Chapter 016 BW2e SM - SOLUTION MANUAL CH16 PDF

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Chapter 16 – General Equilibrium, Efficiency, and Equity

Answers to End-of-Chapter Discussion Questions 1.

Fiona is not convinced that the idea of a general competitive equilibrium makes sense. She reasons as follows: “If people behave according to the assumption of perfect competition, everyone is a price taker, and no one is a price maker. Therefore, there is no way for prices to reach their general equilibrium levels.”

Answer: Fiona's argument is incorrect. Equilibrium in any market does not require that anyone be a price maker. The invisible hand of the marketplace will adjust prices automatically, as disequilibrium prices will result in shortages or surpluses. For example, if the price of wheat is too low relative to its competitive equilibrium price, the resulting shortage will cause the price to increase until the equilibrium price is achieved. The same thing is true for multiple markets. Prices that are too low in one market will reduce the allocation of resources to that market, reducing supply and causing the price to rise until price ratios between markets are equal to the competitive equilibrium price ratio. 2.

For the simple economies studied in Section 16.2, we saw that the general equilibrium effect of a tax on ice cream is bigger than the partial equilibrium effect. Under which of the following conditions might the general equilibrium effect be smaller than the partial equilibrium effect?

Answer: If the supply of each good decreases when the price of the other good increases, then market-clearing curves are upward sloping. (For example, if an increase in the price of pie means that the supply of ice cream decreases, then the price of ice cream will increase as well. Prices in both markets will be positively related.) 3.

Should society pursue equitable economic goals or efficient economic goals, as those terms are used in the text?

Answer: In theory, efficiency and equity are two separate issues and society might have multiple socially efficient points from which it can choose. In practice, however, society most often faces a trade-off between equity and efficiency. Government redistribution programs affect incentives and prices, and therefore impact efficiency. Because of this efficiency/equity trade-off, society must balance efficiency and equity. Other economic goals will always have efficiency and equity implications.

4.

In Section 5.4 you learned about price-consumption curves. Add Humphrey and Lauren’s price-consumption curves to the Edgeworth box in Figure 16.10 (page 560). Explain why the competitive equilibrium corresponds to the point at which the price-consumption curves intersect. 16-1

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Chapter 16 – General Equilibrium, Efficiency, and Equity

Answer: Note that for Lauren the top of the box serves as an axis measuring the amount of food and the right side serves as an axis measuring the amount of water. The numbers on Lauren’s axes are read backward.

Competitive equilibrium Corresponds to the point at which price-consumption curves intersect: point C. This is due to the fact that the price-consumption curves connect the points of the best affordable consumption bundles at a given price. At equilibrium price, the sum of Humphrey and Lauren’s best affordable consumption bundles equals the supply of food and water. 5.

In an exchange economy with two consumers and two goods, is it possible for one of the markets to clear but not the other? Explain your answer graphically by using the Edgeworth box.

Answer: No. With two goods and two consumers, trade must occur in both markets. Each individual trades one good for another good, so trade must occur in both markets, or not at all. 16-2 © 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Chapter 16 – General Equilibrium, Efficiency, and Equity

In an Edgeworth box diagram, since the size of the box is determined by the total supplies of both goods, if there is no surplus or shortage in one market, there must be no shortage or surplus at the current price ratio in the other market.

6.

Figure 16.17 (page 572) shows why, in an economy with a single consumer, output efficiency requires the marginal rates of substitution and transformation to be identical. Explain why the same condition must hold in an economy with many consumers, using a graph (or graphs) to illustrate your explanation.

Answer: For the exchange efficiency condition to hold, the MRS must be equal for each consumer. Every individual maximizes utility by choosing a bundle of goods that equates the ratio of the prices with his/her MRS. Therefore, MRS is the same (at the selected bundles) for all individuals. Therefore, MRT is equal to MRS for all individuals. To explain why this must be the case in an economy with many consumers, first consider that the exchange efficiency condition requires that the MRS for each consumer be equal. If this were not the case, consumers could gain from trading If the exchange efficiency condition holds and the output efficiency condition holds for every individual consumer, then the MRS equals the MRT for all consumers. If this were not the case, the consumer could reach a higher level of utility by choosing a different bundle of goods. Since each consumer must equate his MRT to his MRS, and since the MRS must be equal for all consumers, it follows that the MRT must be equal for all consumers. More intuitively, the MRS represents the value of one good in terms of the other for each consumer; the MRT represents the cost of one good in terms of another. If these are not equal for consumers both individually and collectively, consumers can be made better off by trading and changing the allocation of resources. When the exchange efficiency condition is satisfied, all consumers share the same marginal rate of substitution; therefore, if the condition holds for one of them, it holds for all of them. As long as (1) the PPF and indifference curves are smooth (with no kinks), (2) indifference curves have declining MRSs, and (3) no production technology yields increasing returns to scale, then this condition provides a simple test for output efficiency.

7.

For each of the following hypothetical policies, indicate which of the three efficiency conditions (exchange, input, and output) are violated, if any. (a) The government bans orange juice. (b) The government assigns a house or apartment to each family and prohibits swapping. (c) The government subsidizes the use of capital for oil exploration.

Answer: The government bans orange juice: Output efficiency is violated. The government assigns a house to each family and prohibits swapping: Exchange efficiency is violated. 16-3 © 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Chapter 16 – General Equilibrium, Efficiency, and Equity

The government subsidizes the use of capital for oil exploration: Input efficiency is violated. An allocation satisfies the output efficiency condition if, for every pair of goods, every consumer’s marginal rate of substitution equals the marginal rate of transformation. The exchange efficiency condition holds if every pair of individuals shares the same marginal rate of substitution for every pair of goods. The input efficiency condition holds if, for every pair of inputs, every pair of firms shares the same marginal rate of technical substitution. 8.

The output efficiency condition applies both when firms produce different products (like food and housing), and when they produce the same product. For example, suppose firms A and B both produce apples, and that A’s apples are perfect substitutes for B’s. In this case, the output efficiency condition tells us to allocated inputs between firms A and B so as to maximize total apple production. Explain why. (Your answer should explain why that conclusion follows from the equivalence between marginal rates of substitution and transformation for the products of firms A and B).

Answer: This is because, if the goods are perfect substitutes, there are no gains from trade, and thus we maximize the utility of consumers by maximizing output. In general, the output efficiency condition is satisfied if, for every pair of goods, every consumer’s marginal rate of substitution equals the marginal rate of transformation. If there is only one good, there is no substitution between goods, and likewise the marginal rate of transformation is technically undefined (since apples cannot be transformed into something else by reallocation of goods). Thus an efficient allocation simply means that inputs are allocated in a way that maximizes total output. (If that were not the case, it would be possible to make one consumer better off without harming anyone else.) Consumers cannot trade, since they place the same value on a single good. 9.

If the government wanted to reach point J in Figure 16.20 (page 578), it could simply mandate this allocation through centralized control of resources. Why might it be better to set up competitive markets and allow trading?

Answer: Point J is efficient. Their indifference curves lie tangent to the same straight line at that point. At the right prices, this line is also their budget line. With this budget line, both consumers choose point J. Since neither consumer supplies or demands anything, supply matches demand, creating a competitive equilibrium. Using any other endowments on the green line, like S, the same prices would lead to the same competitive equilibrium. Preferences are hard to observe, especially if there is no incentive for people to reveal 16-4 © 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Chapter 16 – General Equilibrium, Efficiency, and Equity

them. If the government misjudged Humphrey and Lauren’s preferences, it would end up mandating an inefficient allocation of resources that would not be amendable through market mechanisms. However, in competitive markets, revealing of preferences occurs automatically through trade, which results with efficient allocation of resources.

10.

After reading Section 16.6, a student proposes a system of taxes and transfers based on the intelligence quotient (IQ). She argues that intelligence is not chosen, and that it’s closely related to economic success. She concludes that redistributing resources from people with high IQs to people with low IQs will promote equity without compromising efficiency. Is this a good economic proposal? Why or why not?

Answer: Some inefficiency will still be created because high IQs do not always result in economic success and lower IQs do not automatically imply economic need (e.g., wealth can be inherited). There are also likely to be broader implications for work incentives, and resources are unlikely to remain redistributed in this way over time. This is not likely to be a good economic proposal.

Answers to Problems 16.1

Suppose that the demand for pie doesn’t depend on the price of cake, and that the demand for cake doesn’t depend on the price of pie. An increase in the price of pie, however, shifts the supply curve for cake downward, while an increase in the price of cake shifts the supply curve for pie downward (because bakers spend more time making the more profitable product). Assume that demand curves slope downward and supply curves slope upward. Using graphs, show how to construct the market clearing-curves for pie and cake. Do they slope upward or downward? Again using graphs, illustrate the effects of sales tax on cake. Does the cake price change more in general equilibrium or partial equilibrium?

Answer: The market-clearing curve is upward sloping. The sales tax on cake would increase both the price of cake and pie. The cake price changes more in partial equilibrium. Explanation: In this example, the market-clearing curve is upward sloping. A higher price of cake, for example, decreases the supply of pie, which raises the price of pie. Thus, there is a positive relationship between the price of cake and the price of pie along the marketclearing curve. A tax on cake shifts the supply of cake leftward, which results in a price increase. In response to the price increase, the supply curve in the pie market decreases as pie makers 16-5 © 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Chapter 16 – General Equilibrium, Efficiency, and Equity

devote more time to cake. As a result, the equilibrium price of pie increases and the equilibrium quantity decreases. The decrease in the price of pie causes an upward shift in the supply curve for cake. The cake price will change less in general equilibrium, as more cakes are baked in response to the higher price. 16.2

Repeat Problem 1, but now assume that an increase in the price of pie shifts the supply curve for cake upward, and an increase in the price of cake shifts the supply curve for pie upward (because a higher price of either good attracts more bakers into the market).

Answer: The market-clearing curve is downward sloping. The price of cake increases while the price of pie decreases. The cake price changes more in general equilibrium. Explanation: In this example, the market-clearing curve is downward sloping. A higher price of cake, for example, increases the supply of pie, which decreases the price of pie. Thus, there is a negative relationship between the price of cake and the price of pie along the marketclearing curve. A tax on cake shifts the supply of cake leftward, which results in a price increase. In response to the price increase, the supply curve in the pie market increases as more bakers enter the market. As a result, the equilibrium price of pie decreases and the equilibrium quantity increases. The decrease in the price of pie causes a decrease (leftward shift) in the supply curve for cake. The cake price will increase more in general equilibrium, as more bakers exit in response to the lower price of pie. 16.3

Using the same notation as in Worked-Out Problem 16.1, suppose the following formulas describe the weekly supply and demand for ice cream:

Also suppose the following formulas describe the supply and demand for pie:

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Chapter 16 – General Equilibrium, Efficiency, and Equity

Solve for prices and quantities in a general equilibrium. Answers PI = $26 PP = $15 QI = 110 QP = 36 Explanation: Following Worked-Out Problem 16.1, first set quantity supplied equal to quantity demanded in each market. This gives the market-clearing curve for each market. Then set the two market-clearing curves equal to each other to solve for prices. Use those prices to find the quantities in each market. In general equilibrium in the ice cream market, P = $26 and Q = 110. In general equilibrium in the pie market, P = $15 and Q = 36.

16.4

For the same economy as in Problem 3, suppose the government decides to levy an $8 per gallon tax on ice cream. Determine the partial equilibrium and general equilibrium effects of this tax on the prices and quantities of pie and ice cream.

Answer: The partial equilibrium effect on the price of ice cream is an increase of $4. The general equilibrium effect of this tax on the prices and quantities of pie and ice cream: PI = $31 PP = $12.50 QI = 95 QP = 26 Explanation: Following Worked-Out Problem 16.1, first set quantity supplied equal to quantity demanded in each market. This gives the market-clearing curve for each market. Then set the two market-clearing curves equal to each other to solve for prices. Use those prices to find the quantities in each market. In general equilibrium in the ice cream market, P = $26 and Q = 110. In general equilibrium in the pie market, P = $15 and Q = 36.

16-7 © 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Chapter 16 – General Equilibrium, Efficiency, and Equity

The tax changes the ice cream supply formula to:

Set quantity supplied equal to quantity demanded again. The new market-clearing curve for ice cream is:

The market-clearing curve has shifted up by $4, the partial equilibrium change in the price of ice cream. Substitute into the market-clearing curve for pie to find the new general equilibrium prices and quantities. In general equilibrium with the tax in the ice cream market, P = $31 and Q = 95. In general equilibrium in the pie market, P = $12.50 and Q = 26.

16.5

Humphrey and Lauren are splitting 10 gallons of soda and 6 pounds of popcorn. Let's represent Humphrey’s preferences with the utility function

and Lauren’s preferences with

where SH and SL indicate their soda consumption, while PH and PL indicate their popcorn consumption. Consider the social welfare function According to this social welfare function, which of the following two allocations is better: or Which allocation does each consumer prefer? Considering all possible allocations, which is the most socially desirable? [Hint: How is social welfare affected by shifting a gallon of soda between Humphrey and Lauren? What about a pound of popcorn?] Answer: Allocation 2 is better. Lauren prefers allocation1 and Humphrey prefers allocation 2.

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Chapter 16 – General Equilibrium, Efficiency, and Equity

The most socially desirable allocation is for Humphrey to have 10 gallons of soda and Lauren to have 6 pounds of popcorn. Explanation: To determine which allocation is best, calculate the total social welfare achieved with each allocation.

Allocation 2 generates the most social welfare. Lauren prefers the first allocation, since that allocation generates the most individual utility and welfare. Humphrey prefers the second allocation for the same reason. That is: For Lauren:

For Humphrey:

The most socially desirable allocation is for Humphrey to have all 10 gallons of soda (and 0 pounds of popcorn) and Lauren to have all 6 pounds of popcorn (and 0 gallons of soda). In this example:

Any other combina...