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Chapter 6

Simple Trade

 

PART 1 -- POTENTIAL GAINS FROM TRADE

 

Individuals exchange goods. The benefits they receive depend on how much they exchange and on what terms--I am better off (and you worse off) if you buy this book for $100 than if you buy it for $1. We do not yet know how market prices are determined--that is the subject of the next chapter--so we cannot say much about how the gains from trade will be divided among the traders. We do, however, know enough to understand why mutual gains from trade are possible--why one person's gain is not necessarily another person's loss. In this part of the chapter, I will examine the origin of such gains--first in the case where each individual has a stock of goods that can be either consumed or traded for someone else's goods and then in the case where individuals produce goods in order to exchange them.

 

Trade without Production

 

I have 10 apples. You have 10 oranges. We have identical tastes, shown in Figure 6-1 and Table 6-1. Point F is my initial situation; point A is yours. Column 1 of the table shows the bundles that are equivalent to (have the same utility as) 10 oranges plus no apples, corresponding to indifference curve U1 on Figure 6-1. Column 2 shows the bundles equivalent to 10 apples and no oranges, corresponding to U2.

Suppose I trade 5 of my apples for 5 of your oranges. We are now both at point R, with 5 apples and 5 oranges each. Since point R must be on a higher indifference curve than either A or F, we are both better off. The same result can be seen from the table. I was indifferent between my initial 10 apples and a bundle of 5 apples plus 2 oranges. Since oranges are a good, I prefer more of them to fewer. It follows that I prefer 5 apples plus 5 oranges to 5 apples plus 2 oranges; I am indifferent between having 5 apples plus 2 oranges and having 10 apples, hence I prefer 5 apples plus 5 oranges to my original 10 apples. Similarly, you were indifferent between having your original 10 oranges and having 4 apples plus no oranges; obviously you are better off with 5 apples plus 5 oranges. We have both gained from the trade. That is why we were both willing to make it.

 


Table 6-1

Column 1

Column 2

Bundle

Apples

Oranges

Utility

Bundle

Apples

Oranges

Utility

A

0

10

5

F

10

0

10

B

1

6

5

G

7

1

10

C

2

3

5

H

5

2

10

D

3

1

5

K

4

3

10

E

4

0

5

L

3

5

10

M

2

8

10

N

1

12

10

O

0

17

10


Indifference curves between apples and oranges, showing the same preferences as Table 6-1.


There are many other trades we could have made instead that would also have benefited both of us. Since I am indifferent between my initial situation (10 apples) and having 5 apples plus 2 oranges, I gain by trading away 5 apples as long as I get more than 2 oranges in exchange. Similarly you gain by trading away all of your oranges as long as you get more than 4 apples in exchange. So if you give me 10 oranges for 5 apples, we are both better off than when we started (I am at point S on the figure; you are at point T). If you give me 3 oranges for 5 apples, we are also better off than when we started. Obviously I would prefer to get 10 oranges for my 5 apples, and you would prefer to give only 3. There is a bargaining range--a range of different exchanges, some more favorable to me and less favorable to you than others, but all representing improvements for both of us on the original situation. One consequence of the existence of a bargaining range is discussed in the section of this chapter on bilateral monopoly. Other consequences--and ways of dealing with the ambiguity as to which trade will actually occur--are discussed later in the optional section.

In the example I have been using, the gains from trade come about because we start with different endowments--different initial quantities of goods. The same gains could also occur if we had identical endowments--5 apples plus 5 oranges each, for example--but different preferences. Figure 6-2a shows my preferences (the colored indifference curves) and yours (the black indifference curves). We both have the same initial endowment--5 apples and 5 oranges apiece. The arrows show the results of my trading 4 of my apples for 4 of your oranges; both of us are better off. As in the previous case, there are a variety of alternative trades that would also benefit both of us.

It is even possible to draw indifference curves that allow two people with identical preferences and identical endowments to gain by trade. In order to do so, however, I must give the indifference curves a shape inconsistent with our usual assumptions, as shown in Figure 6-2b. The goods shown are beer and apples. G is just enough beer to get drunk (you are not interested in being half drunk), and H is just enough apples to make a pie for your dinner party. F, your original endowment, includes enough apples for too small a pie and enough beer to get you just drunk enough to burn it. You would prefer either G (all beer) or H (all apples) to F. If two people were in that situation, with identical tastes and identical endowments of beer and apples, they could both gain by trade. One would take all the apples, one would take all the beer, and both would be better off.

This is a situation in which your tastes violate the rule of declining marginal utility. One can think of other examples. If it takes a gallon of gasoline to get where you are going, increasing the amount you have from 1/2 gallon to 1 gallon benefits you more than increasing it from zero to 1/2 gallon did. While such situations are possible, we usually prefer to assume them away, since they add complications to the analysis that are usually unnecessary.


Indifference curves, endowments, and trade. Panel (a) shows a situation for two individuals with different tastes but the same initial endowment. The colored indifference curves show my tastes; the black curves show yours. The figure shows a trade (you give me 4 oranges in exchange for 4 apples) that benefits both of us.


In panel (b), we have the same tastes and identical endowments. The trade of 5 apples for 5 beers makes both parties better off, since both point G (10 beers) and point H (10 apples) are preferred to point F (5 of each).

 

Trade and Production--English Version

 

So far, we have been trading a fixed endowment of goods; now we will consider the combination of trade with production, first in a verbal form and later using geometry. We will find it convenient to consider only two traded goods while holding constant our consumption of all other goods (except leisure). In order to simplify the discussion, we assume that over the range of alternatives considered, we always consume the same amount of the traded goods. (Our demand for them is "perfectly inelastic," to use a term with which you will later become familiar.) The benefit of trade then takes the form of increased leisure; if it takes less time to produce consumption goods, we have more time to spend enjoying them.

Assume it takes me 1 hour to mow my lawn and 1/2 hour to cook a meal. You are a better cook; you can cook a meal in 15 minutes. You are also a worse mower; it takes you 2 hours to mow the same lawn. For both of us, production possibility sets are linear--it takes twice as long to produce two meals (or two mowed lawns).

Initially I am mowing my lawn once per day (the grass grows fast around here) and cooking 3 meals per day, for a total of 2-1/2 hours of work. You are doing the same, for a total of 2-3/4 hours.

I offer to mow your lawn in exchange for your cooking my meals. It will take me 2 hours to mow both lawns; it will take you 1-1/2 hours to cook all 6 meals. We will both be better off. Just as in the earlier examples, there are a variety of other trades that would also be improvements for both of us on the initial situation. For example, I could offer to mow your lawn once in exchange for 4 meals (you would cook all my meals; I would mow your lawn three days out of four). Since it takes you 1 hour to cook 4 meals and 2 hours to mow the lawn, you are still better off making the trade.

I am better at mowing lawns than you are, so I mow the lawns; you are better at cooking, so you cook. Since "better" appears to mean "can do it in less time," it seems that I could be better than you at both cooking and mowing, and that if I were there would be no way in which I could benefit from trading with you.

This seems to make sense, but it is wrong--as a simple example will show. Suppose I can cook a meal in 15 minutes and mow a lawn in 1/2 hour. It takes you 1/2 hour to cook a meal and 2 hours to mow a lawn. I am better at everything; what can you offer me to trade?

Just as before, you offer to cook my meals in exchange for my mowing your lawn. Before the trade, you spent 1-1/2 hours cooking 3 meals and 2 hours mowing your lawn, for a total of 3-1/2 hours. After the trade, you spend 3 hours cooking meals for both of us. You are better off by 1/2 hour. What about me?

Before the trade, I spent 45 minutes per day cooking and 1/2 hour mowing, for a total of 1-1/4 hours. After the trade, I spend 1 hour per day mowing both lawns, for a total of 1 hour. I am better off too! How can this be? How can it pay me to hire you to do something I can do better?

The answer is that the relation between cost to me and cost to you in time has nothing to do with whether we can gain by trade; time is not what we are trading. The relevant relation is between my cost of mowing a lawn and yours in terms of meals cooked--our opportunity costs. We are, after all, trading mowed lawns for meals, not for time.

In the first example I gave, the opportunity cost to me of mowing a lawn was 2 meals, since mowing 1 lawn took the time in which I could have made 2 meals. The opportunity cost to you of mowing a lawn was 8 meals. Since lawn mowing cost much more to you (in terms of meals) than to me, it was natural for you to buy lawn mowing from me and pay with meals.

A different way of describing the same situation is to say that the cost to me of producing a meal was 1/2 lawn and the cost to you was 1/8 lawn. Since meals cost you much less than they cost me (in terms of lawns), it was natural for me to buy meals from you, using lawn mowing to pay you. These are two descriptions of the same transaction; when we trade lawn mowing for meal cooking, we can describe it as buying lawns with meals or meals with lawns, according to whose side we are looking at it from.

Since a lawn costs you 8 meals, you are willing to buy lawn mowing for any price less than 8 meals per lawn--it is cheaper than producing it yourself. Since it costs me 2 meals, I am willing to sell for any price higher than 2. Obviously there is a wide range of prices at which we can both benefit--any price of more than 2 meals per lawn and less than 8 will do.

Now consider the second example, where I can cook a meal in 15 minutes and mow a lawn in 30, while you take 30 minutes to cook a meal and 2 hours to mow a lawn. The cost of mowing a lawn to me is 2 meals; the cost of mowing a lawn to you is 4 meals. I benefit by trading lawns for meals as long as I get more than 2 meals per lawn; you benefit by trading meals for lawns as long as you pay fewer than 4 meals per lawn. Again, there is room for both of us to benefit by trade.

Once we realize that the relevant cost of producing one good is measured in terms of other goods, it becomes clear that I cannot be better than you at everything. If I am better at producing lawns (in terms of meals), then I must be worse at producing meals (in terms of lawns). If this is not obvious when put into words, consider it algebraically.

Let L be the time it takes me to mow a lawn and L' the time it takes you. Let M be the time it takes me to cook a meal and M' the time it takes you. The cost to me of mowing a lawn (in terms of meals) is L/M; if a lawn takes 30 minutes and a meal 15, then a lawn takes the time in which I could produce 2 meals. The cost to you is L'/M'. But the cost to me of a meal in terms of lawns is, by the same argument, M/L; the cost to you is M'/L'. If L/M > L'/M' then M'/L' > M/L. If you are better than I am at mowing a lawn, I must be better than you at cooking a meal.

To put the same argument in numbers, imagine that it costs me three meals to mow a lawn and costs you two. 3 > 2. I am a worse mower than you; it costs me more meals to mow a lawn. But 1/3 < 1/2. I am a better cook than you. It costs me only 1/3 lawn to cook a meal, and it costs you 1/2 lawn.

Comparative Advantage. The general principle I have been explaining is called the principle of comparative advantage. It is usually discussed in the context of foreign trade. The principle is that two nations, or individuals, can both gain by trade if each produces the goods for which it has a comparative advantage. Nation A has a comparative advantage over Nation B in producing a good if the cost of producing that good in A relative to the cost of producing other goods in A is lower than the cost of producing that good in B relative to the cost of producing other goods in B.

The error of confusing absolute advantage ("I can do everything better than you can") with comparative advantage typically appears as the claim that because some other country has lower wages, higher productivity, lower taxes, or some other advantage, it can undersell our domestic manufacturers on everything, putting our producers and workers out of work. This is used as an argument for protective tariffs--taxes on imports designed to keep them from competing with domestically produced goods.

There are a number of things wrong with this argument. To begin with, if we were importing lots of things from Japan and exporting nothing to them (and if no other countries were involved), we would be getting a free ride on the work and capital of the Japanese. They would be providing us with cars, stereos, computers, toys, and textiles, and we would be giving them dollars in exchange--pieces of green paper which cost us very little to produce. A good deal for us, but not for them.

Here, as in many other cases, thinking in terms of money obscures what is really happening. Trade is ultimately goods for goods--although that may be less obvious when several countries are involved, since the Japanese can use the dollars they get from us to buy goods from the Germans who in turn send the dollars back to get goods from us. In terms of goods, the Japanese cannot be better at producing everything. If it costs them fewer computers to produce a car (translation: If the cost in Japan of all the inputs used to produce a car divided by the cost in Japan of all the inputs used to produce a computer is smaller than the corresponding ratio in the United States), then it costs them more cars to produce a computer. If they trade their cars for our computers, both sides benefit.

If you still find the claim that tariffs on Japanese automobiles are a way of protecting us from the Japanese in order to keep American workers from being replaced by Japanese workers plausible, consider the following fable.

Growing Hondas. There are two ways we can produce automobiles. We can build them in Detroit or we can grow them in Iowa. Everyone knows how we build automobiles. To grow automobiles, we begin by growing the raw material from which they are made--wheat. We put the wheat on ships and send the ships out into the Pacific. They come back with Hondas on them.

From our standpoint, "growing Hondas" is just as much a form of production--using American farm workers instead of American auto workers--as building them. What happens on the other side of the Pacific is irrelevant; the effect would be just the same for us if there really were a gigantic machine sitting somewhere between Hawaii and Japan turning wheat into automobiles. Tariffs are indeed a way of protecting American workers--from other American workers.

In Chapter 19, we will discuss tariffs again, demonstrating under what circumstances and in what sense American tariffs impose net costs on Americans and in what special cases they do not. At that point, we will also discuss why tariffs exist--and why the industries that actually get protected by tariffs are not the same as the industries that one might be able to argue, on economic grounds, ought to get protected.

 

Trade and Production--Geometric Version

 

There is a problem in using indifference curves to represent our preferences among two produced goods. With only two dimensions, there is no place to put leisure; if we are not careful, we may find that we are treating leisure as if it had no value at all. One way of solving the problem is to put leisure on one axis and all other goods--shown as the income available to buy them--on the other. This is what we did in Chapter 5 in order to use indifference curves to derive a supply curve for labor. While this was a useful diagram for analyzing the division of time between production and leisure, it is of no use for analyzing trade. In order to have trade, we must have two different goods to exchange. Since leisure itself cannot be traded, we need two goods in addition to leisure. With two-dimensional paper, we cannot graph three goods.

If we want to use the geometric approach to analyze trade, we will have to go back to graphing two different tradeable goods (or services) on the axes. We justify this by letting the indifference curves represent our preferences with regard to those two goods, given that we are also consuming some fixed amount of leisure (and possibly other goods). Such diagrams can be used to analyze the choice between two goods while ignoring decisions about how much of other goods (including leisure) we wish to consume.

Figure 6-3 shows the production possibility sets for me and you in the first example of the previous section. The only addition is the assumption that each of us is going to spend exactly 6 hours per day working. Both of us are assumed to have the same preferences, represented by indifference curves U1, U2, and U3--point A is on the highest indifference curve that touches my opportunity set, point B on the highest curve that touches yours.


Production possibility sets for two individuals. The entire shaded region shows the production possibility set for the combined output of two producers. The colored region shows the alternatives available to each producer if they divide their output evenly. C, the optimal point with joint production and even division, is preferred to A, my optimal point if I produce alone, and to B, your optimal point if you produce alone. This shows the possibility of mutual gains from trade.


To see why our combined opportunity set is as I have drawn it and why it is so large, imagine that we start in the upper left-hand corner, at point D on Figure 6-3. All we are doing is mowing lawns--9 of them a day (6 by me and 3 by you).

How much must we give up (in terms of lawns mowed) in order to produce 1 meal? If I cook it, we must give up 1/2 lawn mowed (it takes me 1 hour to mow a lawn, 1/2 hour to cook a meal); if you do it, only 1/8 of a lawn. Obviously we get the meal at lower cost by having you cook it. As we move down and to the right along the boundary of the opportunity set, we are giving up only 1/8 lawn per meal--that is why the line slopes down so slowly.

Eventually we reach point E, where you are spending all of your 6 hours of working time cooking while I am still spending all my time mowing lawns. We are producing 24 meals and 6 mowed lawns per day (if this seems like more than we have any use for, remember that the nonsatiation assumption becomes more plausible when we expand our simple examples to fit a world with many more than two goods in it). If we wish to produce still more meals, I must cook them--at a cost of 1/2 lawn per meal. The boundary turns abruptly down, since my cost for cooking meals is higher than yours. Eventually we reach point F, where we are both cooking full time and producing 36 meals per day.

The entire shaded area on Figure 6-3 shows the production possibility set available to the two of us together. The colored inner section shows how much each of us can have if we choose to split our output evenly, with each of us getting half of the lawns and half of the meals. C is the optimal point (for each of us) on that assumption. Note that it is on a higher indifference curve than either A or B, our optimal points without trade. Obviously many other divisions are possible. The point to note is how much bigger the consumption opportunity set becomes for each of us when we combine our efforts through trade. I am (relatively) good at mowing lawns, and you at cooking meals. Without trade, I cannot make full use of my comparative advantage--there are too many meals I want cooked and not enough lawns I want mowed. The situation is the same (in the opposite direction--too many lawns and not enough meals) for you. Through trade, we solve the problem.

 

PART 2 - COMPLICATIONS OF TWO-PERSON TRADE

 

In the first part of this chapter, we saw why individuals can gain by trade. In this part, we will look a little more carefully at some of the problems associated with two-person trade--in particular, at problems associated with the conflict between the two traders over the division of the gains.

 

Bilateral Monopoly--The Serpent in the Garden

 

So far, I have presented an entirely optimistic view of trade, with individuals cooperating to their mutual benefit. There is one problem that may have occurred to you. In each of these cases, there are many different trades that benefit both parties; some are preferred by one, some by the other. What decides which trade actually occurs?

Consider the following very simple case. I have a horse that is worth $100 to me and $200 to you. If I sell it to you, there is a net gain of $100; the price for which I sell it determines how the gain is divided between us. If I sell it for $100, you get all the benefit; if I sell it for $200, I do. Anywhere in the bargaining range between these two extremes we divide the $100 surplus between us.

Bargaining Costs. If I can convince you that I will not take any price below $199, it is in your interest to pay that; gaining $1 is better than gaining nothing. If you can convince me that you will not pay more than $101, it is in my interest to sell it for that--for the same reason. Both of us are likely to spend substantial real resources--time and energy, among other things--trying to persuade each other that our bargaining positions (the amounts we say we will pay or take) are real.

One way I can do so is by trying to deceive you about how much the horse is really worth to me. When I set up the problem, I (the author of this book) told you (the reader of this book) what the real values were, but the you and I inside the problem do not have that information. Each of us has to guess how much the horse is worth to the other--and each has an incentive to try to make the other guess wrong. If I believe the horse is worth only $101 to you, there is no point in my trying to hold out for more.

One danger in such bargaining is that we may be too successful. If I persuade you that the horse is really worth more than $200 to me (and I may try to do so, in the false belief that you will, if necessary, pay that much for it), then you stop trying to buy it. If you persuade me that it is worth less than $100 to you (ditto, mutatis mutandis), then I stop trying to sell it. In either case, the deal falls through and the $100 gain disappears.

Strikes and Wars--Errors or Experiments? Consider a strike. When it is over, union and management will have agreed to some contract. Typically, both the stockholders whose interest management is supposed to represent and the workers whose interest the union is supposed to represent would be better off if they agreed, on the first day of bargaining, to whatever contract they will eventually sign, thus avoiding the cost of the strike. The reason they do not is that the union is trying to persuade management that it will only accept a contract very favorable to it and management is trying to persuade the union that no such contract will be offered. Each tries to make its bargaining position persuasive by demonstrating that it is willing to accept large costs--in the form of a strike--rather than give in.

Much the same is true of wars. When the smoke clears, there will be a peace treaty; one side or the other will have won, or some compromise will have been accepted by both. If the peace treaty were signed immediately after the declaration of war and just before the first shot was fired, there would be an enormous savings in human life and material damage. The failure of the nations involved to do it that way may in part be the result of differing factual beliefs; if each believes that its tanks and planes are better and its soldiers braver, then the two sides will honestly disagree about who is going to win and hence about what the terms of the peace treaty will be. In this situation, one may regard the war as an (expensive) experiment to settle a disagreement about the military power of the two sides.

But there are other reasons why wars occur. Even if both sides agree on the military situation, they may have different opinions about how high a price each is willing to pay for victory. It is said that when the Japanese government consulted its admiralty on the prospects of a war with the United States, the admiralty replied that they could provide a year of victories, hold on for another year, and would then start losing--a reasonably accurate prophecy. The Japanese attacked anyway, in the belief that the United States--about to become engaged in a more difficult and important war in Europe--would agree to a negotiated peace sometime in the first two years. An expensive miscalculation.

While bilateral monopoly bargaining is a common and important element in real-world economies, it is not the dominant form in which trade occurs. Fortunately (from the standpoint both of saving bargaining costs and of simplifying economic analysis), there are other and more important mechanisms for determining on what terms goods are exchanged, mechanisms that lead to a less ambiguous result as well as considerably lower transaction costs.

 

Getting "Ripped Off"

 

There seems to be a widespread belief that if someone sells something to you for more than he could have--if, for example, he could make a profit selling it to you for $5 but charges $6--he is somehow mistreating you, "ripping you off" in current jargon. This is an oddly one-sided way of looking at such a situation. If you pay $6 for the good, it is presumably worth at least $6 to you. (I am not now considering the case of fraud, where what you think you are getting and what you are really getting are different things.) If it costs him $5 and is worth $6 to you, then there is a $1 gain when you buy it; your claim that he ought to sell it to you for $5 amounts to claiming that you are entitled to get all of the benefit from the transaction. It would seem to make just as much (or as little) sense to argue that he should get all the benefit--that if you buy a good for $5 when you would, if necessary, have been willing to pay $6, then you are ripping him off. Yet I know very few people who, if they see a price of $4 on a new book by their favorite author for which they would gladly pay $10, feel obliged to volunteer the higher price--or even to offer to split the difference.

As it happens, substantial bargaining ranges are not typical of most transactions, for the same reasons that bilateral monopoly is not the dominant form of trade. Most of the goods you buy are sold at about cost (if cost is properly computed) for reasons you will learn in the next few chapters. Nonetheless, bilateral monopolies and bargaining ranges do exist. I am myself a monopolist: I give speeches and write articles on a variety of topics, and I believe that nobody else's speeches and articles are quite the same as mine. I enjoy writing and speaking. I would give some speeches and write some articles even if I did not get paid for them; indeed I do (sometimes) write articles and give speeches for which I am not paid. That is no reason why I should not charge for my services if I can. If someone is willing to pay me $500 for a speech I would be willing to give for free, then that is evidence that giving the speech produces a net gain of at least $500. I see no reason why I should feel obliged to turn all of that gain over to my audience.

 

OPTIONAL SECTION

 

THE EDGEWORTH BOX

 

In the case of two-person trade, there may be many different exchanges, each of which would be beneficial to both parties; some exchanges will be preferred by one person, some by the other. There are then two different questions to be settled. One is how to squeeze as much total gain as possible out of the opportunities for trade; the other is how that gain is to be divided. The two individuals who are trading have a common interest in getting as much total gain as possible but are likely to disagree about the division.

An ingenious way of looking at such a situation is the Edgeworth Box, named after Francis Y. Edgeworth, the author of a nineteenth century work on economics called Mathematical Psychics (which does not mean what it sounds like).

In the simplest two-person trading situation (such as the one discussed at the beginning of this chapter), there are only two goods and no production. There are then four variables--how much of good X I have (x1), how much you have (x2), how much of good Y I have (y1), and how much you have (y2). Since exchange does not change the total amounts of the two goods, we have two constraints: x1 + x2 = x and y1 + y2 = y, where x and y are the total endowments of X and Y. Since we have four variables and two constraints, the constraints can be used to eliminate two of the variables, leaving us with two--which can be plotted on a two-dimensional surface such as this page. Here is how you do it.

How to Build a Box. First draw a box, such as Figure 6-4, with length x and height y (20 and 15). Any division of x and y between you and me can be represented by a point, such as point A. The horizontal distance from the left-hand edge of the box to A is x1 (=15), the vertical distance from the bottom of the box is y1 (=3); so A represents the amount of x and y I have, seen from the lower left-hand corner of the box (which is where the origin of a graph usually is). Since the length of the box is x (=20), the horizontal distance from A to the right-hand edge of the box is x - x1 = x2 (=5); the vertical distance from A to the top edge of the box is y - y1 = y2 (=12). So A also represents your holdings of X and Y--as seen, in an upside-down sort of way, from the upper right-hand corner of the box. Any point inside the box represents a possible division of the total quantity of X and Y, with my share measured from the lower left-hand corner, yours from the upper right-hand corner. Any possible trade is represented by a movement from one point in the box, such as A, to another, such as B. The particular trade that moves us from A to B consists of my giving you 2 units of X in exchange for 1 unit of Y.


An Edgeworth Box. A point, such as A or B, represents a division between us of the total quantity of X and Y. x1 is how much X I have and x2 is how much you have; similarly y1 is how much Y I have and y2 is how much you have. My quantities are measured from the bottom left corner of the box; your quantities are measured from the top right corner.


The Edgeworth Box is the opportunity set of the two traders; it shows all the ways in which the existing stock of goods could be divided between them. Any trade simply moves them from one point in the box to another. In order to see what trades they will be willing to make, we also need their preferences. Figure 6-5 shows the same box, with my indifference curves (the blue lines--U1, U2, U3) and yours (the red lines--V1, V2, V3) drawn in. Note that my indifference curves are shown in terms of my consumption (x1,y1), while yours are shown in terms of your consumption (x2,y2). Hence mine are convex to my origin at the bottom left-hand corner and yours to your origin at the top right-hand corner. My utility increases as I move up and to the right (increasing my consumption); yours increases as you move down and to the left (increasing your consumption).

Trading. This makes it sound as though any trade must help one of us and hurt the other, but that is not the case. A trade that moves us down and to the right or up and to the left may put both of us on higher indifference curves. Consider the move from point A to point B on Figure 6-5. Since B is on a higher indifference curve for both of us than A, the trade benefits both of us. If we start at point A, any point in the shaded and colored areas bounded by U1 and V1 is preferred by both of us; we might both agree to a trade that moved us from A to such a point.

Suppose we make the trade that moves us from A to B. The points that are preferred to B make up a smaller area bounded by U2 and V2, shown colored in the figure. It is in our interest to make another trade. The process stops only when we reach a point such as E. At E our indifference curves are tangent to each other. Since they curve in opposite directions, this means that starting from point E, any point that is on a higher indifference curve for me must be on a lower curve for you; any trade that makes me better off makes you worse off. This is easier to see on the diagram than to explain in words.


An Edgeworth Box showing indifference curves and possible gains from trade. Blue indifference curves show my preferences; red ones show yours. The entire shaded area is preferred to A by both of us; the colored area is preferred to B by both of us. Once we reach point E, no further trade can benefit both of us.


The Contract Curve. The point E is not unique. Figure 6-6 shows the same box with the indifference curves drawn in such a way as to show the contract curve--the set of all points from which no further mutually beneficial trading is possible. As we saw in the previous paragraph, these are the points where one of my indifference curves is tangent to one of yours. If we continue trading as long as there is any gain to be made, we must eventually end up at some point on the contract curve. The arrows in the figure show two different series of trades, each starting at point A, leading to different points on the contract curve. Once we reach the curve, there is no further trade that can make both of us better off.


An Edgeworth Box showing the contract curve and ways of reaching it. Starting at point A, the arrows show two possible sequences of trades that reach the contract curve.


TRADE BALANCES, EXCHANGE RATES, AND FOSSIL ECONOMICS

 

In recent years, foreign trade has been a popular topic with newspaper writers and television commentators. The peculiar thing about the public discussion, which largely centers on the issue of trade deficits and American "competitiveness," is that most of it is based on ideas that have been obsolete for more than a hundred and fifty years --at least since David Ricardo discovered the principle of comparative advantage. It is rather as though discussions of the space program started out by assuming that the earth was sitting still in the middle of the universe, with the sun, the other planets, and the stars rotating around it.

The discussion of trade earlier in this chapter provides the essential ideas necessary to understand why most of what you see on the subject in the media is nonsense. So far, we have examined those ideas in the context of two individuals or two nations, trading goods for goods; we have said nothing about issues such as exchange rates, money prices, or the balance of trade. In this section, I will try to show more clearly how the logic of comparative advantage works itself out in modern international trade.

It is useful to start with the frequently made claim that the United States is not competitive in international trade, and that the reason is that our production costs, and thus the prices at which we try to sell our goods, are too high relative to the cost of goods abroad. A fundamental problem with this claim is that American costs are in dollars and Japanese costs are in yen. In order to compare them, we must first know how many yen you can get for a dollar--the exchange rate. Until we understand how the exchange rate is determined, we cannot say to what extent the high cost of an American car in Japan, measured in yen, is a result of the number of dollars it takes to produce a car, and to what extent it is a result of the number of yen it takes to buy a dollar.

How is the exchange rate determined? Some people wish to trade dollars for yen; some wish to trade yen for dollars. The equilibrium price, as we will see in more detail in the next chapter, is the price at which buyers choose to buy as much as sellers choose to sell. If more yen are supplied than demanded, the price falls; if fewer, the price rises. When the two numbers are equal, the price is at its equilibrium level, just as on any other market.

Why do people want to trade dollars for yen, or vice versa? To simplify the analysis, we will start with a situation where there are no capital flows--Japanese do not want to buy U.S. government debt, or U.S. land, or shares in U.S. corporations, nor do Americans want to buy similar assets in Japan. The only reason for Japanese to want dollars is in order to buy American goods; the only reason Americans want yen is to buy Japanese goods.

Suppose that at some particular exchange rate, say 200 yen to the dollar, most goods are cheaper in Japan than in the United States--America is "not competitive." In that case lots of Americans will want to trade dollars for yen in order to buy Japanese goods and import them, but very few Japanese will want to sell yen for dollars, since practically nothing in America is worth buying. The supply of yen is much lower than the demand, so the price of yen goes up. Yen now trade for more dollars than before, and dollars for fewer yen.

The fewer yen you get for a dollar, the more expensive Japanese goods are to Americans, since Americans have dollars and the Japanese are selling for yen. The more dollars you get for a yen, the less expensive American goods are to the Japanese. The exchange rate continues to move until prices are, on average, about the same in both countries--more precisely, until the quantity of dollars offered for sale by Americans equals the quantity that Japanese wish to buy. Since the only reason people in one country want the other country's money is to buy goods, that means that the dollar value of U.S. imports (the number of dollars we are selling for yen) is now the same as the dollar value of U.S. exports (the number of dollars they are buying with yen). Americans are now exporting those goods in which we have a comparative advantage (our production cost for those goods, relative to our production cost for other goods, is low compared to the corresponding ratio in Japan) and importing those goods in which the Japanese have a comparative advantage.

One implication of this analysis is that trade automatically balances. If the quality of one country's goods improves or their cost falls, the result is not an imbalance of trade but a change in the exchange rate. Improved production makes a country richer, but it does not make it more competitive.

This raises an obvious question: if trade automatically balances, how is that the United States has a trade deficit? To answer that question, we must drop the assumption that there are no capital flows, that the only reason Japanese want dollars is to buy United States goods.

Suppose that, for some reason, the United States is an attractive place to invest. Foreigners--Japanese in our example--wish to acquire American assets: shares of stock, land, government bonds. To do so, they must have dollars. Demand for dollars on the dollar-yen market now consists in part of demand by Japanese who want dollars to buy American goods and in part of demand by Japanese who want them to buy land or stock. At the equilibrium exchange rate, American imports (supply of dollars) equal American exports plus Japanese investment (demand for dollars). America now has a trade deficit; our imports are more than our exports.

Seen from the standpoint of a firm trying to export American goods, the reason for the trade deficit is that our costs are too high--we cannot export as much as we import. But that "reason" confuses a cause with an effect. The fact that our dollar costs are high compared to Japan's yen costs is a statement not about our costs but about the exchange rate. The real reason for the trade deficit is the capital inflow; indeed, the capital inflow and the trade deficit are simply two sides of an accounting identity. If the exchange rate were not at a level at which the United States imported more than it exported, there would be no surplus of dollars in Japanese hands with which to buy capital assets from Americans.

One implication of this analysis is that terms such as "trade deficit" and "unfavorable balance of payments" are highly deceptive. There is nothing inherently bad about an inflow of capital. The United States had a capital inflow, and consequently an "unfavorable balance of payments," through most of the nineteenth century; we were building our canals and railroads largely with European money.

Whether our present trade deficit should be viewed as a problem depends on what you think the reason for it is. If capital is flowing into the United States because foreigners think America is a safe and prosperous place to invest, then the trade deficit is no more a problem now than it was a hundred and fifty years ago. If capital is flowing into the United States because Americans prefer to live on borrowed money and let their children worry about the bill, then that is a problem; but the trade deficit is the symptom, not the disease.

 

PROBLEMS

 

1. Table 6-2a shows the utility to individual A of various bundles of apples and oranges. Table 6-2b shows the utility to B of various bundles of apples and oranges.


Table 6-2

(a)

(b)

Apples

Oranges

Utility

Apples

Oranges

Utility

10

0

10

6.5

0

5

6

1

10

5

1

5

4

2

10

3.9

2

5

2

3

10

3

3

5

1

4

10

2.2

4

5

0

5

10

1.5

5

5

10

1

15

1

6

5

6

2

15

0

10

5

4.5

3

15

10

0

10

3

4

15

7

1

10

2.2

5

15

5.5

2

10

1.5

6

15

4

3

10

1

7

15

3

4

10

0

10

15

2.5

5

10

10

2

19

2.1

6

10

8

3

19

1.6

8

10

6.2

4

19

9

2

15

5

5

19

7.2

3

15

3.9

6

19

6

4

15

3

7

19

5

5

15

1.5

10

19

4.1

6

15

3.4

7

15

2.3

10

15

a. Draw indifference curves for A and B.

b. Suppose A starts with 10 apples and no oranges; she can trade apples for oranges at a price of 2 apples per orange. How many of each will she end up with?

c. Suppose B starts with 10 oranges and no apples. He can trade apples for oranges at a price of 1/2 apple per orange. How many of each will he end up with?

d. A starts with 10 apples (and no oranges) and B with 10 oranges (and no apples). They engage in voluntary trade with each other. What can you say about the bundles they will end up with?

2. Person A of Problem 1 starts with 1 apple and 9 oranges. She can trade apples for oranges (or oranges for apples) at a rate of 1 apple for each orange. What bundle does she end up with?

 

3. Table 6-3 shows how many hours it takes each of three people to produce a table or a chair.

a. If only A and B exist, will A buy chairs from B, sell chairs to B, or neither?

b. If only A and C exist, will A buy chairs from C, buy tables from C, or neither?

c. If only B and C exist, will B buy chairs from C, sell tables to C, or neither?


Table 6-3

Time to Produce

A

B

C

1 Table

10 hours

15 hours

12 hours

1 Chair

2 hours

5 hours

6 hours


4. I am better than my wife at bargaining with contractors, repair people, and the like; with a given amount of time and effort, I am likely to get a lower price. Also, I rather enjoy such bargaining, while she dislikes it. Are these two separate reasons why I should do the bargaining and she should do other family work, or are they two parts of one reason? Discuss. Does the fact that my wife and I are not selfish with regard to each other (i.e., I have a high value for her happiness, and she for mine) mean that we should ignore the principle of comparative advantage in allocating household jobs? Does it simplify any of the problems normally associated with exchange (between us)?

5. I can write one economics textbook/year or discover one oil well every three years (including the time for me to learn enough geology to discover the oil well). My wife can discover one oil well per year or write an economics textbook every two years (ditto, mutatis mutandis).

a. Draw my opportunity set for annual production of textbooks and oil wells.

b. Draw hers.

c. Draw our combined opportunity set.

6. The situation is as in the previous question.

A. For each textbook we write we are paid $50,000. For each oil well we discover we are paid $75,000. All we care about is money (economists and geologists are mercenary types). Draw our combined opportunity set for producing textbooks and oil wells and the relevant indifference curves. Given that all we care about is money, what other term might you use for our indifference curves? How many textbooks do I write each year and how many oil wells do I discover? How about my wife?

B. As before, we are paid $50,000/textbook. How high would the price we are offered to discover oil wells have to be to make us decide to produce no textbooks and spend all of our time discovering oil wells?

C. We are paid $75,000/well to discover oil wells. How much would we have to be paid/textbook to make us decide to spend all our time writing textbooks?

7. After spending the mid-70s discovering oil wells, I decide I would prefer never to look at another well log. After spending the mid-80s writing textbooks, my wife decides she would prefer never to look at another indifference curve. After considering the matter at some length we decide that we are not as mercenary as we thought. I decide to redraw our indifference curves, taking account of the fact that, for any given income, I would prefer to write textbooks and she would prefer to discover oil wells--although either one of us may be willing to do the other's job if paid enough. What do my indifference curves between oil wells produced and textbooks written look like (assume the same prices as in part a of the previous question)? What do hers look like?

(Note: the question does not give enough information to tell you exactly what the indifference curves look like, but it does give enough that you should be able to draw some plausible ones.)

8. I have a very talented wife. She is as good as I am at writing textbooks (1/year) and phenomenally good at discovering oil wells (2/year). She is also very lazy; I cannot persuade her to work more than half time. My talents are the same as in question 5. Answer the same questions as in problem 6. Discuss.

9. Suppose that instead of marrying my wife (Betty) I trade with her. I want to consume half an economics textbook and a quarter of an oil well each year (there's no accounting for tastes). I am such a good bargainer that I can get all of the benefit from trading with her, leaving her neither better nor worse off than if we had not traded.

a. We have the same abilities as in question 5; how much of the year do I work?

b. We have the same abilities as in question 8; how much of the year do I work?

c. In answering parts a and b, did you have to make any assumptions about Betty's tastes?

d. What principle does this question illustrate? Explain.

10. Figure 6-3 corresponds to the first example in this chapter's verbal discussion of trade with production. Draw a similar figure corresponding to the second example (where I can cook a meal in 15 minutes and mow a lawn in 1/2 hour; it takes you 1/2 hour to cook a meal and 2 hours to mow a lawn.)

11. Figures 6-7a and 6-7b correspond to two possible situations discussed in the optional section of Chapter 5. Use them to show how two people with identical production possibility sets, identical preferences and normally shaped indifference curves can still gain from trade. (Hint: It only works with one of the figures.)

12.When I do your work for you (in exchange for something else), I give up leisure and you get it. Why is this not quite the same thing as my trading leisure for whatever you are paying me for my work?

13. Figure 6-9 shows an Edgeworth Box for individuals A and B; their initial situation is at point D.

a. Show the region of possible trades--outcomes that both prefer to D.

b. Draw in the contract curve.

c. Draw a possible series of trades leading to a point on the contract curve.


Nonlinear production possibility frontiers. Figure 6-8a represents the production possibility frontier for each of two identical individuals with identical preferences; so does Figure 6-8b.



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