Chapter 18W

GENERAL EQUILIBRIUM AND MARKET EFFICIENCY
Boiling Down Chapter 18W
Although an individual market is often studied in isolation, no market ever operates that way. In fact, the interconnectedness of the markets is what really makes resources flow to their best use. The easiest way to explore the interactions of markets is to construct a model where only two markets are observed.
The Edgeworth exchange box is a tool to show how exchange of goods from two separate markets by two individuals will occur in a mutually beneficial manner. The box dimensions set the initial resource amounts that are owned by the two individuals. One person's preference pattern begins from the lower left corner of the box, and the other person's indifference curves proceed from the upper right corner. A given point in the commodity space gives the starting distribution of the goods among the individuals. The indifference curves that pass through that point will tell each individual's marginal rate of substitution (MRS) between goods at that resource endowment point.
If the MRS of one good for the other differs between the people, it is logical that they can both profit by exchanging what they value least for what they value most. Therefore, a mutually beneficial trade can occur until the people have the same MRS for the goods. At that point, optimality in consumption is reached and the individuals are said to be on the contract curve. (Figures 18W-2 through 18W-5 in the text illustrate this process.) However, where on the contract curve the people end up depends on what the initial distribution of goods was and how effective each person was in the bargaining process. A voluntary move from off the contract curve to the contract curve is said to be a Pareto optimal move. Movements brought about by voluntary exchange that move the parties toward the contract curve are said to be Pareto preferred. All of this implies what logic tells us: namely, that no one voluntarily makes herself worse off, so a voluntary exchange will not hurt either party. In fact, both are likely to be better off.
In the larger world, people are not in a position to bargain with each other, so they relate to a market price rather than a personal bartering arrangement. The prices adjust if the people are not on the contract curve at a given price. If there is benefit to be gained by more trading, the relative price in the market will adjust through the supply and demand mechanism until all beneficial trades are made. Any given initial income distribution and relative price structure will provide incentives for the adjustments necessary to reach the contract curve. These incentives and the accompanying transactions are the invisible hand that Adam Smith spoke of two centuries ago.
Efficiency in production is also part of general equilibrium. If all resources are put to their best use, the marginal rate of technical substitution of labor and capital will be the same in the production of all goods. If this were not true, it would be possible to shift resources from one production process to another and gain output. Again the Edgeworth box tool is helpful if the box dimensions represent the endowment of inputs available and one product's production isoquants move from southwest to northeast in the usual pattern, while the other product's isoquants move from northeast to southwest. Just as the consumers reach equilibrium on the contract curve of consumption, production efficiency is reached at the contract curve of production where the marginal rates of input substitution are identical. In other words, inputs are employed until the last dollar spent by each producer on each input generates the same output value. This exchanging of inputs can be seen graphically as production moves from a point off the contract curve toward the contract curve. When the contract curve is reached, the isoquants of the two production processes are tangent and no further shifting of inputs could increase the output of one product without reducing the output of the other. In other words, there is no waste in production and, therefore, efficiency has been reached.
The obvious question now becomes, which efficient output combination is most desirable? In other words, what point on the production contract curve is preferred? To answer this question, a production possibility curve is derived by plotting all points on the contract curve on a graph, showing the alternative efficient product combinations. The slope of the production possibilities curve shows the rate at which society is able to trade off one good for the other, given its production processes. This tradeoff rate is called the marginal rate of transformation and equals the marginal cost of one good in terms of the other.
The final piece of the puzzle of Pareto optimality is the selection of the best point on the production possibility curve. To find this point, we need to discover how society values the two products and then compare those values with the marginal costs of producing the goods. This is the same as equating the slope of the production possibility curve with the slope of the indifference curves of the consumers. Market interaction will bring these two curves into a tangency position where the slope of the curves at the tangency will equal the relative price of the two goods in the market. This must be true because if consumers value a good higher than its production costs, the good will be viewed as a bargain and demand will rise causing more production to occur until marginal costs rise to meet the value consumers place on the good. This process finally brings together the slope of the production possibility curve and the slope of the consumer indifference curves.
At this point, consumer exchanging, producer input juggling, and product mix shifting reach the optimal level with the resources going to their best use at the lowest possible price. This is true for a given initial resource distribution. If another starting point is chosen, then an alternative efficient outcome results.
When international trade is present, the rate at which goods can be traded is established by the world price of the good. This relative world price becomes the product transformation curve in effect, and consumer equilibrium is obtained by equating the world price with the marginal rate of substitution of the consumer. This will result in some importing and exporting unless all countries have identical production possibility curves and therefore identical costs of production.
All this analysis so far has assumed perfect competition with no government sector. In the real world where taxes alter the true relative prices of products, consumers are led to solutions that misallocate resources because the price signals are not true signals of resource cost. Only if taxes do not alter the relative prices of goods are they neutral with respect to resource allocation. A head tax, or lump-sum tax, is an example of a tax that does not destroy efficiency.
Anything that causes prices to reflect less than the true opportunity cost of the product will spoil the efficiency of this general equilibrium model. Monopoly pricing puts price above marginal cost, and externalities in production or consumption understate the true cost or benefit of a product. In both cases misallocation occurs unless a government tax or regulation corrects the incorrect prices at zero cost. Finally, public goods, which are used jointly by many people, create a situation where true consumer preferences are hard to measure. Therefore, the true consumer value is not easily measured and allocation may be only approximate at best.
Chapter Outline

1. General equilibrium can be explored most easily with a simple two-person exchange model.
2. An Edgeworth exchange box shows the initial endowment of goods and the distribution of those goods.
3. If marginal rates of substitution of the two goods differ for the two people, both people can improve their lot by exchange.
4. Pareto optimality and a location on the contract curve results when no one can improve further without hurting the other person.
5. The location on the contract curve, although efficient, may not be fair if the initial endowments were not equitable.
6. The actual trading process is enhanced by the fluctuation of the prices of the goods until supply equals demand in each market.
7. The invisible hand theorem summarizes this action, by stating that the equilibrium in competitive markets is Pareto optimal.
8. An Edgeworth production box shows the initial resource endowments and how they are allocated among the two production processes.
9. If the marginal rates of technical substitution differ, there will be in­centive for the firms to exchange inputs until they reach the contract curve of production, where the MRTS are identical.
10. The contract curve of production is efficient because one firm could not increase its output without the other firm losing output.
11. Efficiency in production and consumption could exist in an economy that produced the wrong mix of goods.
12. Deriving a production possibilities curve from the production con­tract curve will give a menu of alternative efficient output combina­tions.
13. The slope of the production possibilities curve shows the rate at which society is able to exchange one good for the other.
14. The slope of the consumer's indifference curve shows the rate at which society would be willing to trade the two goods.
15. When society values goods at the cost of producing the goods, then the right mix of goods exists.
16. If the society is viewed as part of an international exchange environment, then the world price becomes the cost of acquiring output rather than the individual country production menu.
17. Firms will be unsuccessful if they try to sell goods that cost more than the world price.
18. Accordingly, each country produces where it has its best advantage and buys goods that it is not equipped to produce, providing for a more efficient world.

1. Market intrusions alter the ideal outcomes.
2. Taxes that affect relative prices destroy the efficiency of the system, unlike head taxes that do not alter relative price ratios.
3. Monopoly pricing above the marginal cost leads to the wrong product mix.
4. Externalities distort the true costs and benefits of decision making, unless public policy offsets the distortion.
5. Public goods cannot be efficiently supplied by markets because of the nondiminishability and nonexcludability qualities of those goods.

Important Terms

A Case to Consider

1. The suppliers of computer motherboards and memory chips have gone on strike. Matt has 100 motherboards left, but he has memory chips stocked for only 20 computers.  On the other hand, Megan has memory chips for 100 computers and motherboards for only 20. Show this information using a production Edgeworth box, where the lower left corner of the box is labeled "Matt’s computers" and the upper right corner of the box is labeled "Megan’s computers." Label the vertical side of the box as motherboards and the horizontal side as memory chips. Label the initial endowment point with the letter A.

1. Now sketch into your Edgeworth box above an isoquant for both Matt and Megan that reflects the fact that chips and motherboards are perfect complements. (L shaped isoquants)

1. Shade in the area where mutually beneficial trade can take place.
2. Next, sketch into the box a typical set of isoquants (4 for each person) that are points on the contract curve of production for computers.

1. Describe in words why the initial starting point is not optimal using the words "marginal rate of technical substitution."

1. If no trade of inputs takes place and neither producer can get outside parts, how many completed computers can be sold by these producers?

1. If Matt and Megan exchange inputs until they reach the contract curve, how many computers will be produced if all resources are used?

1. How will the sales be divided up between the two vendors if both have equal bargaining power?

Multiple-Choice Questions
1.   General equilibrium analysis
a.   broadens the horizon of analysis to include the  interrelationships of all the previous chapters in the book.
b.   generalizes  equilibrium conditions in markets by using a model which involves only one consumer and one producer..
c.   considers national but not international implications for markets. 
d.   is described in part by all of the above statements.
2.   In the commodity space of a consumer’s Edgeworth box,
a.   every point represents a given distribution of available commodities.
b.   every point of tangency among indifference curves is considered efficient.
c.   the available production of the economy is represented.
d.   all of the above points are true.

1. Which statement is true about the Edgeworth box sketched below?
2. At C Joe has more of everything than does Bill.
3. At B the distribution of utility is more equal than at C or A
4. C cannot be an efficient allocation.
5. A production possibility curve can be derived from this graph.

1. All points on a production possibility curve imply that
2. labor and capital are being used efficiently.
3. both goods are being allocated efficiently by all consumers.
4. the rate at which consumers are willing to exchange goods is equal to the rate at which society can exchange goods in production.
5. none of the above are true.
6. Which statement is true?
7. A system can be technically efficient but not fair.
8. Pareto optimality implies fairness as well as efficiency.
9. A starting point of resource endowment between two people that strongly favors one person relative to the other cannot be efficient in the long run.
10. All the above are true.
11. None of the above are true.
12. In a general equilibrium framework, the deadweight welfare loss of monopoly pricing behavior is
13. larger than it appears in partial equilibrium analysis because the ac­companying detrimental effects of the labor market are now con­sidered.
14. smaller than it appears in partial equilibrium because the competi­tive markets adjust and offset some of the loss.
15. identical to the partial equilibrium analysis.
16. either larger or smaller than partial equilibrium analysis depending on factors outside the model.
17. In a consumer product Edgeworth box, a position on the contract curve
18. is always preferred by consumers to some position off the contract curve.
19. is always more fair than some other position somewhere off the con­tract curve.
20. is always Pareto optimal.
21. is described by none of the above.
22. A Pareto preferred transaction is one where
23. the loser in a transaction loses less than the gainer gains.
24. all must gain welfare compared with the pre-transaction position.
25. no one loses and at least one person gains in the transaction.
26. the consumers must have moved to the contract curve.
27. A Pareto optimal transaction in consumption is one where
28. the loser in a transaction loses less than the gainer gains.
29. everyone must gain welfare in the transaction.
30. no one gains and no one loses.
31. the consumers must have moved to the contract curve.
32. The "invisible hand" of Adam Smith's markets could be restated in our terms by saying that
33. equilibrium will occur in all markets.
34. people will be guided by the market to their optimal happiness.
35. competitive market equilibrium brings Pareto preferred moves but not necessarily Pareto optimal moves.
36. competitive market equilibrium will be Pareto optimal.
37.  
38. In the Edgeworth box shown below,
39. there is more food demanded than is available.
40. there is more clothing demanded than is available.
41. the relative prices shown will bring equilibrium without changing.
42. none of the above are true.

1. In the Edgeworth box shown above for question 9,
2. the price for food is too low relative to the clothing price.
3. the price for food is too high relative to the clothing price.
4. the price is the correct one, but the consumers have not yet exhausted all beneficial market purchases and sales.
5. the indifference curves are inaccurately drawn so that a Pareto optimal market position is impossible to show.
6. In order to derive systematically the size of any single consumer good’s Edgeworth box, we need to know
7. the amount of production inputs and the production function of the consumer goods.
8. the Edgeworth box of production and its contract curve.
9. either a or b because they both amount to the same information.
10. both a and b plus the location on the contract curve of production.
11. If society is inside its production possibility frontier,
12. it is also off the contract curve of the production Edgeworth box.
13. consumers cannot have equal marginal rates of substitution for the goods that are produced.
14. goods are distributed less equally than they would be if a point on the production possibility frontier were reached.
15. all the above are true.
16. none of the above are true.
17. If society can transform 2 units of food into 1 unit of clothing and citizens are willing to trade 1 unit of food for 1 unit of clothing, then
18. the product mix in the economy is weighted too heavily toward cloth­ing and should be shifted toward more food.
19. the product mix in the economy is weighted too heavily toward food and should be shifted toward more clothing.
20. the slope of society's production possibility curve is not as steep as the slope of the citizen's indifference curve if clothing is on the horizontal axis and food is on the vertical axis.
21. both a and c are correct.
22. none of the above are correct.
23. In a perfectly competitive society, firms that profit maximize will produce where price is equal to marginal cost. This implies that
24. the right combination of goods will be produced.
25. the value of the last unit of output produced will be equal to the mar­ginal cost of producing it.
26. the marginal rate of transformation will equal the marginal rate of substitution.
27. all the above are true.
28. none of the above are true.
29. If an economy trades internationally at world prices, it
30. will always generate greater utility for its people than if it had an effi­cient closed economy in which it ignored world markets.
31. will generate greater utility for its people than if it had an efficient closed economy in which it ignored world markets, except in the rare case where its marginal rate of transformation was exactly equal to the ratio of world prices.
32. will improve itself only if it is a developed country with a production possibility curve that is farther to the right than its competitors' in world markets.
33. will be better off only if it has low cost inputs and a production pos­sibility frontier that is farther left than its competitors' in world markets.
34. Which of the following will improve efficiency in an economy?
35. A lump-sum tax instead of a sales tax imposed on a good
36. A pollution tax equal to environmental damage imposed on a manufacturing firm
37. User charges applied wherever the consumer benefit of a public good can be measured
38. All the above improve efficiency.
39. None of the above improve efficiency.

Problems

1. The economics department has a 2-person faculty, and the dean expects half of each 50-hour-per-person week to be spent in research and half to be spent in teaching. The dean does not care how the department divides up its tasks between the faculty as long as the overall balance is kept. Loren is presently doing all the research, and Melissa is doing all the teach­ing. Both have a normal-shaped utility function with respect to teaching and research. First, sketch an Edgeworth box depicting the present state of affairs with indifference curves for both Loren and Melissa.

1. Label the initial allocation of tasks as point A on the graph.

1. Next, reallocate the teaching and research loads so that Loren is as pleased as he could be with the change and Megan is indifferent to the switch in scheduled work. Show this reallocation graphically in your graph above. Label the new point B.

1. In the same graph, show a situation where the beginning workload has been reallocated substantially but neither professor is any better or any worse off. Label this location point C.

1. If you were department chair, pick some point within the Edgeworth graph (label it D) and explain why you would try to allocate the work effort in that manner.

1. Why is this not an equilibrium position?

1. Sketch below the situation for loaves and fishes using a supply and demand curve for each product to show the nature of disequilibrium.

1. What will happen if markets are free to respond? Show this adjustment in both the supply and demand graphs in question b and in the Edgeworth box in the first part of this question.

1. How does this show that equilibrium in competitive markets is also Pareto optimal? Explain.

1. If the markets and the entrepreneurs all adjust, and the final price of labor is 2 and the capital price is 2, what will the ratio of the marginal products of labor and capital be when all the adjustments are made? Show in your Edgeworth box from section (a) of this question an input combination for both popcorn and DVDs that would illustrate a new efficient situation. Label the new outcome B.

1. List the three important conditions of systemic efficiency and explain how taxes, monopoly prices, and externalities interfere with these optimal conditions.

6.   Show graphically how a country can move outside its production possibility frontier by trading in the world economy.  Indicate the rare condition under which world  trade would not be advantageous for the country in question.
Answers to Questions for Chapter 18W
Case Questions

1. See the sketch labeled Case 18W-1 below.
2. See sketch labeled Case 18W-1 below.

1. b, The indifference curves will be less disparate no matter who has the bargaining power.
2. d, Edgeworth boxes as a tool to understand general equilibrium include all the options in this question and much more.
3. a, The production possibility curve is derived from the contract curve of production.
4. a, In the graph in 1 above, A or C might be on the contract curve, but they may be considered unjust compared with B, which is inefficient.
5. b, Consumers who are not served in the monopoly market will recover some welfare by purchasing in other markets that may give some consumer surplus.
6. c, No consumer can improve herself without hurting another person.
7. c, Pareto preferred improves at least one person without hurting another. Pareto optimal moves put one on the contract curve where no more gains from trade are possible.
8. d, See 6 above.
9. d, Smith's work was more philosophical than this question might imply.
10. b, Draw in the sketch the basket of goods for each person and the market disequilibriums will be apparent.
11. b, From the question above you can see that the price for clothing must rise.
12. c, The system starts with a given amount of resources and then works through production efficiency to a market for consumers who make choices that drive the entire movement of resources.
13. a, All points on the production Edgeworth box are on the production possibilities curve.
14. a, The marginal rate of transformation is not equal to the marginal rate of substitution.
15. d, The genius of markets is that all this happens automatically, at least in theory.
16. b, This is true because international trade opens up a whole new area of Pareto optimal exchanges that are lost if trade protection is practiced.
17. d, Since the world is not full of perfect markets there is much that can be done to help solve the misallocation problems providing the cure isn't more wasteful than the disease.

Problems

1. a-d) The sketch labeled Problem 18W-1 below answers all of these questions. Point D improves both faculty members' situation and still gets the job done.

            
50 hours               Problem 18W-1                              Melissa

1.  a) There is an excess demand for loaves and an excess supply of fish in the figure as presented.

2.   b) The simple supply and demand curve for loaves has a below-equilibrium price, and the same graph for fish shows an above-equilibrium price.
2.   c) The price line in the Edgeworth box will rotate clockwise, and the prices will adjust to equilibrium on the supply and demand graphs so the fish price rises and the loaves price falls.
2.   d) Product markets are in equilibrium and consumers and producers are on their contract curve.

1. Locate a sample point where the marginal rate of technical substitution (MRTS) of labor for capital in the production of food is greater than the MRTS of labor for capital in the production of shelter. Label that point A. Also label with the letter B one of the points where all gains from trade have been exhausted.

1. Sketch a contract curve from at least three appropriate points and label it CC. Explain what the contract curve means.

1. Use the numerical information generated so far to sketch a production possibilities curve on the graph below.

1. Locate with an A’ and a B’ on the sketch in (c) above the points that correspond with A and B respectively in question (a) above. Explain, in non-technical terms, what is wrong with point A’ and what action would solve the problem.
2. Finally, sketch an indifference curve on the graph in (c) above that will show that the marginal cost of producing food is equal to the marginal benefit consumers receive from food. If this condition is true for food, what will be true in the market for shelter?

1. Which equation, of the three required for efficiency, is adversely effected if monopoly is present? How is it altered?

1. Which equation of the three conditions required for efficiency is effected by a tax on one of the commodities in the economy?

1. How might efficiency be affected if the tax in (b) above is levied on a product that externalizes part of its production cost through pollution?

5.   In the end, a rational choice study of the economy is a powerful method of exploring human behavior.  Things come together beautifully in general equilibrium where all conditions for efficiency are met.  But upon deeper reflection, as the text points out along the way, many other forces drive behavior and they will alter outcomes suggesting that efficiency as economists often narrowly define it, is often an inadequate measure of wellbeing. List some of the other forces that will qualify outcomes that rational choice considers optimal.