of the market? (3 marks) (c) Suppose the four firms join together to form a single firm monopoly. What price will the cartel charge and how much output does the cartel produce? What is producer surplus for the cartel? (Hint: the marginal cost curve for the cartel firm is the supply curve found in part (a) with MC replacing P in this equation and MR = 200 -Q). What happens to consumer surplus and total welfare? (4 marks) 4. Calculate the own price elasticity of demand in the following situations (a) A price rise from po = 2 to p1 = 5 causes quantity demand to fall from go = 30 to q1 = 15 (1 mark) (b) The demand curve is given by q = 1/p with the slope of the demand curve given by $ = -1/p2. What is the own price elasticity of demand at any point?(2 marks) (c) The demand curve is given by q = 4 - 2p with the slope of the demand curve given by dp = -2. What is the own price clasticity of demand at: (i) p = 4; and (ii) p = 10? (2 marks) 5. Suppose the cost of producing q cars and q2 trucks is 45000 +80q1 + 10092. Calculate the measure of economies of scope when (1 mark each): (a) q1 = 100 and q2 = 200 (b) q1 = 500 and q2 = 800 6. Answer the following questions True, False, or Uncertain. Give a brief explanation of your answer. 1 mark for correctly identifying T, F. or U. 4 marks for explanation. (a) If a single price monopoly is instituted in what was a competitive market, consumer surplus will decrease more than producers gain. (b) If a firm's marginal cost is less than the firm's marginal revenue then the firm should decrease output and increase price. (c) If price is less than average cost then a firm will shut down. (d) A monopolist does not make a shutdown decision in the short-run and an exit decision in the long run since only competitive firms make these decisions