ECON 200. Introduction to Microeconomics Homework 3 Part II Name:________________________________________ [Multiple Choice] 1. When the government imposes a binding price floor, it causes (d) a. the supply curve to shift to the left. b. the demand curve to shift to the right. c. a shortage of the good to develop. d. a surplus of the good to develop. 2. In a market with a binding price ceiling, an increase in the ceiling will ___________ the quantity supplied, ___________ the quantity demanded, and reduce the ___________. (c) a. increase, decrease, surplus b. decrease, increase, surplus c. increase, decrease, shortage d. decrease, increase, shortage 3. A $1 per unit tax levied on consumers of a good is equivalent to (a) a. a $1 per unit tax levied on producers of the good. b. a $1 per unit subsidy paid to producers of the good. c. a price floor that raises the good’s price by $1 per unit. d. a price ceiling that raises the good’s price by $1 per unit. 4. Which of the following would increase quantity supplied, decrease quantity demanded, and increase the price that consumers pay? (a) a. the imposition of a binding price floor b. the removal of a binding price floor c. the passage of a tax levied on producers d. the repeal of a tax levied on producers 5. When a good is taxed, the burden of the tax falls mainly on consumers if (d) a. the tax is levied on consumers. b. the tax is levied on producers. c. supply is inelastic, and demand is elastic. d. supply is elastic, and demand is inelastic. 6. Jane pays Chuck $50 to mow her lawn every week. When the government levies a mowing tax of $10 on Chuck, he raises his price to $60. Jane continues to hire him at the higher price. What is the change in producer surplus, change in consumer surplus, and deadweight loss? (b) a. $0, $0, $10 b. $0, -$10, $0 c. +$10, -$10, $10 d. +$10, -$10, $0 7. Eggs have a supply curve that is linear and upward-sloping and a demand curve that is linear and downward sloping. If a 2 cent per egg tax is increased to 3 cents, the deadweight loss of the tax (c) a. increases by less than 50 percent and may even decline. b. increases by exactly 50 percent. c. increases by more than 50 percent. d. The answer depends on whether supply or demand is more elastic. 8. If a policymaker wants to raise revenue by taxing goods while minimizing the deadweight losses, he should look for goods with __________ elasticities of demand and __________ elasticities of supply. (a) a. small, small b. small, large c. large, small d. large, large [Short Answer] 1. Which causes a shortage of a good: price ceiling or a price floor? Justify your answer with a graph. A shortage of a good arises when there is a binding price ceiling. A binding price ceiling is one that is placed below the market equilibrium price. This leads to a shortage because quantity demanded exceeds quantity supplied. 2. The government has decided that the free-market price of cheese is too low. a. Suppose the government imposes a binding price floor in the cheese market. Draw a supply-anddemand diagram to show the effect of this policy on the price of cheese and the quantity of cheese sold. Is there a shortage or surplus of cheese? The imposition of a binding price floor in the cheese market is shown in the figure. In the absence of the price floor, the price would be P1 and the quantity would be Q1. With the floor set at Pf, which is greater than P1, the quantity demanded is Q2, while quantity supplied is Q3, so there is a surplus of cheese in the amount Q3 – Q2. b. Producers of cheese complain that the price floor has reduced their total revenue. Is this possible? Explain. The producers’ complaint that their total revenue has declined is correct if demand is elastic. With elastic demand, the percentage decline in quantity would exceed the percentage rise in price, so total revenue would decline. c. In response to cheese producers’ complaints, the government agrees to purchase all the surplus cheese at the price floor. Compared to the basic price floor, who benefits from this new policy? Who loses? If the government purchases all the surplus cheese at the price floor, producers benefit and taxpayers lose. Producers would produce quantity Q3 of cheese, and their total revenue would increase substantially. However, consumers would buy only quantity Q2 of cheese, so they are in the same position as before. Taxpayers lose because they would be financing the purchase of the surplus cheese through higher taxes. 3. A recent study found that the demand and supply schedules for Frisbees are as follows: Price per Frisbee $11 10 9 8 7 6 Quantity demanded Quantity supplied 1 million Frisbee 2 4 6 8 10 15 million Frisbee 12 9 6 3 1 a. What are the equilibrium price and quantity of Frisbees? The equilibrium price of Frisbees is $8 and the equilibrium quantity is six million Frisbees. b. Frisbee manufacturers persuade the government that Frisbee production improves scientists’ understanding of aerodynamics and thus is important for national security. A concerned Congress votes to impose a price floor $2 above the equilibrium price. What is the new market price? How many Frisbees are sold? With a price floor of $10, the new market price is $10 because the price floor is binding. At that price, only two million Frisbees are sold, because that is the quantity demanded. c. Irate college students march on Washington and demand a reduction in the price of Frisbees. An even more concerned Congress votes to repeal the price floor and impose a price ceiling $1 below the former price floor. What is the new market price? How many Frisbees are sold? If there’s a price ceiling of $9, it has no effect, because the market equilibrium price is $8, which is below the ceiling. So the market price is $8 and the quantity sold is six million Frisbees. 4. Suppose the federal government requires beer drinkers to pay a $2 tax on each case of beer purchased. (In fact, both the federal and state governments impose beer taxes of some sort.) a. Draw a supply-and-demand diagram of the market for beer without the tax. Show the price paid by consumers, the price received by producers, and the quantity of beer sold. What is the difference between the price paid by consumers and the price received by producers? The figure shows the market for beer without the tax. The equilibrium price is P1 and the equilibrium quantity is Q1. The price paid by consumers is the same as the price received by producers, P1. b. Now draw a supply-and-demand diagram for the beer market with the tax. Show the price paid by consumers, the price received by producers, and the quantity of beer sold. What is the difference between the price paid by consumers and the price received by producers? Has the quantity of beer sold increased or decreased? When the tax is imposed, it drives a wedge of $2 between supply and demand, as shown in the figure. The price paid by consumers is P2, while the price received by producers is P2 – $2. The difference between the price paid by consumers and the price received by producers is the $2 tax. The quantity of beer sold declines to Q2 5. Congress and the president decide that the United States should reduce air pollution by reducing its use of gasoline. They impose a $0.50 tax on each gallon of gasoline sold. a. Should they impose this tax on producers or consumers? Explain carefully using a supply-and-demand diagram. It does not matter whether the tax is imposed on producers or consumersthe effect will be the same. With no tax, as shown in the figure, the demand curve is D1 and the supply curve is S1. If the tax is imposed on producers, the supply curve shifts upward by the amount of the tax (50 cents) to S2. Then the equilibrium quantity is Q2, the price paid by consumers is P2, and the price received (after taxes are paid) by producers is P2 – 50 cents. If the tax is instead imposed on consumers, the demand curve shifts downward by the amount of the tax (50 cents) to D2. The downward shift in the demand curve (when the tax is imposed on consumers) is exactly the same magnitude as the upward shift in the supply curve when the tax is imposed on producers. So again, the equilibrium quantity is Q2, the price paid by consumers is P2 (including the tax paid to the government), and the price received by producers is P2 – 50 cents b. If the demand for gasoline were more elastic, would this tax be more effective or less effective in reducing the quantity of gasoline consumed? Explain with both words and a diagram. The more elastic the demand curve is, the more effective this tax will be in reducing the quantity of gasoline consumed. Greater elasticity of demand means that quantity falls more in response to the rise in the price. The figure illustrates this result. Demand curve D1 represents an elastic demand curve, while demand curve D2 is more inelastic. The tax will cause a greater decline in the quantity sold when demand is elastic c. Are consumers of gasoline helped or hurt by this tax? Why? The consumers of gasoline are hurt by the tax because they get less gasoline at a higher price d. Are workers in the oil industry helped or hurt by this tax? Why? Workers in the oil industry are hurt by the tax as well. With a lower quantity of gasoline being produced, some workers may lose their jobs. With a lower price received by producers, wages of workers might decline 6. A case study in this chapter discusses the federal minimum-wage law. a. Suppose the minimum wage is above the equilibrium wage in the market for unskilled labor. Using a supply-and-demand diagram of the market for unskilled labor, show the market wage, the number of workers who are employed, and the number of workers who are unemployed. Also show the total wage payments to unskilled workers. The figure shows the effects of the minimum wage. In the absence of the minimum wage, the market wage would be w1 and Q1 workers would be employed. With the minimum wage (wm) imposed above w1, the market wage is wm, the number of employed workers is Q2, and the number of workers who are unemployed is Q3 − Q2. Total wage payments to workers are shown as the area of rectangle ABCD, which equals wm times Q2 b. Now suppose the secretary of labor proposes an increase in the minimum wage. What effect would this increase have on employment? Does the change in employment depend on the elasticity of demand, the elasticity of supply, both elasticities, or neither? An increase in the minimum wage would decrease employment. The size of the effect on employment depends only on the elasticity of demand. The elasticity of supply does not matter, because there is a surplus of labor c. What effect would this increase in the minimum wage have on unemployment? Does the change in unemployment depend on the elasticity of demand, the elasticity of supply, both elasticities, or neither? The increase in the minimum wage would increase unemployment. The size of the rise in unemployment depends on both the elasticities of supply and demand. The elasticity of demand determines the change in the quantity of labor demanded, the elasticity of supply determines the change in the quantity of labor supplied, and the difference between the quantities supplied and demanded of labor is the amount of unemployment d. If the demand for unskilled labor were inelastic, would the proposed increase in the minimum wage raise or lower total wage payments to unskilled workers? Would your answer change if the demand for unskilled labor were elastic? If the demand for unskilled labor were inelastic, the rise in the minimum wage would increase total wage payments to unskilled labor. With inelastic demand, the percentage decline in employment would be lower than the percentage increase in the wage, so total wage payments increase. However, if the demand for unskilled labor were elastic, total wage payments would decline, because then the percentage decline in employment would exceed the percentage increase in the wage 7. At Fenway Park, home of the Boston Red Sox, seating is limited to 39,000. Hence, the number of issued is fixed at that figure. Seeing a golden opportunity to raise revenue, the City of Boston levies a per ticket tax of $5 to be paid by the ticket buyer. Boston sports fans, a famously civic-minded lot, dutifully send in the $5 per ticket. Draw a well-labeled graph showing the impact of the tax. On whom does the tax burden fall - the team’s owners, the fans, or both? Why? Since the supply of seats is perfectly inelastic, the entire burden of the tax will fall on the team’s owners. The figure shows that the price the buyers pay for the tickets will fall by the exact amount of the tax 8. A subsidy is the opposite of a tax. With a $0.50 tax on the buyers of ice-cream cones, the government collects $0.50 for each cone purchased; with a $0.50 subsidy for the buyers of ice-cream cones, the government pays buyers $0.50 for each cone purchased. a. Show the effect of a $0.50 per cone subsidy on the demand curve for ice-cream cones, the effective price paid by consumers, the effective price received by sellers, and the quantity of cones sold. The effect of a $0.50 per cone subsidy is to shift the demand curve upward by $0.50 at each quantity, because at each quantity a consumer's willingness to pay is $0.50 higher. The effects of such a subsidy are shown in the figure. Before the subsidy, the price is P1. After the subsidy, the price received by sellers is PS and the effective price paid by consumers is PD, which equals PS minus $0.50. Before the subsidy, the quantity of cones sold is Q1; after the subsidy the quantity increases to Q2 b. Do consumers gain or lose from this policy? Do producers gain or lose? Does the government gain or lose? Consumers are better off with the subsidy, because they consume more at a lower price. Producers are also better off, because they sell more at a higher price. The government loses, because it has to pay for the subsidy 9. Draw a supply-and-demand diagram with a tax on the sale of a good. Show the deadweight loss. Show the tax revenue. The figure illustrates the deadweight loss and tax revenue from a tax on the sale of a good. Without a tax, the equilibrium quantity would be Q1, the equilibrium price would be P1, consumer surplus would be A + B + C, and producer surplus would be D + E + F. The imposition of a tax places a wedge between the price buyers pay, PB, and the price sellers receive, PS, where PB = PS + tax. The quantity sold declines to Q2. Now consumer surplus is A, producer surplus is F, and government revenue is B + D. The deadweight loss of the tax is C+E, because that area is lost due to the decline in quantity from Q1 to Q2. 10. How do the elasticities of supply and demand affect the deadweight loss of a tax? Why do they have this effect? The greater the elasticities of demand and supply, the greater the deadweight loss of a tax. Because elasticity measures the responsiveness of buyers and sellers to a change in price, higher elasticity means the tax induces a greater reduction in quantity, and therefore, a greater distortion to the market. 11. The market for pizza is characterized by a downward-sloping demand curve and an upward-sloping supply curve. a. Draw the competitive market equilibrium. Label the price, quantity, consumer surplus, and producer surplus. Is there any deadweight loss? Explain. The figure illustrates the market for pizza. The equilibrium price is P1, the equilibrium quantity is Q1, consumer surplus is area A + B + C, and producer surplus is area D + E + F. There is no deadweight loss, as all the potential gains from trade are realized; total surplus is the entire area between the demand and supply curves: A + B + C + D + E + F. b. Suppose that the government forces each pizzeria to pay a $1 tax on each pizza sold. Illustrate the effect of this tax on the pizza market, being sure to label the consumer surplus, producer surplus, government revenue, and deadweight loss. How does each area compare to the pre-tax case? With a $1 tax on each pizza sold, the price paid by buyers, PB, is now higher than the price received by sellers, PS, where PB = PS + $1. The quantity declines to Q2, consumer surplus is area A, producer surplus is area F, government revenue is area B + D, and deadweight loss is area C + E. Consumer surplus declines by B + C, producer surplus declines by D + E, government revenue increases by B + D, and deadweight loss increases by C + E. c. If the tax were removed, pizza eaters and sellers would be better off, but the government would lose tax revenue. Suppose that consumers and producers voluntarily transferred some of their gains to the government. Could all parties (including the government) be better off than they were with a tax? Explain using the labeled areas in your graph. If the tax were removed and consumers and producers voluntarily transferred B + D to the government to make up for the lost tax revenue, then everyone would be better off than without the tax. The equilibrium quantity would be Q1, as in the case without the tax, and the equilibrium price would be P1. Consumer surplus would be A + C, because consumers get surplus of A + B + C, then voluntarily transfer B to the government Producer surplus would be E + F, because producers get surplus of D + E + F, then voluntarily transfer D to the government. Both consumers and producers are better off than the case when the tax was imposed. If consumers and producers gave a little bit more than B + D to the government, then all three parties, including the government, would be better off. This illustrates the inefficiency of taxation 12. Consider the market for rubber bands. a. If this market has very elastic supply and very inelastic demand, how would the burden of a tax on rubber bands be shared between consumers and producers? Use the tools of consumer surplus and producer surplus in your answer. With very elastic supply and very inelastic demand, the burden of the tax on rubber bands will be borne largely by buyers. As the figure shows, consumer surplus declines considerably, by area A + B, but producer surplus decreases only by area C+D b. If this market has very inelastic supply and very elastic demand, how would the burden of a tax on rubber bands be shared between consumers and producers? Contrast your answer with your answer to part (a). With very inelastic supply and very elastic demand, the burden of the tax on rubber bands will be borne largely by sellers. As the figure shows, consumer surplus does not decline much, just by area A + B, while producer surplus falls substantially, by area C + D. Compared to part (a), producers bear much more of the burden of the tax, and consumers bear much less 13. Suppose that the government imposes a tax on heating oil. a. Would the deadweight loss from this tax likely be greater in the first year after it is imposed or in the fifth year? Explain. The deadweight loss from a tax on heating oil is likely to be greater in the fifth year after it is imposed rather than the first year. In the first year, the demand for heating oil is relatively inelastic, as people who own oil heaters are not likely to get rid of them right away. But over time they may switch to other energy sources and people buying new heaters for their homes will more likely choose gas or electric, so the tax will have a greater impact on quantity. Thus, the deadweight loss of the tax will get larger over time b. Would the revenue collected from this tax likely be greater in the first year after it is imposed or in the fifth year? Explain. The tax revenue is likely to be higher in the first year after it is imposed than in the fifth year. In the first year, demand is more inelastic, so the quantity does not decline as much and tax revenue is relatively high. As time passes and more people substitute away from oil, the quantity sold declines, as does tax revenue 14. Suppose that the government subsidizes a good: For each unit of the good sold, the government pays $2 to the buyer. How does the subsidy affect consumer surplus, producer surplus, tax revenue, and total surplus? Does a subsidy lead to a deadweight loss? Explain. The figure illustrates the effects of the $2 subsidy on a good. Without the subsidy, the equilibrium price is P1 and the equilibrium quantity is Q1. With the subsidy, buyers pay price PB, producers receive price PS (where PS = PB + $2), and the quantity sold is Q2. The following table illustrates the effect of the subsidy on consumer surplus, producer surplus, government revenue, and total surplus. Because total surplus declines by area D + H, the subsidy leads to a deadweight loss in that amount Before Subsidy After Subsidy Change Consumer Surplus A+B A+B+E+F+G +(E + F + G) Producer Surplus E+I B+C+E+I +(B + C) Government Revenue 0 –(B + C + D + E + F + G + H) –(B + C + D + E + F + G + H) Total Surplus A+B+E+I A+B–D+E–H+I –(D + H) 15. Hotel rooms in Smalltown go for $100, and 1,000 rooms are rented on a typical day. a. To raise revenue, the mayor decides to charge hotels a tax of $10 per rented room. After the tax is imposed, the going rate for hotel rooms rises to $108, and the number of rooms rented falls to 900. Calculate the amount of revenue this tax raises for Smalltown and the deadweight loss of the tax. (Hint: The area of a triangle is 1/2 x base x height.) The figure shows the effect of a $10 tax on hotel rooms. The tax revenue is represented by areas A + B, which are equal to ($10)(900) = $9,000. The deadweight loss from the tax is represented by areas C + D, which are equal to (0.5)($10)(100) = $500 b. The mayor now doubles the tax to $20. The price rises to $116, and the number of rooms rented falls to 800. Calculate tax revenue and deadweight loss with this larger tax. Are they double, more than double, or less than double? Explain. The figure shows the effect of a $20 tax on hotel rooms. The tax revenue is represented by areas A + B, which are equal to ($20)(800) = $16,000. The deadweight loss from the tax is represented by areas C + D, which are equal to (0.5)($20)(200) = $2,000. When the tax is doubled, the tax revenue rises by less than double, while the deadweight loss rises by more than double. The higher tax creates a greater distortion to the market 16. Suppose that a market is described by the following supply and demand equations: QS = 2P QD = 300-P a. Solve for the equilibrium price and the equilibrium quantity. Setting quantity supplied equal to quantity demanded gives 2P = 300 – P. Adding P to both sides of the equation gives 3P = 300. Dividing both sides by 3 gives P = 100. Substituting P = 100 back into either equation for quantity demanded or supplied gives Q = 200 b. Suppose that a tax of T is placed on buyers, so the new demand equation is QD = 300-(P+T) Solve for the new equilibrium. What happens to the price received by sellers, the price paid by buyers, and the quantity sold? Now P is the price received by sellers and P +T is the price paid by buyers. Equating quantity demanded to quantity supplied gives 2P = 300 − (P+T). Adding P to both sides of the equation gives 3P = 300 – T. Dividing both sides by 3 gives P = 100 –T/3. This is the price received by sellers. The buyers pay a price equal to the price received by sellers plus the tax (P +T = 100 + 2T/3). The quantity sold is now Q = 2P = 200 – 2T/3 c. Tax revenue is T x Q. Use your answer to part (b) to solve for tax revenue as a function of T. Graph this relationship for T between 0 and 300. Because tax revenue is equal to T x Q and Q = 200 – 2T/3, tax revenue equals 200T − 2T 2 /3. The figure shows a graph of this relationship. Tax revenue is zero at T = 0 and at T = 300 d. The deadweight loss of a tax is the area of the triangle between the supply and demand curves. Recalling that the area of a triangle is 1/2 x base x height, solve for deadweight loss as a function of T. Graph this relationship for T between 0 and 300. (Hint: Looking sideways, the base of the dead-weight loss triangle is T, and the height is the difference between the quantity sold with the tax and the quantity sold without the tax.) As the left figure shows, the area of the triangle (laid on its side) that represents the deadweight loss is 1/2 × base × height, where the base is the change in the price, which is the size of the tax (T) and the height is the amount of the decline in quantity (2T/3). So the deadweight loss equals 1/2 × T × 2T/3 = T 2 /3. This rises exponentially from 0 (when T = 0) to 30,000 when T = 300, as shown in the right figure e. The government now levies a tax on this good of $200 per unit. Is this a good policy? Why or why not? Can you propose a better policy? A tax of $200 per unit is a bad policy, because tax revenue is declining at that tax level. The government could reduce the tax to $150 per unit, get more tax revenue ($15,000 when the tax is $150 versus $13,333 when the tax is $200), and reduce the deadweight loss (7,500 when the tax is $150 compared to 13,333 when the tax is $200).
