Please provide detailed answers to questions for these econ questions. Thank you.
CHAPTER 19: General Equilibrium Analysis and Economic Efficiency
CHAPTER 19
General Equilibrium Analysis and Economic Efficiency
CHAPTER ANALYSIS
This chapter is concerned with the way various economic arrangements affect the welfare of the members of society. We recognize that markets are interrelated, and introduce general equilibrium analysis, which is the study of how equilibrium is determined in all markets simultaneously. It is then shown that the general competitive equilibrium is efficient. Chapter 20 introduces and discusses some situations for which a competitive market will not generate efficient outcomes.
19.1 Partial and General Equilibrium Analysis Compared
Partial equilibrium analysis studies the determination of an equilibrium price and quantity in an individual market viewed as self-contained and independent of other markets. When partial equilibrium analysis is used, it is assumed that certain variables, such as the prices of other goods, are held constant when in fact they may actually change. The ceteris paribus assumption of partial equilibrium analysis permits us to focus on the factors most important in determining an equilibrium price and quantity in a given market.
General equilibrium analysis recognizes the interrelationships among markets and focuses on the characteristics of equilibrium in each market simultaneously. All prices are permitted to vary. We have considered market interrelationships in studying goods that are complements or substitutes and in studying cross-price elasticity, however, these analyses do not take into account the interrelationships that exist among all markets. For example, a change in demand for automobiles will affect the demand for tires, a complementary good. However, it can also affect the price of cooking utensils by affecting the demand for steel, which affects the price of aluminum, which affects the price of all products made with aluminum, including cooking utensils. Spillover effects, which are ignored in partial equilibrium analysis, occur when a change in equilibrium in one market affects variables in other markets. Further, the spillover effects in one market may also induce changes in that market and have a feedback effect on the original market. A feedback effect takes place when a change in equilibrium in a market that is caused by events in other markets that are a result of the initial change in equilibrium in the market under consideration. For example, a change in the demand for automobiles may cause a disequilibrium in the market for motorcycles (spillover effect), but as the market for motorcycles adjusts toward a new equilibrium, it may affect the automobile market (feedback effect). As these examples show, markets are mutually interdependent, a fact that is taken into account in general equilibrium analysis.
Economists use both partial equilibrium and general equilibrium analyses, depending on the problem under consideration. An important area in which general equilibrium analysis has been used successfully is international trade.
19.2 Economic Efficiency
Economists are unwilling to make interpersonal comparisons of utility (or well-being) because an individual's well-being is subjective and personal. Instead, economists attempt to identify efficient, or Pareto optimal, outcomes. An allocation of resources is efficient (Pareto optimal) if it is impossible, through any feasible change in resource allocation, to make one person better off without making another person worse off. The assessments of being better or worse off are made by the individuals themselves. Any allocation of resources for which it is possible to make at least one person better off without making another person worse off is inefficient.
There is more than one efficient allocation of resources. Figure 19.2 in the text illustrates a welfare frontier, which is a curve that separates welfare levels that are attainable from those that cannot be reached given the availability of resources. Any point on the welfare frontier is efficient, while any point inside the welfare frontier is inefficient. There is no way to identify the "best" point on the frontier, since interpersonal comparisons of utility would involve value judgements.
19.3 Conditions for Economic Efficiency
Any economy must find a way to determine how much of each good to produce, how much of each input to use in the production of each good, and how to distribute the goods among consumers. It is desirable that these three tasks are performed in an efficient manner.
In Chapter 6 we examined the distribution of goods among consumers using the Edgeworth exchange box diagram to illustrate exchange between two consumers. Recall that the contract curve was the locus of points where the consumer’s indifference curves were tangent to each other, indicating that the marginal rate of substitution for one consumer equaled the marginal rate of substitution for the other. The equality of the marginal rates of substitution is the necessary condition for consumption to be efficient. The concept was extended to many consumers; in general, an efficient distribution of goods requires the marginal rates of substitution between any two goods are equal for all consumers: MRS1 = MRS 2 = …= MRS i.
19.4 Efficiency in Production
Efficiency in production can be analyzed in a similar fashion to efficiency in consumption. An Edgeworth production box is a diagram identifying all of the ways two inputs, such as land and labor, can be allocated between industries in a simplified economy. The Edgeworth production box is analogous to the Edgeworth exchange box presented in Chapter 6.
An Edgeworth production box is depicted by Figures 19.3 and 19.4 in the text. The contract curve is the locus of points at which an isoquant for food is tangent to an isoquant for clothing. Any point on the contract curve is a possible equilibrium point because the condition of cost minimization, w/ = MPL/MPA = MRTSLA, is met. While the contract curve in an Edgeworth exchange box with indifference curves is the locus of equilibria that are efficient distribution of goods, the contract curve in an Edgeworth production box with isoquants is the locus of equilibria that are efficient allocations of inputs. At every point on the contract curve, the marginal rate of technical substitution for the production of one good equals the marginal rate of technical substitution for the production of the other good.
19.5 The Production Possibility Frontier and Efficiency in Output
Figure 19-1 provides a contract curve for the production of wine and corn. Each point on the contract curve corresponds to a specific rate of wine and corn production that uses all the available land and labor. Figure 19-2 presents a production possibility frontier, which shows the alternative combinations of wine and corn that can be produced with the available land and labor. Each point on the contract curve corresponds to a point on the production possibility frontier. That is, point A in Figure 19-1 corresponds to point A in Figure 19-2, B to B, and so on. The slope of the production possibility frontier is called the marginal rate of transformation (MRT) which measures the rate at which one product can be “transformed” into another. If we are on the production possibility frontier it implies production is efficient.
To produce an efficient output requires that the subjective preferences of consumers be balanced with the objective conditions of production. This condition is met when the slope of the production possibility frontier equals the marginal rates of substitution between the products. Since the marginal rates of substitution equal the price ratio, the marginal rate of transformation also equals the price ratio, MRS = MRT. Figure 19.6 in the text provides a graphical representation of this concept.
Price equals marginal cost in a competitive industry, so we know that Pc = MCc, Pw = MCw, and MCw/MCc = Pw/Pc. That is, the ratio of each product's marginal cost equals the ratio of prices. The ratio of monetary marginal costs is the slope of the production possibility frontier, and the ratio of prices is the slope of the consumer budget line. Since consumers equate their MRSwc to the price ratio, the MRS of a consumer is equal to the MRT. When the total quantities of wine and corn demanded by all consumers equal the quantities produced, at the prevailing prices, the product markets are in equilibrium.
19.6 Competitive Markets and Economic Efficiency
In general, economists are advocates of perfect competition because it satisfies all three conditions for economic efficiency. First, since each consumer equates his or her MRS with the price ratio, and the price ratio is the same for everyone, the MRSs of everyone will be equal. Therefore, this implies there is an efficient distribution of goods among consumers.
Second, when each firm minimizes cost, it equates the marginal rate of technical substitution between the inputs to the input price ratio. Under competition, all firms face the same input prices, so the MRTS is the same for all firms. When the MRTS is the same for all firms, there is efficiency in production.
Finally, perfectly competitive firms equate price and marginal cost. The ratio of prices is equal to the MRS and the ratio of marginal costs is equal to the MRT. Therefore, the MRS is equal to the MRT, implying the efficient output is achieved and perfect competition is efficient.
The chart below summarizes the conditions and criteria necessary for economic efficiency.
Efficiency Conditions Criteria
1. Distribution of products MRSHwc = MRSSwc
among consumers must be efficient.
2. Allocation of inputs must MRTSCLA = MRTSWLA
be efficient.
3. The output mix must be efficient. MRSwc = MRTwc
19.7 The Causes of Economic Inefficiency
A market may fail to attain Pareto optimality for several reasons. For example, economic inefficiency occurs when firms have market power. For a monopoly, price exceeds marginal cost which violates the condition for efficient output. If there are two goods, x and y, and one is monopolized (x), then Px/Py > MCx/MCy. Consumers equate their MRSs to the price ratio, so MRSyx = Px/Py. The ratio of the marginal costs equals the MRT. This implies MRSyx > MRTyx.
Three other circumstances that prevent economic efficiency are imperfect competition, externalities, and public goods. Chapter 20 examines these situations in more detail.
ILLUSTRATIONS
Ecology and Economics
Ecology is a branch of biology that deals with the relationships of organisms to their environment and to other organisms. Equilibrium will exist when the populations of the various organisms are constant over time. When this balance of nature is disrupted, the effects can be great.
Suppose, for example, there are farmers and sheep ranchers near a wilderness area. Coyotes occasionally raid the flocks of sheep and kill off some of the sheep. The shepherds may seek to eliminate the coyote population. If they use a partial equilibrium analysis, they may conclude that eliminating the coyotes will save the lives of sheep but have no other effects. A general equilibrium approach recognizes that there are other effects. Coyotes also feed on rabbits and rodents. Extermination of coyotes will result in an increase in the population of rabbits and rodents, which may increase the rate at which crops are destroyed. Rodents carry diseases that may ultimately infect the sheep and reduce the size of the flocks. Given the interrelationship of the organisms in the environment, policies that are designed to affect one organism only will likely affect many other organisms as well. Similarly, policies designed to affect one economic market are likely to affect many other markets as well.
Consumer Sovereignty
The notion of consumer sovereignty is that a competitive market economy produces the goods and services that consumers want. Of course, this does not imply that each and every consumer is able to buy every type of good they want. Some things, such as vacations to the moon, are too costly to produce. Markets generally do not produce goods that only a few people want because the cost of production would be too high.
There are critics of market organization who claim that the market fails to produce what people "really" want, or need. Instead, the market provides things people really do not want but are persuaded to buy through heavy advertising. Technically, the model of perfect competition assumes perfect information so there is no role for advertising in competitive markets. However, the real world is characterized by imperfect information and advertising provides a useful role. However, there are numerous examples of heavily-advertised products that failed to garner a market. A prominent example was the Edsel, introduced by Ford a number of years ago. A more recent example is the XFL. The football league was sponsored by a successful wrestling company, shown on two networks, and heavily advertised. After obtaining decent ratings at first, the ratings steadily declined as consumers decided in large numbers that they did not want the XFL. Consequently, the XFL failed in spite of heavy advertising.
KEY CONCEPTS
general equilibrium analysis partial equilibrium analysis
spillover effect feedback effect
Pareto optimality efficient
Inefficient welfare frontier
Edgeworth production box
marginal rate of transformation
REVIEW QUESTIONS
True/False
1. The difference between general equilibrium analysis and partial equilibrium analysis is the extent to which market interrelationships are considered.
2. If we are interested in only one market, then spillover effects are important only if they generate feedback effects.
3. Every point on the welfare frontier is efficient.
4. The midpoint on the welfare frontier is the most efficient point.
5. Every point in an Edgeworth production box corresponds to a point on the production possibility frontier.
6. The marginal rate of transformation is measured by the slope of the production possibility frontier.
7. If MRSxy = 3x/1y and MRTxy = 1x/1y, then consumers can be made better off by producing more y and less x.
8. When perfectly competitive markets are in equilibrium, the three conditions for economic efficiency are satisfied.
9. In a general equilibrium, the rate at which one good can be substituted for another good is equal to the rate at which any consumer would be willing to exchange one good for another good.
10. Prices serve a rationing function in determining how much of available supplies each person will receive.
11. Under monopoly, the marginal rate of substitution is greater than the marginal rate of transformation.
12. Even though the market power of unions leads to inefficiency, society is still on the production possibilities frontier.
Multiple Choice/Short Answer
1. If steel and aluminum are substitutes and the demand for steel increases, which of the following would be true of the aluminum market?
a. The supply of aluminum will increase.
b. The quantity supplied of aluminum will decrease.
c. The quantity demanded of aluminum will increase.
d. The demand for aluminum will increase.
2. Assume the change in Question 1 has taken place. Which of the following describes the feedback effect in the steel market?
a. The supply of steel will increase.
b. The quantity supplied of steel will decrease.
c. The demand for steel will increase.
d. The demand for steel will decrease.
3. If it is possible to make someone better off without making someone else worse off, then the situation is
a. efficient.
b. Pareto optimal.
c. optimal.
d. inefficient.
Questions 4 to 6 refer to Figure 19-3.
4. Points C, D, and E are on the _______________.
5. Indicate which of the following statements are true and which are false.
a. Points C, D, and E are efficient while F is inefficient. True False
b. Point D is preferred to C. True False
c. Point D is preferred to F. True False
d. Point C is preferred to F. True False
6. The movement from F to C
a. is not an efficient move because C is not an efficient point.
b. is not an efficient move because it makes A worse off.
c. is an efficient move because C is an efficient point.
d. is an efficient move because it makes B better off without harming A.
7. Efficiency in the distribution of products among consumers occurs when
a. marginal rates of technical substitution are equated.
b. P = MC.
c. Px = MUx.
d. consumer’s marginal rates of substitution are equal.
8. The dimensions of an Edgeworth production box are determined by
a. the total quantities of the products.
b. the total quantities of the inputs.
c. the contract curve.
d. the tastes of consumers.
Questions 9 and 10 refer to Figure 19-4.
9. a. Which good uses relatively more labor than capital?
b. Which good uses relatively more capital than labor?
c. The curve connecting the origins is called a _______________ curve.
10. Which of the following is a true statement?
a. The price of labor to price of capital ratio is greater at B than at A.
b. The price of labor used to produce sweaters is greater than the price of labor used to produce machinery.
c. The price of labor to price of capital ratio is greater at A than at B.
d. The price of labor to price of capital ratio is the same at A and B, since the same amount of labor and capital exists at both points.
11. If the contract curve is a straight line connecting the two origins, then the production possibility frontier is
a. bowed out.
b. bowed in.
c. a straight line.
d. Cannot tell without more information.
12. The slope of the production possibility frontier measures
a. the marginal cost of one good in terms of the other.
b. the marginal cost of substitution.
c. the marginal rate of technical substitution.
d. the input price ratio.
13. In Figure 19-5, which output is efficient?
a. A.
b. B.
c. C.
d. D.
14. Efficiency in output occurs when
a. marginal rates of substitution are equal.
b. MRS = MRT.
c. Px = MUx.
d. marginal rates of technical substitution are equal.
15. A perfectly competitive economy results in an efficient distribution of products among consumers because
a. firms maximize profits by equating price and marginal cost.
b. firms minimize costs.
c. all consumers face the same prices.
d. P = MC.
16. Monopoly is inefficient because it does not satisfy which condition for efficiency?
a. Distribution of goods among consumers.
b. Allocation of inputs among firms.
c. Output mix.
d. Monopoly does not satisfy any of the conditions.
17. An important function of price is to
a. ration existing supplies among consumers.
b. distribute goods fairly to the consumers who need them most.
c. Both of the above.
d. None of the above.
18. General equilibrium analysis should be used instead of partial equilibrium analysis when
a. a change in conditions affects primarily one market.
b. a change in conditions affects many markets but the quantitative effects are small.
c. a change in condition affects many markets at the same time or to the same degree.
d. a change in conditions has no feedback effects.
Discussion Questions and Problems
1. What are the primary differences between partial equilibrium analysis and general equilibrium analysis?
2. The spillover and feedback effects of a tax on margarine are discussed in the text. What other markets would be affected by a tax on margarine? What would be the spillover and feedback effects?
3. How is it determined whether an allocation of resources is efficient or inefficient?
4. Any point on the welfare frontier is preferred to any point inside the frontier. Do you agree or disagree? Why?
Redistributing income from the rich to the poor generally is efficient. Do you agree or disagree? Why?
6. Explain how the contract curve in an Edgeworth production box is found and why a general equilibrium must lie on the contract curve.
7. Explain how a production possibility frontier is derived.
8. What does the slope of the production possibility frontier measure? How is this slope related to the general competitive equilibrium of consumers?
9. Suppose the production possibility frontier between corn and wine is a straight line with a slope of -1.
a. What do we know about the competitive general equilibrium?
b. Suppose the demand for corn increases. What effects will there be?
10. State the three conditions for economic efficiency and provide an intuitive explanation of each.
11. Explain why perfect competition is Pareto optimal.
12. Assume we are initially at point A on the production possibility frontier shown in Figure 19-6. Bearing in mind that cotton production is more labor-intensive than automobile production, describe the effects of a change in demand that moved society to point B on the production possibility frontier.
13. Under a monopoly, society is not on the welfare frontier. Do you agree or disagree? Explain.
14. Can you offer an explanation for trade between nations?
15. a. Suppose there exists two industries consisting of wine and corn. What are the welfare effects of an excise tax on wine? Assume that the government makes a lump-sum payment to individuals to keep their wealth at the pre-tax level.
b. How do the effects differ if the government does not make a lump-sum payment to taxpayers?
SOLUTIONS
True/False
1. True
2. True
3. True
4. False
5. False. Every point on the contract curve corresponds to a point on the production possibility frontier.
6. True
7. True
8. True
9. True
10. True
True
False
Multiple Choice/Short Answer
1. d
2. c
3. d
4. welfare frontier
5. a. True
b. False
c. True
d. False. C is not preferred to F for person A.
6. b
7. d
8. b
9. a. sweaters
b. machinery
c. contract
10. c
11. c
12. a
13. c
14. b
15. c
16. c
17. a
18. c
Discussion Questions and Problems
1. General equilibrium analysis takes into consideration more of the interrelationships in the economy than partial equilibrium, but still does not include all the interrelationships among all markets. In either case, we try to focus on the important interrelationships and factors and ignore the trivial ones.
2. There is no single correct answer to this question. Many markets could be affected by a tax on margarine: bread, jelly, muffins, cheese, milk, cattle, feed for cattle, farm laborers, and factory workers, to name just a few. The spillover and feedback effects would be numerous. For example, the tax on margarine may affect the demand for jelly, which could affect the demand for margarine in return. The tax on margarine increases the demand for butter, and milk is used in the processing of butter. Hence, the demand for milk may increase, which may induce an increase in the demand for dairy cows, which increases the demand for cattle feed, etc. The above answer mentions only a few markets.
3. If there is any way that the allocation of resources can be changed that permits someone to be better off without making someone else worse off, then the allocation of resources is inefficient. If this cannot be done, it is efficient.
4. Disagree. Figure 19-3 above illustrates. Point F is inside the welfare frontier. Any points on the welfare frontier between D and E are preferred to F since either A or B (or both) can be made better off without the other being made worse off. However, a move to C required that A be made worse off, so we cannot conclude that C is preferred to F.
5. Disagree. For a move to be efficient, it must be the case that no one is harmed. Taking money from the rich harms the rich so that would not be efficient. Of course, societies do make such changes since efficiency is not the sole goal of society.
6. The contract curve is found by connecting all the points of tangency between the isoquants of the two goods. When isoquants of the two goods are tangent to each other, the ratios of marginal products for both goods are equal to each other and equal to the ratio of input prices. When this occurs, firms in both industries are minimizing costs. Hence a general equilibrium must be on the contract curve.
7. Every point on the contract curve identifies a combination of the two goods that can be produced with the available supply of inputs when firms minimize costs. The production possibility frontier plots these various combinations of output directly. See Figures 19-1 and 19-2 in the study guide.
8. The slope of the production possibility frontier measures the amount of one good that must be given up to produce one more unit of the other good. In other words, it measures the ratio of the monetary marginal costs of the two goods. Since P = MC in perfect competition, the slope also measures the price ratio of the goods. Consumers equate their MRS with the price ratio, so the slope of the production possibility frontier equals the slope of the consumer's indifference curve at equilibrium.
9. a. The MRTScw = - 1. We know that MRT = MCw/MCc = Pw/Pc, so all these ratios must also equal 1. The production possibility frontier must have been derived from a contract curve that is the diagonal of the Edgeworth production box, since the constant MRT implies that the inputs that leave one industry go into the second industry at a constant rate. Thus input prices are constant too.
b. The increase in the demand for corn causes the price of corn to increase relative to the price of wine. Some resources shift from producing wine to producing corn. But the constant MRT implies that the new long-run equilibrium must have the same price ratio as the original equilibrium. Input prices also will not change, although more land and labor will be employed in the production of corn than before.
10. Efficiency in the distribution of products among consumers requires that the marginal rates of substitution are the some for all consumers. When this condition holds, all consumers value an additional unit of a product, in terms of the other product, equally. Hence there are no further gains from trade. Efficiency in the allocation of inputs requires that the marginal rates of technical substitution are equal in the production of all goods. When this condition holds, there is no way to increase production by rearranging the allocation of the inputs. Efficiency in output requires that MRT = MRS. When this occurs, consumers value an additional unit of a good, in terms of the other good, in the same proportion for which it is possible to produce one more unit of the good. The marginal benefit to consumers of one more unit equals the marginal cost of producing it.
11. Perfect competition fulfills the three conditions for Pareto optimality: (1) There is an efficient distribution of products among consumers under perfect competition. Each individual chooses his consumption bundle by setting MRSxy = Px/Py. Since prices are the same for everyone, MRSAxy = MRSBxy, where A and B represent any two consumers. (2) Inputs are allocated efficiently in perfect competition. Each firm minimizes costs by employing units such that PL/PK = MRTSLK. All firms face the same prices for labor and capital, so MRTSXLK = MRTSYLK. (3) In a perfectly competitive economy, firms maximize profits by setting P = MC. Thus, Px = MCx, Py = MCy, and Px/Py = MCx/MCy. Further, MRTxy = MCx/MCy, and MRSxy = Px/Py. Therefore, MRSxy = MRTxy. When perfectly competitive markets are in equilibrium, all three conditions for Pareto optimality are satisfied.
12. A movement from A to B causes the price ratio to change such that the price of automobiles rises relative to the price of cotton. Resources leave the cotton industry and flow to the automobile industry. Since automobile production is more capital-intensive than cotton production, capital becomes scarcer relative to consumers’ demands. The price on capital rises and the wage rate falls, so capital owners are wealthier than before, while wage earners are poorer. The change in demand affects the prices of the goods, the prices of inputs, and the income distribution.
13. Agree. Price is greater than marginal cost under monopoly, so we know that MRS > MRT. So, it is possible to change the output mix and make both consumers better off. Since both can be made better off, we must not be on the welfare frontier.
14. Trade between nations exists because the total amounts of different goods differ between nations. This results in consumers in different countries having different marginal rates of substitution. Exchange between nations, just like exchange between individuals, makes the parties to the exchange better off.
15. a. See Figure 19-7. Production moves from E to M as less wine and more corn is produced. The price of wine consumers pay (Pcw) is greater than the price of wine received by producers (Ppw). Hence (Pcw/Pc) > (Ppw/Pc) = MCw/MCc. Therefore, MRS > MRT, and the output is inefficient.
Consumers have less money to spend, so they consume less wine and less corn. Society moves inside the production-possibility frontier to F.
122
