Homework 4 Economics 501.01 Manisha Goel Due: Tuesday, March 1, 011 (beginning of class). Draw and label all graphs clearly. Show all work. Explain. Question 1. Governments often regulate the price of apartments. The best example is in New York City where many people (including some government officials and famous celebrities) rent apartments for a small fraction of their market clearing price. The government imposes these rent regulations in order to make apartments more affordable. Assume that the demand for apartments is given by Q D 0 P. The supply of apartments is given by Q S P. i) Graph the supply and demand for apartments. Show where each curve crosses each axis. Calculate the equilibrium price and quantity of apartments. Show these on your graph. Note: these supply and demand curves are like the one s we have been using all quarter except that the number multiplying P in each is 1 and the constant term in the supply function is 0. This should make them relatively easy to plot. If it helps, think about them as Q D 0 1P and Q S 0 1P. ii) On your graph indicate the original consumer and producer surplus (CS and PS). Calculate each. iii) To make apartments more affordable, the government restricts the price to 5. What is the quantity demanded at 5? What is the quantity supplied? What is the excess demand? On a new graph show the price ceiling, the quantity demanded, the quantity supplied, and the excess demand. iv) On your new graph indicate the new consumer and producer surplus (CS and PS). Show the deadweight loss from the price ceiling (Loss). Calculate the new consumer and producer surplus. Question. The demand for a monopolist s product is given by QD 0 P. In this case, the firm s marginal revenue is given by MR 0 Q (note that this is a function of Q). The firm s marginal cost is given by MC Q. If we assume that the firm has no fixed costs, it s average total cost curve is given by ATC Q. i) Graph the monopolist s demand, marginal revenue, marginal cost, and average total cost curves. Indicate where the curves cross the axes. ii) Calculate the monopolist s optimal output and the monopoly price. Show them on your graph. Show the profits per unit on your graph. iii) Compute the competitive price and quantity. Show these on your graph.
iv) On your graph indicate the areas corresponding to the (1) the consumer surplus under monopoly, () the portion of the consumer surplus under competition that the monopolist captures, (3) the deadweight loss of the monopoly. You should number the areas on your graph in this way for clarity. What is the producer surplus under monopoly? What would the firm s producer surplus be under competition? v) If the government wanted to achieve the efficient output how would it regulate the price the firm charges? Question 3. A country which does not tax cigarettes is considering the introduction of a $0.40 per pack tax. The economic advisors to the country estimate the supply and demand curves for cigarettes as: Q D = 140,000-5,000P and Q S = 0,000 + 75,000P, where Q = daily sales in packs of cigarettes, and P = price per pack. The country has hired you to provide the following information regarding the cigarette market and the proposed tax. i) What are the equilibrium values in the current environment with no tax? ii) What price and quantity would prevail after the imposition of the tax? What portion of the tax would be borne by buyers and sellers respectively? iii) Calculate the deadweight loss from the tax. Could the tax be justified despite the deadweight loss? What tax revenue will be generated? Question 4. McCullough has a monopoly on rental dwellings in the local community. The demand for rental dwellings is Q D = 70,000-50P P = 1,400-0.0Q D. The resulting marginal revenue function is MR(Q) = 1,400-0.04Q D. McCulloughʹs marginal cost of providing rental dwellings is MC(Q) = 0.01Q + 0. Suppose that to ease the burden on renters, the local community has instituted a price ceiling of $480. i) Does consumer surplus increase due to this price ceiling? ii) Does social welfare increase as a result of the price ceiling? Question 1. Extra Practice Questions With Answers Consider a competitive market with supply and demand curves expressed as: Supply: P = 5 + 0.036Q, Demand: P = 50-0.04Q, where P represents unit price in dollars and Q represents sales rate in units per day. i) Determine the equilibrium price and sales rate. ii) If this were the labor market for low skilled workers, what would be the loss in consumer surplus (purchaser surplus) when the minimum wage is set at $40 per day (an eight hour day)?
iii) What is the loss or gain in producer surplus (seller surplus) in part b. above? Answer i) Equilibrium price (wage rate) and sales rate (employment rate) are computed as follows: 5 + 0.036Q = 50-0.04Q 0.076Q = 45 Q = 59.11 units per day Wage rate = P = 50 -.04(59.11) = $6.3 per day ii) iii) Consumer surplus lost would be the area bounded by the minimum wage $40, the market equilibrium wage $6.3, the employment rates, before and after wages, and zero employment. We have a trapezoid made up of a rectangle and a triangle. The rectangle is bounded by the two wages, zero sales, and sales rate at the minimum wage. Height of rectangle = W M - W E = 40-6.3 = 13.68 Base of rectangle = Q M =? P M = 50-0.04Q M 40 = 50-0.04Q M Q M = 50 Area of rectangle = b h = (50)(13.68) = 3,40. Area of triangle with base measured on the vertical. Base length = P M - P E = 13.68 Height = Q E - Q M = 59.11-50 = 34.11 Area = (1/)b h = (0.5)(13.68)(34.11) =,340 Thus, consumer surplus lost = 340 + 340 = $5760 per day. The producer surplus also has two parts. Producers gain the surplus in the rectangle lost by consumers in part b. Area = 3,40. But, the loss in employment (sales) represents a loss in surplus. This loss is a triangle bounded by supply, equilibrium wage rate, and the two levels of employment (sales rates). The only thing left to compute is the height of the supply curve at Q M = 50. Supply P = 5 + 0.036(50) = 14. The area of the triangle of loss is (1/)(b h). Base = b = 34.11 (measured horizontally). Height = h = 6.3-14 = 1.3. Area of triangle = (0.5)(34.11)(1.3) =,107.40. Net change in producer surplus = $340-107.40 = $1,31.60 Question. This question continues the cigarette example from Homework 3. Before we get started, some facts are in order. The fine the government imposed on cigarette companies has a small fixed
component. Most of the fine depends on the number of cigarettes each firm sells. Essentially, it is a tax on cigarettes that is imposed on producers. Assume that the demand for cigarettes is given by Q D 300 1/ P and that the supply is given by P. We are measuring the price in cents here. (If it helps you to think about it, Q S perhaps the quantity is in billions of cigarettes.) The inverse demand curve is P D 600 Q. The inverse supply curve is given by P S Q. i) Graph the demand and supply curves. Calculate the equilibrium price and quantity (in the absence of any fine). Show these on your graph. What is the price elasticity of demand at the equilibrium point? ii) Now assume that the fine is 60 cents per pack. Calculate the equilibrium quantity and the price paid by consumers and producers. Show these on your graph. iii) Calculate the new producer and consumer surpluses, the government s revenue, and the iv) deadweight loss. Indicate each area on your graph. Based on your answer how much of the tax ends up being paid producers? How much is paid by consumers? v) The government says that this fine will finally make cigarette companies pay for the harm they have caused smokers. For their part, cigarette manufacturers expended enormous lobbying resources to make sure that the fine would depend on output. Contrast the outcome under the fine that depends on output (analyzed here) to the fine that did not depend on output (which you analyzed in question of problem set 3). In answering this question be sure to (1) explain why cigarette companies favored a fine that did depend on output to one that did not and () analyze the government s argument that cigarette companies will pay for the harm they caused smokers. Answer i) The original equilibrium is where QS QD. In this case, 1 3 P 300 P; P 300; P 00 QD P 1 00 1 The quantity is 00. The price elasticity of demand is E P. P Q 00 D ii) With a tax the price consumers pay, P D, exceeds the price producers receive, P S, by the amount of the tax, PS PD t. Substitute the inverse D- and S- curves into this formula to obtain the solution: Q 600 Q 60; 3Q 540; Q 180 This gives us the quantity, which is the same for both. We can solve for the prices, which will be different for producers and consumers, by plugging this quantity into the inverse demand and supply curves. Doing so essentially asks how much consumers would pay for the 180 th unit of cigarettes or how much producers would need to produce 180 units. P D 600 Q 600 (180) 40 P S Q 180 These are the producer s and consumer s prices which differ by the amount of the tax.
P 600 QS(P) PD=40 00 PS=180 iii) CS CS Rev. PS 180 (360)(180) Loss 00 3,400 t=60 QD(P) 300 Q PS (180)(180) 60 * 0 16,00 Loss 600 Revenue Q* t 180*60 10,800 iv) The price paid by consumers rises from 00 to 40. Thus they pay 40 more per unit. The total amount paid by consumers is 40*180 700. The price received by producers declines from 00 to 180. Thus they receive 0 less per unit. The total amount producers pay in the form of lower (net) prices is 0*180 3600. Thus consumers pay /3 rds of the tax while producers pay 1/3 rd. v) If the fine does not depend on output (as was the case in HW 3) then it will be a fixed cost to firms. Provided, the companies remain in business, the price and output will remain the same. If the price and output remain the same then the firms pay the entire fine amount. Consumers pay none of the fine in the form of higher prices. With a fine that does depend on output, some of the fine gets passed through to consumers (here 67% of it) in the form of higher prices while producers pay less of the fine. Producers favor a fine that does depend on output (i.e. a tax) because they pay only a portion of it. The government s claim that they are making producers pay seems is fairly weak because a large portion of the tax ends up being paid by cigarette consumers not by producers.