1. The elected officials in a southern university town are concerned about the \"exploitative" rents being charged to college students. The town council is contemplating the imposition of a $350 per month rent ceiling on apartments in the city. An economist at the university estimates the demand and supply curves as: Qo = 5600 BP 05 = 500 + 4P, where P = monthly rent. and Q = number of apartments available for rent. For purposes of this analysis, apartments can be treated as identical. (a) Calculate the equilibrium price and quantity that would prevail without the price ceiling. Calculate producer and consumer surplus at this equilibrium (sketch a diagram showing both). (b) What quantity will eventually be available if the rent ceiling is imposed? Calculate any gains or losses in consumer andlor producer surplus. [hintz if demand exceeds supply, producers produce at the demand level] (c) Does the proposed rent ceiling result in net welfare gains? Would you advise the town council to implement the policy? (d) Are all consumers betterlworse off with the rent ceiling policy? Explain In a city with a medium sized population, the equilibrium price for a city bus ticket is $1, and the number of riders each day is 10,800. The short-run price elasticity of demand is -0.6, and the short-run elasticity of supply is 1. (a) Estimate the short run linear supply and demand curves for bus tickets. (b) If the demand for bus tickets increased by 10% because of a rise in the world price of oil, what would be the new equilibrium price of bus tickets? (c) If the city council refused to let the bus company raise the price of bus tickets after the demand for tickets increases (see (b) above), what daily shortage of tickets would be created? (cl) Would the bus company have an incentive to increase the supply in the long run given the city council's decision in (c) above? Explain your answer. Two firms compete by choosing a price. That is, a price competition. Their demand functions are 01:20P1+P2 and Q2=20+P1P2 where P1 and P2 are the prices charged by each firm, respectively, and 01 and Q2 are the resulting demands. Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high as they wanted, and earn infinite profits. Marginal costs are zero. (a) Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.) (b) Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will it sell, and what will its profit be? 4. For each city across the U.S., economists construct a price index for a similar basket of goods. In Los Angeles the index is 127.3 and the index for Dallas is 94.8. If you have been offered $137,000 for a job in Los Angeles and $117,000 for a similar job in Dallas, which job affords you the highest purchasing power of the bundle of goods in the price index? Use the Los Angeles value as the base.5. Silverscreen Movie Rentals has market power in the previously viewed video sales market. The demand curve for Silverscreen movies is QP = 10 - 0.4P. Silverscreen's marginal cost curve is MC(Q) = 0.53 + 0.026Q. (a) Determine Silverscreen's profit maximizing price. (b) Calculate Silverscreen's elasticity of demand at this price. (c) What is Silverscreen's mark-up over marginal cost as a percentage of price?6.. In the local cotton market, there are 1,000 producers that have identical short-run cost functions. They are: C(q) = 0.025q2 + 200, where q is the number of bales produced each period. (a) If the local cotton market is perfectly competitive, what is each cotton producer's short-run supply curve? (b) Derive the local market supply curve of cotton. (c) Assume the market demand for cotton is given by QD = 400, 000 20, OOOP find the market equilibrium price and quantity produced by each seller. (d) Do you think the number of sellers would go up or down in the long run? Two firms at the Burlington airport have franchises to carry passengers to and from hotels in downtown Burlington. These two firms, Teddy Limo and Walker Limo, operate nine passenger vans. These duopolists cannot compete with price, but they can compete through advertising. Their payoff matrix is below: Walker Limo _ Increase Ads iDon't Increase Ads i w Increase Ads 25,15 i 30,0 i Don't Increase Ads 15,20 i 40,5 ' (a) Does each firm have a dominant strategy? If so, explain and what that strategy is. (b) What is the Nash equilibrium? Explain where the Nash equilibrium occurs in the payoff matrix