FRAMINGHAM STATE COLLEGE PRINCIPLES OF MICROECONOMICS PROBLEM SET NUMBER 6

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1 FRAMINGHAM STATE COLLEGE PRINCIPLES OF MICROECONOMICS PROBLEM SET NUMBER 6 My Name is? Text Chapter 7 Producer Surplus and Market Efficiency 2. Ernie owns a water pump. Because pumping large amounts of water is harder than pumping small amounts, the cost of producing a bottle of water rises as he pumps more. Here is the cost he incurs to produce each bottle of water: Cost of first bottle $1 Cost of second bottle $3 Cost of third bottle $5 Cost of fourth bottle $7 a. From this information, derive Ernie's supply schedule. Ernie s supply schedule for water is: Price Quantity Supplied More than $7 4 $5 to $7 3 $3 to $5 2 $1 to $3 1 Less than $1 0 b. Graph his supply curve for bottled water. Ernie s supply curve is shown in Figure 2. Principles of Microeconomics 1 Problem Set Number 6

2 Figure 2 c. If the price of a bottle of water is $4, how many bottles does Ernie produce and sell? When the price of a bottle of water is $4, Ernie sells two bottles of water. d. How much producer surplus does Ernie get from these sales at $4 a bottle? Show Ernie's producer surplus in your graph. His producer surplus is shown as area A in the figure. He receives $4 for his first bottle of water, but it costs only $1 to produce, so Ernie has producer surplus of $3. He also receives $4 for his second bottle of water, which costs $3 to produce, so he has producer surplus of $1. Thus Ernie s total producer surplus is $3 + $1 = $4, which is the area of A in figure 2. e. If the price rises from $4 to $6, how does quantity supplied change? Tell me about the change in quantity not the new quantity! When the price of a bottle of water rises from $4 to $6, Ernie sells three bottles of water, an increase of one. Principles of Microeconomics 2 Problem Set Number 6

3 f. How does Ernie's producer surplus change as the price rises from $4 to $6? Show these changes in your graph. His producer surplus consists of both areas A and B in the figure, an increase by the amount of area B. He gets producer surplus of $5 from the first bottle ($6 price minus $1 cost), $3 from the second bottle ($6 price minus $3 cost), and $1 from the third bottle ($6 price minus $5 price), for a total producer surplus of $9. Thus producer surplus rises by $5 (which is the size of area B) when the price of a bottle of water rises from $4 to $6. 3. Consider a market in which Bert from Problem 1 is the buyer and Ernie from Problem 2 is the seller. a. Use Ernie's supply schedule and Bert's demand schedule to find the quantity supplied and quantity demanded at prices of $2, $4, and $6. Which of these prices brings supply and demand into equilibrium? Price Quantity Supplied Quantity Demanded $2 1 3 $3 2 2 $6 3 1 b. Which of these prices brings supply and demand into equilibrium? Only a price of $4 brings supply and demand into equilibrium, with an equilibrium quantity of 2. Principles of Microeconomics 3 Problem Set Number 6

4 c. What are consumer surplus, producer surplus, and total surplus in this equilibrium? The consumer surplus is: At a price of $4, consumer surplus is $4 The producer surplus is: producer surplus is $4 Total surplus is $4 + $4 = $8. d. If Ernie produced and Bert consumed one fewer bottle of water, what would happen to total surplus? If Ernie produced one fewer bottle, his producer surplus would decline to $3, as shown in problem 2. If Bert consumed one fewer bottle, his consumer surplus would decline to $3, as shown in problem 1. So total surplus would decline to $3 + $3 = $6. e. If Ernie produced and Bert consumed one additional bottle of water, what would happen to total surplus? If Ernie produced one additional bottle of water, his cost would be $5, but the price is only $4, so his producer surplus would decline by $1. If Bert consumed one additional bottle of water, his value would be $3, but the price is $4, so his consumer surplus would decline by $1. So total surplus declines by $1 + $1 = $2. Principles of Microeconomics 4 Problem Set Number 6

5 Using the material covered in CHAPTER The market for pizza is characterized by a downward-sloping demand curve and an upwardsloping supply curve. a. Draw the competitive market equilibrium. Label the price, quantity, consumer surplus, and producer surplus. Figure 3 illustrates the market for pizza. The equilibrium price is P 1, the equilibrium quantity is Q 1, consumer surplus is area A+B+C, and producer surplus is area D+E+F. Figure 3 b. Is there any deadweight loss? Explain. 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. Principles of Microeconomics 5 Problem Set Number 6

6 c. 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, P B, is now higher than the price received by sellers, P S, where P B = P S + $1. The quantity declines to Q 2, 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. d. 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 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 Q 1, as in the case without the tax, and the equilibrium price would be P 1. 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, since 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. Principles of Microeconomics 6 Problem Set Number 6

7 5. Senator Daniel Patrick Moynihan once introduced a bill that would levy a 10,000 percent tax on certain hollow-tipped bullets. a. Do you expect that this tax would raise much revenue? Why or why not? This tax has such a high rate that it is not likely to raise much revenue. Because of the high tax rate, the equilibrium quantity in the market is likely to be at or near zero. b. Even if the tax would raise no revenue, what might be Senator Moynihan's reason for proposing it? Senator Moynihan's goal was probably to ban the use of hollow-tipped bullets. In this case, a tax is as effective as an outright ban. Principles of Microeconomics 7 Problem Set Number 6