Problem set 2 solutions PDF

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Problem set 2: Government Policies

Problem 1. Suppose that your demand schedule for pizza is as follows: Price ($)

Quantity (pieces)

8 10 12 14

40 32 24 16

1. Calculate the price elasticity of demand as the price of pizza increases from $8 to $10. 2. Suppose that at the price of $12, your demand for pizza increases from $24 to $30 as your income increases from $20000 to $24000. Calculate your income elasticity of demand for pizza. Is pizza a normal good or an inferior good? 3. Suppose as the price of pizza increases from $10 to $12, your demand for pasta increases from 20 to 24 servings. Calculate the cross-price elasticity of demand for pasta with respect to the price of pizza. What does this tell you about the relationship between pizza and pasta? Solution. 1. The price elasticity of demand for pizza is (8/40)/(2/8), or 0.8. 2. If income increases from $20,000 to $24,000, the quantity demanded of pizzas at $12 increases from 24 to 30. Hence the income elasticity of demand is (6/24)/(4000/20000) or 1.25. 3. The cross-price elasticity of demand for pasta with respect to the price of pizza is (4/20)/(2/10), or 1 (unit elastic). Problem 2. The government has decided that the free-market price of cheese is too low. 1

1. Suppose the government imposes a binding price floor in the cheese market. Draw a supply-and-demand 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? 2. Farmers complain that the price floor has reduced their total revenue. Is this possible? Explain. 3. In response to farmers’ 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? Solution. 1. The effects of a binding price floor are shown in the figure below. In the absence of the price floor, the price would be PE and the quantity would be Q E . With the floor set at P F , which is greater than PE , the quantity demanded is Q D , while quantity supplied is Q S , so there is a surplus of cheese in the amount Q S − Q D .

2. The farmers’ 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. 3. If the government purchases all the surplus cheese at the price floor, producers benefit and taxpayers lose. Producers would produce quantity Q S of cheese and their total revenue would increase substantially. But consumers would buy only quantity Q D 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. Problem 3. A market is described by the following supply and demand curve: Q = 2P, Q = 300 − P. 2

1. Solve for the equilibrium price and quantity. 2. If the government levies a tax on consumer of $30, will the price paid by consumers rise by more than $30, less than $30 or exactly $30? 3. As a result of the tax, the new demand curve is Q = 300 − ( P + 30 ). What are the price, quantity supplied, quantity demanded, and the size of the shortage or surplus? 4. Instead of a consumption tax, the government levies a tax on producers of $30. As a result, the new supply curve is Q = 2( P − 30 ). What are the price, quantity supplied, quantity demanded, and the size of the shortage or surplus? Solution. 1. Set the two equations equal to each other to find the market equilibrium price. Thus 2P = 300 − P or, 3 P = 300, hence P = $100. Substitute this value of P into either the demand or supply equation. This gives the equilibrium quantity Q = 200. 2. If the government levies a $30 tax on consumers, the price paid by consumers will be rise by less than $30. Both consumers and producers share the burden of the tax. The price paid by consumers rises and the price received by producers falls, with the difference between the two equals to the amount of the tax. 3. Set the new demand equation equal to supply to find the price the buyers pay. Thus 300 − ( P + 30) = 2P or, 3P = 270, hence P = $90. The price consumers pay will be $30 more than the price the sellers receive, or $120. Substituting the value of P into either the demand and supply equation gives the equilibrium quantity Q = 180. The quantity supplied will equal the quantity demanded (180). 4. Set the new supply equation equal to demand, to find the price the buyers pay. This will be $120 and the buyer’s quantity demanded will decrease to 180 from 200. The price sellers receive will be $30 less than price the buyers pay, or $90. The quantity supplied will equal the quantity demanded (180). Regardless of whether the tax is on buyers or sellers, the outcomes are the same. Problem 4. A subsidy is a payment from the government to buyers or sellers for each unit of a good that is bought or sold. A subsidy can be thought of as a negative tax, because instead of sending money to the government each time the good is sold, money is received from the government. Many industries receive subsidies from the government. Let’s think about the market for electric cars. 3

1. Use a supply-and-demand graph to illustrate the equilibrium in the market for electric cars without a subsidy. 2. On the same graph show the effects of a $5000 subsidy per electric car subsidy paid to consumers. What happens to the equilibrium price and quantity? 3. Do sellers benefit from the subsidy? Explain your answer. 4. To encourage the production of electric cars, the government decided to pay the $5000 subsidy to producers instead. What happens to the price paid by consumers, the price received by producers, and the size of the electric car market? Solution. 1. The equilibrium for electric cars, before any subsidy is applied, is given as P1 and Q1 in the graph.

2. After the $5000 subsidy (on the graph, P2 − P3 ) is applied the demand curve shifts from D1 to D2 . This causes the equilibrium quantity to increase from Q1 to Q2 . 3. Both the buyers and sellers receive the benefit of the subsidy. The price that buyers pay falls from P1 to P3 , while the price the sellers receive increases from P1 to P2 . 4. If the subsidy was paid to producers instead, the supply curve would shift to the right the equilibrium quantity Q2 . This would increase the price received by sellers to P2 but with the subsidy, buyers would only pay P3 . The result is thus identical to giving the subsidy to the electric car buyers.

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