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Intermediate Microeconomics ECO 340 Problem Set 5

1. (12 Points) In a perfect competitive market, the demand curve is given by = 200 ? 2and the supply curve is given by = 4 ? 40.a. (4 Points) What are the equilibrium quantity and equilibrium price in this market?Compute the price elasticity of demand and supply at the equilibrium.b. (4 Points) If a $4 excise tax is levied on consumers, what is the incidence of the taxon the firm (?Ps) and consumers (?Pd)? Please explain why the incidence of the tax issplit this way.c. (4 Points) Find the new price paid by consumers, the price received by firms, and thequantity traded in the market. Compute the consumer surplus, producer surplus,government revenue, and deadweight loss due to the tax. Graph the marketequilibrium and identify as many points as you can.2. (12 points) Assume the supply and demand for a large pepperoni pizzas is = 250 ? 3and = 6 ? 20. Now the government imposes a price ceiling for pepperoni pizza atPc=$10.a. (2 points) Compute the equilibrium quantity and price without the price ceiling. Findthe amount of the shortage due to the price ceilingb. (5 Points) Assume that the consumers who are able to buy the product are the oneswith the highest willingness to pay. What is the consumer surplus, the producersurplus and the total surplus in this case? Compute the deadweight loss in thisscenario.c. (5 Points) Assume that the consumers who are able to buy the product are the oneswith the lowest willingness to pay, but are still willing to pay at least 10 for a largepepperoni pizza. What is the consumer surplus, the producer surplus and the totalsurplus in this case? Compute the deadweight loss in this scenario. 3. (11 pts) The domestic demand curve for olive oil is given by Qd = 50 ?0.5P. Thedomestic supply curve for olive oil is given by Qs = 2P. Suppose olive oil can beobtained in the world market at a price of $10 for a 16oz bottle.a. (5 pts) Draw a graph illustrating the free trade equilibrium. Clearly illustrate theequilibrium price, the number of units produced domestically, and the number ofunits imported. Estimate and clearly identify in your graph the domestic consumersurplus and the domestic producer surplus.b. (6 pts) Domestic olive oil producers have successfully lobbied Congress toimpose a tariff of $4 per bottle. Draw a graph illustrating the equilibrium with thetariff. Clearly illustrate the equilibrium price, the amount produced domestically,and the amount imported. Estimate and clearly identify in your graph thedomestic consumer surplus, the domestic producer surplus, the governmentrevenue, and the deadweight loss from the tariff. 4. (15 pts) Suppose you are a monopolist operating two plants at different locations. Thequantity produced in the two plants are 1 2 . The cost function for the two plantsare 1 = 2 + 0.51 2 and 2 = 2 + 1.52 2 . The demand in the market is = 14 ? 0.5.a. (10 pts) What is the optimal level of output for each plant? What is the price thatmaximize profits? Explain why the output is split this way between the twoplants. Compute the total profits for the monopolist?b. (5 pts) Compute the elasticity of demand at the profit-maximizing output andprice. Compute and interpret the Lerner index and the Markup factor for this firm.5. (15 pts) Assume that a corn farmer is the only employer in a small town in Indiana. As alocal non-discriminating monopsonist, the farmer faces a labor supply curve given by:L = 5W –10, where L is the number of workers hired each hour and w is the hourly wagerate. Assume, the production function for corn workers is given by Q=6L. Where theoutput (Q) has a price of $5 per unit in a perfectly competitive output market.a. (5 pts) Find the farmer’s profit maximizing level of employment, the optimalwage it would pay to its workers, the corresponding level of output, and theoptimal profits. How does this wage compare to Marginal Expenditure on Labor(MEL) and the Marginal Revenue Product of Labor (MRPL)?b. (5 pts) Compute the elasticity of labor supply at the profit-maximizingemployment and wage. Compute and interpret the Lerner index and the Markupfactor for this firm.c. (5 pts) In a single graph, draw the results you found in part (a) and identity theworker surplus, the farmers surplus and the deadweight loss to society fromhaving this monopsony. 6. (20 Points) Assume that a monopolist has many identical consumers and faces an inversedemand curve = 70 ? 0.5. The total cost of production for the firm is C=10.a. (5 pts) Find the optimal price and output if the monopolist uses a uniform pricingstrategy. Compute the consumer surplus, the firm’s profits and the deadweight loss tosociety in this case.b. (5 pts) Describe the optimal first degree price discrimination strategy. Compute theconsumer surplus, the firm’s profits and the deadweight loss to society if thismonopolist engages in first-degree price discrimination.c. (5 pts) Find the optimal second degree price discrimination strategy with twoblocks. In other words, what choices of P1, Q1 for the first block and P2, Q2 for thesecond block will maximize profit? Compute the consumer surplus, the firm’s profits,and the deadweight loss to society under this optimal two-block tariff.d. (5 pts) Find the optimal two-part tariff strategy and the profits under this pricingstrategy? How much extra profits the store earns using this two-part pricing strategycompared with using a uniform pricing strategy.7. (15 Points) Consider a television company that owns two channels. A sport channel and amovie channel. There are four types of costumers with 1 million costumers of each type.Each type willingness to pay and marginal cost for the firm for 2 Channels is summarizedin the following table. Customer 1Customer 2Customer 3Customer 4Marginal Cost=Average Cost Sports20151252 Movies21215152 a. ( 5 pts) If the firm does not bundle the products, what single price should the firmcharge for the Sports channel to maximize profits? What are the profits fromselling the sports channel? What single price should the firm charge for theMovies channel to maximize profit? What are the profits from selling the Movieschannel? What are the total profits for the firm under this pricing strategy?b. (5pts) If the firm bundles the products, what single price should the firm chargefor the bundle to maximize profits? What are the profits from selling the bundle?c. (5pts) If the firm implements a first-degree price discrimination scheme, whatprices should it charge to maximize profits? what are the profits for the firm?

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