Introduction

The principal changes in trade theory since Ricardo’s time have centred on a fuller development of the demand side of the analysis and on the development of the production side of the economy in a manner that does not rely on the labor theory of value. 

To set the stage for this analysis, this chapter presents basic microeconomic concepts and relationships employed in analysing trade patterns and the gains from trade. This chapter should prepare the reader for the way the tools are employed in trade theory:

• We first present the theoretical analysis of decision making by consumers as they seek to maximise their satisfaction by proper allocation of their spending among final goods and services. 

• Next, we describe a similar kind of process that occurs when producers allocate expenditures among factors of production in order to maximise efficiency. 

• Finally, the meaning of efficient production in the entire economy is developed. 

The systematic application of the concepts and relationships in the context of international trade begins in the next chapter. 

The Theory of Consumer Behaviour

Consumer Indifference Curves 

Traditional microeconomic theory begins the analysis of individual consumer decisions through the use of the consumer indifference curve. The originator of the concept of the consumer indifference curve was F. Y. Edgeworth. This curve shows, in an assumed two-commodity world, the various consumption combinations of the two goods that provide the same level of satisfaction to the consumer. A typical indifference curve diagram is shown in Figure 1.

Adopting the basic postulate that more of any good is preferred to less, the S1, S2, and S3 curves illustrate different levels of satisfaction, with level S3 being greater than level S2, which in turn is greater than level S1. 

Economists recognise that it is impossible to measure an individual’s levels of satisfaction precisely; for example, we cannot say that S1 represents 20 units of welfare while S2 represents 35 units of welfare. 

Such a numbering of the indifference curves would indicate cardinal utility, instead micro theory uses the concept of ordinal utility.

Cardinal utility: actual numerical values can be attached to levels and changes of welfare. 

Ordinal utility: which means that we can say only that welfare or utility on curve S2 is greater than welfare on curve S1. 

How much greater cannot be determined, but the concept of ordinal utility reflects the assumption that a consumer can rank different levels of welfare, even if he or she cannot specify precisely the degree to which welfare is different. 

It is also important to note that consumers are assumed to have transitivity in their preferences. 

Transitivity: if a bundle of goods B2 is preferred (or equal) to a bundle of goods B1 and if a bundle of goods B3 is preferred (or equal) to B2, then bundle B3 must be preferred (or equal) to bundle B1.

TITANS OF INTERNATIONAL ECONOMICS: FRANCIS YSIDRO EDGEWORTH (1845–1926)

F. Y. Edgeworth was born in Edgeworthstown, County Longford, Ireland, on February 8, 1845. He was educated at home by tutors and then entered Trinity College, Dublin, in 1862, where he specialised in the classics. 

He then went on to Oxford University where he earned the highest distinction in his field. Possessed of a prodigious memory, he supposedly could recite complete books of Homer, Milton, and Virgil. 

At his final oral examination at Oxford, he is said to have responded to a particularly difficult question by asking, “Shall I answer briefly, or at length?” Subsequently, Edgeworth studied mathematics and law, and he was admitted to the bar. 

Edgeworth lectured for a number of years on English language and literature at London’s Bedford College. The scholarly Edgeworth used vocabulary seldom heard in conversational English. 

The poet Robert Graves (quoted in Creedy, 1986, p. 11) tells the story that when Edgeworth met T. E. Lawrence (Lawrence of Arabia) upon Lawrence’s return from a visit to London, he asked, “Was it very caliginous in the metropolis?” Lawrence replied, “Somewhat caliginous, but not altogether inspissated.” (To save you a trip to the dictionary, caliginous means “misty or dim; dark,” and inspissated means “thickened; dense”) .

In 1891, Edgeworth became professor of political economy at Oxford University. There he remained for the rest of his career. In addition, he served as editor of the prestigious Economic Journal from 1890 to 1911, when he was succeeded by John Maynard Keynes. Edgeworth died at the age of 81 on February 13, 1926. Today students are familiar with Edgeworth through his box diagram (see pages 75–78), sometimes called the Edgeworth-Bowley box diagram, in joint recognition of the contribution of Professor A. L. Bowley. 

Edgeworth first formulated the concept of the consumer indifference curve in Mathematical Psychics (1881). His work in microeconomic theory and mathematical economics has been widely recognised, particularly his forceful demonstration of the application of mathematics to economics. 

He argued that mathematics can assist “unaided” reason, as is reflected in the following quotation (Mathematical Psychics, p. 3): "He that will not verify his conclusions as far as possible by mathematics, as it were bringing the ingots of common sense to be assayed and coined at the mint of the sovereign science, will hardly realise the full value of what he holds, will want a measure of what it will be worth in however slightly altered circumstances, a means of conveying and making it current." 

Sources: John Creedy, Edgeworth and the Development of Neoclassical Economics (Oxford: Basil Blackwell, 1986), chap. 1; F. Y. Edgeworth, Mathematical Psychics (London: C. Kegan Paul, 1881); John Maynard Keynes, Essays in Biography (London: Macmillan, 1933), part II, chap. 3; Peter Newman, “Francis Ysidro Edgeworth,” in John Eatwell, Murray Milgate, and Peter Newman, eds., The New Palgrave: A Dictionary of Economics, Vol. 2 (London: Macmillan, 1987), pp. 84–98.

Given this indifference curve map, it is instructive to focus next on a given curve, S1 (see Figure 1):

• The definition of the curve indicates that this consumer is indifferent among all points on the curve. Thus, possession of quantity 0x1 of good X and quantity 0y1 of good Y (at point G) brings the same level of satisfaction as does possession of quantity 0x2 of good X and quantity 0y2 of good Y (at point F). 

• Note that point J (on curve S2) is preferred to point F because the consumer has the same amount of good Y at the two points but more of good X (0x4 > 0x2). The consumer is better off at point J than at point F in terms of well-being. By applying the concept of transitivity, it is also clear that J is preferred to G and H, because the latter two points provide the same welfare as F. 

• Another feature of the indifference curve is its shape. First, we know that the curve must be downward sloping because, since goods are substitutes, less of one good must be compensated with more of the other good to maintain the same satisfaction level. But we can make an even stronger statement. 

• The indifference curve is not only downward sloping but also convex to the origin, as are the curves in Figure 1. The reason for this convexity lies in the economic principle of the diminishing marginal rate of substitution, reflecting the law of diminishing marginal utility. 

• The marginal rate of substitution (MRS): is the name given to reflect the slope of the indifference curve. (It is actually the slope, which is negative, multiplied by a minus sign, which gives a positive number.) 

• In economic theory, the MRS is defined as the quantity of good Y that must be taken away from a consumer to keep that individual at the same level of welfare when a specified additional amount of good X is given to the consumer.

• Along any indifference curve in Figure 1, successive additional units of X are associated with successively smaller reductions in Y. This is because each additional unit of X brings less utility than did the previous unit; likewise, a reduction in the number of units of Y brings a higher utility for the last unit consumed. Hence, the MRS is diminishing as we move toward consumption of a greater number of units of good X along any given indifference curve. 

• The MRS can be expressed in useful economic terms:

  • If we reduce the amount of good Y consumed,

  • the change in utility (ΔU, where Δ indicates a small change) is equal to the change in Y (ΔY) multiplied by the marginal utility associated with the amount of Y lost (MUY)

  • or ΔU = (ΔY) × (MUY). 

  • If we offset this loss by giving additional X to the consumer, the change in utility from this additional X is equal to the amount of new X (ΔX) times the marginal utility associated with that X (MUX). Hence:

This expression indicates that the (negative of the) slope of the indifference curve equals the ratio of the marginal utilities of the two goods. 

Note that we do not need the actual marginal utilities, for example, 5 units of satisfaction for MUY and 4 units of satisfaction for MUX, in order to measure the MRS. All that is required is a knowledge of the ratio, for example, of the marginal utilities.

One final obvious property associated with an indifference curve is that it cannot intersect for the individual consumer. If they did, then one combination of X and Y (at the intersection) would yield two different levels of satisfaction, and this makes no economic sense. 

The nonintersecting indifference curves are important to the study of international economics, because in Chapter 6, indifference curves will be used to represent welfare not for an individual consumer but for a country. 

The community indifference curve (or country indifference curve) drawn in Figure 2 shows the combinations of goods X and Y that yield the same level of well-being for the community (or country) as a whole. 

To obtain this curve, we do not add together individual consumer indifference curves; economists do not believe that utilities of different consumers can be compared. Rather, the following question is answered as we plot the community indifference curve: if a given quantity of good Y is taken away from the community so that each person’s consumption of good Y is reduced in proportion to that person’s share of the country’s total consumption of good Y, "how much of good X must be given to consumers so that each consumer is brought back to his or her original level of utility"? 

When the total amount of good Y removed from all consumers (ΔY immediately below point A) is replaced by the total of good X necessary to bring all consumers back to each consumer’s original utility level (ΔX), we have traced out the movement from point A to point B. 

The entire curve CI1 can be plotted when this exercise is done for each point on the curve.

If consumers differ in their tastes, a crucial point is that a community indifference curve for one distribution of income in the country can intersect a community indifference curve for another possible income distribution in the country. 

• In Figure 3, curve CI1 represents the community indifference curve for a given income distribution, and curve CI′1 is a more preferred curve for the same income distribution. 

• Community indifference curve CI2 represents a curve for another income distribution, one in which consumers with less relative preference for good X have a greater weight in the income distribution. (Curve CI′2 is a less preferred curve for this second income distribution.) 

• If we start at point A, the removal of ΔY would require that ΔX be given to consumers in the first income distribution (moving to A′ on curve CI1) to keep community welfare the same as at point A. 

• However, with the second income distribution, more of good X (amount ΔX′) must be given to consumers to compensate for the loss of ΔY (moving consumers to point A″). More of good X must be provided because it does not bring as much marginal utility as in the first income distribution; thus, more units of X are needed to offset the loss of Y. In other words, because consumers who have a greater preference for good Y at the margin and a smaller preference for good X at the margin have a greater proportion of the income in this second distribution, they require more X to be compensated for a loss of good Y. 

• What is the point of this discussion? Very simply, suppose that some economic event moves the country from point A to point B. This event can change the income distribution so that curve CI1, for example, is relevant before the event but curve CI′2 is relevant after the event.

• What can be said about welfare change for the community? On the basis of the first income distribution, the community is better off since point B on curve CI′1 is preferred to point A on curve CI1. However, on the basis of the second income distribution, the community is worse off, because B on curve CI′2 is inferior to A on curve CI2. 

• Thus, the possibility that changes in income distribution may alter the community indifference map must be kept in mind when employing this concept. 

Although this presents a potential problem when the community indifference map is employed in the analysis of the impact of international trade, community indifference curves will be employed in subsequent chapters assuming that the community indifference map, like those for individuals, does not change within the period of analysis. Further discussion of the intersecting indifference curve problem will be presented in subsequent chapters but the point should be clear: the use of indifference curves to represent community welfare is a more complex phenomenon than the use of indifference curves to represent welfare for an individual consumer.

The Budget Constraint 

To determine actual consumption on the individual consumer’s indifference curve, we need to examine the income level of the consumer:

• The income level is represented by the budget constraint (or budget line) as shown in Figure 4. This line shows the various combinations of goods X and Y that can be purchased with a given level of income at fixed commodity prices. 

• Income level I1 gives this constraint for one level of income (say, $500 per week), and income level I2 (say, $600 per week) shows the constraint for a higher level of income. 

• Consider income level I1. If all income is spent on good X, then quantity 0x1 (at point B) can be purchased, but none of good Y. Alternatively, quantity 0y1 (at point A) can be purchased, but there is no income remaining with which to purchase any X. It is assumed that an infinite number of such combinations could be selected, and thus a straight line can be drawn connecting all feasible consumption combinations, given income level I1. 

• Hence, an intermediate position such as point C can also be attained. The slope of the budget line can be determined in the following way: 

  • If all income were spent on good X (at point B), then the quantity purchased of X is simply the income I1 divided by the price of good X, that is, 0x1 = I1/PX. 

  • Similarly, if all income were spent on good Y (at point A), the quantity purchased is the income divided by the price of Y, that is, 0y1 = I1/PY. The slope of the curve as movement occurs from point B to point A is the change in Y divided by the change in X, or

The (negative of the) slope of the budget line is thus simply the price of X divided by the price of Y. An increase in the price of X (or a decrease in the price of Y) would yield a steeper budget line, and a decrease in the price of X (or an increase in the price of Y) would yield a flatter budget line.

Consumer Equilibrium 

With the concepts of the consumer indifference curve and the budget constraint in mind, it is a straightforward matter to indicate consumer equilibrium. The objective of the consumer is to maximise satisfaction, subject to the income constraint. 

Because the individual indifference curves show (ordinal) levels of satisfaction, and the budget line indicates the income constraint, the consumer maximises satisfaction when the budget line just touches the highest indifference curve attainable. The point of maximum satisfaction with budget line FG is shown as point E on indifference curve S2 in Figure 5. 

Clearly, the consumer would not settle at point B because B is on a lower indifference curve (curve S1), or welfare level, than point E. Also, although the consumer would like to be at point A (on higher indifference curve S3), this point is not possible given the income level of the consumer. If income rises so that the consumer faces budget constraint F′G′, then point A could be attained and more of both goods could be consumed. (For a look at consumer allocation of expenditures among various categories of goods in the United States, see page 71.)

It is important to grasp the economic meaning of consumer equilibrium point E in Figure 5. Because budget line FG is tangent to indifference curve S2 in equilibrium, the slope of S2 at point E is therefore equal to the slope of budget line FG at point E. Thus, in consumer equilibrium,

This last expression indicates that, at the margin, the utility obtained from spending $1 on good X is equal to the utility obtained from spending $1 on good Y. If this were not the case, the consumer could increase welfare by reallocating purchases from one good to the other. For example, consider a position such as point B. The consumer will not wish to remain at B because

In this situation, the marginal utility obtained from spending the last dollar on good X exceeds the marginal utility obtained from spending the last dollar on good Y. The consumer can increase total utility by switching a dollar spent on good Y to good X. The consumer will continue to reallocate expenditures until this difference in marginal utility per dollar of the two goods disappears, at point E.

Production Theory

Having examined consumer behavior, we now turn to producers. Our focus is not on every aspect of production—for example, we do not examine the producer’s decision of what price to charge for a product—but on input choice and production efficiency within the firm.

Isoquants

In considering producer choice of inputs, assume that there are two factors of production, capital (K) and labor (L), employed in generating output. 

Isoquant: is the concept that relates output to the factor inputs. An isoquant shows the various combinations of the two inputs that produce the same level of output; a typical production isoquant is illustrated in Figure 6.

For example, output Q0 (say, 75 units) could be produced with the quantity 0k1 of capital and the quantity 0l1 of labor (point A). Alternatively, that level of output could be produced by using 0k2 of capital and 0l2 of labor (point B).

Consumer Expenditure Patterns in the United States

The tangencies of consumer indifference curves (reflecting tastes) with budget lines (reflecting incomes and relative prices) determine household expenditure patterns.

Table 1 indicates the percentages of personal consumption expenditures in the United States devoted to broad categories of goods and services in 1960, 1980, 2000, and 2014. 

• These figures show that, as incomes have grown over time, U.S. families have chosen to devote a somewhat smaller percentage of their consumption expenditures to durable goods and a much smaller percentage to nondurable goods. 

• Particularly important declines in spending shares occurred in food, clothing and footwear, while recreational goods and vehicles rose in relative importance. 

• A dramatic rise in consumer expenditure share has occurred in services, with 66.7% in 2014. Within services, considerable growth occurred in purchases of health care, where the share rose from 4.8% in 1960 to 16.7% in 2014, and the share spent on financial services and insurance almost doubled.

The exact shape of an isoquant reflects the substitution possibilities between capital and labor in the production process. 

Curves Q0, Q1, and Q2 in Figure 6 illustrate how capital and labor can be relatively easily substituted for each other. If substitution were difficult, the curve would be drawn more like a right angle. If substitution were easier, the isoquant would have less curvature. 

A precise measure of the curvature, and thus of the substitution possibilities, is the elasticity of substitution (see Chapter 8). A major feature of isoquants is that they, unlike consumer indifference curves, have cardinal properties rather than simply ordinal properties. Thus, in Figure 6, the three isoquants represent different absolute levels of output, with isoquants farther from the origin representing higher levels of output.

Clearly, isoquants are downward sloping, but not vertical or horizontal or upward sloping, because reducing usage of one input requires greater usage of the other to maintain the same level of output. In addition, isoquants cannot intersect. If they could intersect, doing so would mean that, at the intersection point, the same quantity of capital and labor would be producing two different levels of output. 

Because an assumption behind isoquants is that maximum technical or engineering efficiency is achieved along each curve, an intersection makes no sense.

Finally, consider the slope of the isoquant. 

• Suppose that the producer reduces the amount of capital used in production and offsets the effect on output by adding labor. 

• The loss in output from the removal of capital is the change in the amount of capital employed (ΔK) multiplied by the marginal physical product of that capital (MPPK):
  ΔQ = (ΔK) × (MPPK)

• The addition to output (ΔQ) from the extra labor is equal to the amount of that additional labor (ΔL) multiplied by the marginal physical product of that labor (MPPL):
  ΔQ = (ΔL) × (MPPL)

• Hence, since output remains unchanged after the substitution of labor for capital:

Because the slope at any point on the isoquant is ΔK/ΔL, this last expression states that the (negative of the) slope of the isoquant at any point is equal to the ratio of the marginal productivities of the factors of production (MPPL/MPPK). 

The ratio of marginal productivities is often referred to as the marginal rate of technical substitution (MRTS). 

Marginal rate of technical substitution (MRTS): is defined economically as the amount of capital that must be removed to keep output constant when one unit of labor is added. 

Clearly, the MRTS declines as more labor and less capital are used. This decline reflects the fall of MPPL as we use more labor and the rise of MPPK as we use less capital (because of the law of diminishing marginal productivity).

A final point needs to be made about isoquants as they relate to international trade theory. 

The assumption usually employed in trade theory is that the production function is characterised by constant returns to scale. This means that if all the inputs are changed by a given percentage, then output will change in the same direction by the same percentage. Thus, in Figure 7, a doubling of the inputs (labor from 20 to 40 units and capital from 10 to 20 units) will double the output (from 100 to 200 units). 

If increasing returns to scale existed, then isoquant Q2 would have an output value greater than 200, as the doubling of the inputs would more than double the output. Analogously, decreasing returns to scale means that output Q2 would be less than 200 units.

Isocost Lines

In making the decision of how many units of each factor of production to employ, the firm must know not only the technical relationship between inputs and output but also the relative cost of those inputs. The costs of the factors of production are illustrated by isocost lines. An isocost line shows the various combinations of the factors of production that can be purchased by the firm for a given total cost at given input prices. 

Thus, if the given wage rate is $10 per hour and the rental rate on machinery is $50 per hour, then a “budget” or “cost” of $500 per hour means that:

• The firm could hire 25 workers and 5 pieces of machinery. (If machinery is owned rather than rented, there is still an “opportunity cost” equal to the rental rate on machinery.) 

• Alternatively, the firm could use 8 machines and 10 workers. 

Clearly, there are many such possibilities; these possibilities are reflected in an isocost or budget line, such as line B1 in Figure 8.

Before indicating the optimal choice of how much of each factor to employ, consider the slope of an isocost line. 

• In Figure 8, if all of budget B1 were spent on capital, then 0k1 units could be purchased but no labor could be employed (point A). 

• Or 0l1 of labor could be hired but no capital could be used (point C). 

• If we imagine a movement from point C to point A, the slope is simply ΔK/ΔL or (0k1)/(–0l1). The distance 0k1 can be restated as the size of the budget (B1) divided by the rental rate on capital or price of capital (r); the distance 0l1 can be restated as the size of the budget divided by the wage rate (w):

Thus, the (negative of the) slope of the isocost is equal to the ratio of the wage rate to the rental rate on capital; and, for this reason, the isocost line is often referred to as the factor price line. 

A steeper isocost line reflects a rise in the wage rate relative to the rental rate on capital, while a flatter factor price line indicates the opposite.

Producer Equilibrium

The choice of the combination of factors of production to employ involves consideration of factor prices and technical factor requirements. 

• Point E in Figure 8 indicates the producer equilibrium position for a given cost B1. 

• At this point the isoquant is tangent to the isocost, and the firm is obtaining the maximum output for the given cost (i.e., production efficiency). 

• The firm would not settle at a point like G because this point yields less output for the given cost than does point E. 

• Alternatively, the producer equilibrium can be viewed as the point where the given output (Q1) is obtained for the lowest cost. 

• Isocost line B2 (e.g., at point H) also could be used to get Q1 of output, but B2 involves greater cost than B1. 

• In straightforward economic terms, it is clear why point E would be chosen but point G would not. Because the isoquant is tangent to the isocost at point E, this means that:

• Thus, the entrepreneur has an incentive to employ more labor services and fewer capital services, which decreases MPPL and increases MPPK, and the firm moves down the isocost line from point G to point E.

The Edgewoth Box Diagram and The Production Possibilities Frontier

From the standpoint of understanding international trade theory, two other concepts need to be introduced in this chapter. Both concepts look at the entire economy, not simply individual consumers and producers. 

The Edgeworth Box Diagram

This diagram is useful for discussion of a number of economic concepts and relationships. It will be used in this book to study efficient economy wide production. (It can also be used to discuss economy wide consumption). 

Construction of a typical Edgeworth box diagram begins by considering firms in two separate industries, industry X and industry Y (see Figure 9):

• Part (a) shows the isoquants for firms in industry X

• part (b) shows the isoquants for firms in industry Y. 

• Because ray 0X A is flatter than ray 0Y B, the X industry is the more labor-intensive industry and the Y industry is the more capital-intensive industry. 

• It should be remembered that, in a competitive economy with factor mobility between industries, the relative factor prices (w/r)1 facing the two industries will be identical.

The Edgeworth box diagram takes the isoquants of these two industries (assumed to be the only two industries in the economy) and puts them into one diagram as in Figure 10. 

• The isoquants of industry X are positioned as in part (a) of Figure 9. However, the Y isoquants of part (b) of Figure 9 are positioned differently in Figure 10. 

• The origin for the Y industry, 0Y, is positioned so that increased use of capital is indicated by downward movements from 0Y and increased use of labor is indicated by leftward movements from 0Y. 

• Hence, from 0Y, increased output of the Y industry is indicated by moving to isoquants that are further downward and to the left of 0Y. 

• An important feature of the Edgeworth box diagram is that its dimensions measure the total labor and total capital available in the economy as a whole. 

• Thus, horizontal distance 0XF and horizontal distance 0YG each indicate the total labor available, while vertical distance 0XG and vertical distance 0YF each measure the total capital available. 

• The total labor and the total capital in the economy will be divided between the two industries. 

• The economy can produce at any point within the confines of the Edgeworth box. However, some points of production are better (i.e., yield more total output) than other points. 

• The points of “best” production are those where isoquants of the two industries are tangent, such as point Q (isoquants x1 and y5) or point R (isoquants x2 and y4). 

• The line connecting these points of tangency is called the production efficiency locus, or the “contract curve”. 

• It is evident that this efficiency locus runs from 0X through Q, R, S, T, W to 0Y. At any given point on the locus, MPPL/MPPK is identical in both industries (and equal to w/r if the economy chooses to produce at that particular point).

Why do efficiency locus points represent the points of best production? To illustrate, consider point V off the locus:

• At V, the X industry is producing quantity x3 of output and is using quantity 0Xl1 of labor and 0Xk1 of capital. 

• The Y industry is producing y1 of output and is using 0Yl2 (= l1F) of labor and 0Yk2 (= k1G) of capital. 

• Note also that the labor used in the two industries adds up to the total labor available in the economy because 0Xl1 + 0Yl2 = 0Xl1 + l1F = 0XF (or = l2G + 0Yl2 = 0YG). 

• By similar analysis, the sum of the capital used in the two industries is the total capital available in the economy. 

But consider point S, which is on the efficiency locus:

• This production point yields x3 of X output, the same as point V because the two points are on the same isoquant. 

• However, point S yields y3 of Y output, which is greater than the Y output at point V because S is on a Y isoquant with greater production. 

• Hence, point S is a superior point to V because S has the same amount of X output but a larger amount of Y output. 

• From point V, point S could be reached by shifting l4l2 (= l1l3) of labor from Y production to X production and shifting k3k1 (= k2k4) of capital from X production to Y production.

• These shifts move labor out of the capital-intensive industry into the labor-intensive industry, and they move capital out of the labor-intensive industry into the capital-intensive industry.

By a similar argument, point W is superior to point M because W has the same Y output as M but more X output.

Finally, a point such as T has greater X output and greater Y output than either points V or M. 

The important conclusion is that, for each point not on the efficiency locus, some point on the efficiency locus involves greater production of at least one good and no less production of the other good. 

What comparisons can be made of points along the production efficiency locus itself?

• From the production standpoint alone, no judgments can be made about the relative desirability of these points because movement from one point to another leads to greater output of one good and less output of the other. Thus, for example, point S has more Y output but less X output than point W. 

• Only when demand in the economy is brought into the analysis (see Chapter 6) can we indicate the relative desirability of points along the locus and the output combination that will actually be chosen.

• Nevertheless, we can conclude that points off the locus are inefficient for the economy as a whole because any such point can be improved upon by moving to the production efficiency locus. 

• Points on the locus are efficient, because moving along the locus requires giving up output of one good in order to get more output of the other good. The economist’s term for this trade-off characterizing the efficiency locus is called Pareto efficiency, after Vilfredo Pareto (1848–1923). 

The Production-Possibilities Frontier

A typical production-possibilities frontier (PPF) is drawn in Figure 11. Unlike the PPF used by the Classical economists, however, this PPF demonstrates increasing opportunity costs.

• If the economy is located at point A, it is producing 0x1 of the X good and 0y4 of the Y good. 

• If movement takes place to point B, then x1x2 of the X good is being added, but y3y4 of Y is being given up.

• If we add an additional amount of X, x2x3, which is equal to x1x2, the amount y2y3 of the Y good must be forgone. 

• Increasing amounts of Y must be1 given up in order to get the same additional amount of X because y1y2 > y2y3 > y3y4, and so on.

• Similarly, if the economy moves in the other direction (say, from point D), increasing opportunity costs occur because giving up equal amounts of good X (e.g., x3x4, then x2x3, then x1x2) yields smaller increments of good Y (y1y2, then y2y3, then y3y4). 

• With increasing opportunity costs, the shape of the PPF is thus concave to the origin or bowed out, as shown in Figure 11.

The formal name for the (negative of the) slope of the PPF is the marginal rate of transformation (MRT), which reflects the change in Y (ΔY) associated with a change in X (ΔX). Because the slope itself (ΔY/ΔX) is negative, the negative of the slope or –ΔY/ΔX is a positive number (the MRT). 

It can be shown mathematically that MRT = MCX/MCY, or the ratio of the marginal costs in the two industries.

• Because firms incur rising marginal costs when they expand output, movement toward more X production means that MCX will rise; similarly, as less Y production is undertaken, MCY will fall. As more X and less Y production is undertaken, the ratio MCX/MCY will rise.

• In other words, the PPF gets steeper as we produce relatively more X. 

There are several other ways to explain the concave shape of the PPF. One of the early explanations (given by Gottfried Haberler in 1936) involved “specific factors” of production. 

• Suppose we move from point D to point C in Figure 11. 

• In Haberler’s view, the factors of production in the X industry that will move into Y production are the more mobile and adaptable factors. Their adaptability enables them to contribute a good deal to Y output. As we continue to shift resources from X to Y (e.g., from C to B), however, the factors being shifted are less adaptable. They contribute less to Y production than the previous factors. 

• It is evident that the additional output of Y attained for given reductions in X output is declining. Thus, increasing opportunity costs are occurring. 

Another way to explain the shape of the PPF has been offered by Paul Samuelson (1949, pp. 183–87). 

• Suppose that each industry is characterised by constant returns to scale; suppose, too, that the industries have different factor intensities: the X industry is relatively labor intensive and the Y industry is relatively capital intensive. 

• Then, in Figure 12, assume that all factors (only capital and labor in this discussion) are devoted to Y production, so that the economy is located at point R and is producing 0y1 of good Y and none of good X. 

• Now assume that one-half of the economy’s labor and capital are removed from Y production and devoted to X production. Where would the economy then be situated? 

• With constant returns to scale, Y production will be cut in half because one-half the factors have been removed, and X production will reach one-half of its maximum amount. Thus, the economy will be located at point M, where 0x1/2 and 0y1/2 are being produced. 

• If various proportions of the factors were switched in this fashion, the straight line RMQ would be traced. 

However, as Samuelson has indicated, this switching of factors in proportionate fashion from one industry to the other does not make economic sense (the technical term for this is “dumb”). 

Because X is the labor-intensive industry and Y is the capital-intensive industry, it makes more sense to switch relatively more labor from Y to X and relatively less capital. The industries will then be using factors in greater correspondence with their optimum requirements than in the equiproportional switching strategy, and the economy can do better than straight line RMQ. 

Thus, the PPF will be outside RMQ except at endpoints R and Q, and the concave line connecting R and Q is the PPF, which clearly has increasing opportunity costs. 

Finally, a useful way to look at the PPF and its slope is to examine the relationship between the PPF and the Edgeworth box diagram, because the Edgeworth box diagram is the analytical source of the PPF. To demonstrate this point, consider Figure 13.

The Edgeworth box in panel (a) has the properties discussed earlier, while panel (b) shows an increasing-cost PPF. 

• In the Edgeworth box, suppose that production is taking place at the X industry origin, also labeled as point R′. At this point, maximum Y production and zero X production are occurring. We can thus transfer this point R′ onto Figure 13(b) as point R, with 0y7 of good Y and none of good X being produced. 

• Similarly, point Q′ in the box (with maximum X production and zero Y production) translates in Figure 13(b) as point Q, with 0x4 of good X and none of good Y being produced.

• To facilitate the discussion, we have placed illustrative output numbers on the axes of the PPF diagram in Figure 13(b).

What about points where some production of both goods occurs? Keeping in mind the assumption of constant returns to scale, move along the diagonal of the box. 

• If M′ is midway along the diagonal between R′ and Q′, then one-half of the economy’s capital and one-half of the economy’s labor is devoted to each industry. Thus, isoquant x2 is one-half the output level of isoquant x4, and isoquant y3 is one-half the output level of isoquant y7. Point M′ in the Edgeworth box is then plotted as point M in Figure 13(b). 

• Further, suppose that point T′ in the box involves one-quarter of the economy’s labor and capital being used in the X industry and three-quarters in the Y industry. Point T′ will then be plotted as point T in panel (b), where 0x1 is one-quarter of 0x4 and 0y5 is three-quarters of 0y7. 

• A similar analysis yields point W in panel (b) if point W′ in the box in panel (a) represents employment of three-quarters of the economy’s labor and capital in the X industry and one-quarter of the economy’s labor and capital in the Y industry.

• Hence, the dashed line RTMWQ in panel (b) represents the plotting of the diagonal R′T′M′W′Q′ in panel (a). Clearly, any point in the Edgeworth box, not only those on the diagonal, has a corresponding point in panel (b).

Introduction

The Effects of Restrictions on U.S. Trade

In 1999, economist Howard J. Wall of the FED of St. Louis investigated the extent to which trade barriers restricted U.S. trade and the size of the welfare costs of U.S. interferences with free trade.

Wall focused his attention on U.S. trade with countries other than Mexico and Canada since the U.S. had been removing barriers to trade with those countries due to the start of the North American Free Trade Agreement (NAFTA) in 1994. Wall indicated that the US imported $723.2 billion of goods from non-NAFTA countries in 1996, but it would have had imports that were $111.6 billion greater (15.4 % larger) that that if there had been no U.S. import restrictions. 

Wall also calculated that U.S. exports to non-NAFTA countries, which were $498.8 billion in 1996, would have been $130.4 billion (26%) larger if foreign countries had not had barriers to U.S. exports.

Hence, interferences with free trade substantially reduced the amount of U.S. trade. The reduction in U.S. imports imposed a welfare cost on the U.S. of $97.3 billion in 1996, which was 1.4% of U.S. GDP at the time. Although unable to estimate the welfare cost of the restrictions on U.S. exports, it is nevertheless clear that sizeable welfare losses in general can occur because of interferences with free trade.

Autarky Equilibrium

Autarky: total absence of participation in international trade.

In this situation, as well as the one with trade, the economy is assumed to be seeking to maximise its well-being through the behaviour of its economic agents. Crucial assumptions made throughout this chapter include the following:

1. Consumers seek to maximise satisfaction.

2. Suppliers of factor services and firms seek to maximise their return from productive activity.

3. There is mobility of factors within the country but not internationally.

4. There are no transportation costs of policy barriers to trade.

5. Perfect competition exists.

In autarky, as in trade, production takes place on the PPF. The particular point at which producers operate on the PPF is chosen by considering their costs of inputs relative to the prices of goods they could produce. 

Producer equilibrium on the PPF is illustrated in Figure 1, the equilibrium is at point E, where the PPF is tangent to the price for the two goods.

• The slope of the budget line or relative price line for goods X and Y is PX/PY. 

• The slope of the PPF is the Marginal Rate of Transformation of the two goods, which in turn is equal to the ratio of the marginal costs of production in the two industries, MCX/MCY. Thus, in production equilibrium on the PPF:

PX/PY = MRT = MCX/MCY

PX/MCX = PY/MCY

• Which indicates that, at point E, producers have no incentive to change production because the price received in the market for each good relative to the marginal cost of producing that good is the same. 

• Only if these price/cost ratios were different would there be an incentive to switch production (for perfect competition, price equals marginal cost in equilibrium).

Producer Equilibrium in Autarky

Suppose that the economy is not at point E, but at Point A, this would surely not be an equilibrium as at point A the given price line is steeper than the PPF:

PX/PY > MCX/MCY 

PX/MCX = PY/MCY

• Hence, point A cannot be an equilibrium production position for the economy because the price of good X relative to its marginal cost exceeds the price of good Y relative to its marginal cost. 

• Producers have an incentive to produce more X and less Y because X production is relatively more profitable at the margin than Y production. 

• As resources consequently move from Y to X, the economy slides down the PPF toward point E, and it will continue to move toward more X production and less Y production until point E is attained. 

• As the movement from A to E takes place, the expanded X production raises MCX, and reduced Y producer lowers MCY. 

• Therefore, the ratio PX/MCX is falling and the ratio PY/MCY is rising; because PX/MCX was originally greater than PY/MCY at point A - this means that the two ratios are converging toward each other. 

• They will continue to converge until point E is reached, where PX/MCX = PY/MCY. 

• Movement to E would also occur from Point B, where PX/PY  < MCX/MCY .

Next consumers are brought into the picture and the economy is portrayed in autarky equilibrium at point E. The attainment of this point is the result of the country attempting to reach its highest possible level of well-being, given the production constraint of the PPF.

• Notice that the resulting price line is tangent to only to the PPF but also to the (community) indifference curve CI1.

• The tangency between an indifference curve and the price line reflects the fact that the relative price ratio (PX/PY) is equal to the marginal price ratio of marginal utilities (MUX/MUY), which in turn is defined as the marginal rate of substitution. 

MRS = PX/PY = MUX/MUY

• Thus, in autarky equilibrium for the economy as a whole:

MRT = MCX/MCY  = PX/PY = MUX/MUY = MRS

• With equilibrium at point E and given prices PX/PY, production of good X is 0x1 and production of good Y is 0Y1. 

• Note that under equilibrium consumption under autarky is also 0x1 of good X and 0Y1 of good Y.

• Without trade, production of each good in a country must equal the consumption of that good because none of the good is exported or imported.

• If the good were imported, then home consumption would exceed home production because some of the consumption demand is met from production in other countries.

Introduction of International Trade

Suppose international trade opportunities are introduced into this autarkic situation. The most important feature to keep in mind is that the opening of a country to international trade means exposing the country to a new set of relative prices. When these different prices are available, the home country's consumers and producers will adjust to them by reallocating their production and consumption patterns. 

This reallocation leads to gains from trade. The ultimate source of gain from international trade is the difference in relative prices in autarky between countries.

The reallocation of production and consumption and the gains from trade are illustrated above. 

• Under autarky the optimal point for the economy is at point E, producing and consuming 0X1 of the X good and 0Y1 of the Y good. 

• The welfare level is indicated by the indifference curve CI1, and prices in autarky are (PX/PY)1.

• Suppose that the country now faces international prices of (PX/PY)2. This new set of prices is steeper than the prices in autarky, reflecting the assumption that relative prices in the home market are lower for X and higher for Y than in the international market.

• Thus, the home country has a comparative advantage in good X and a comparative disadvantage in good Y. The difference between relative prices in the home country and the set of international prices indicates that the home country is relatively more efficient in producing X and relatively less efficient in producing Y. 

• With producers now facing a relatively higher price of good X in the world market than in autarky, they will want to shift production toward X and away from Y because they anticipate greater profitability in X production. 

• Thus, production will move from point E to point E'.

• The stimulus for increasing X production and decreasing Y production is that the new relative price ratio (PX/PY)2 exceeds the ratio MCX/MCY at E and will continue to exceed MCX/MCY until equality between relative prices and relative marginal costs is restored as point E'. 

• At E', production of good X has risen from 0X1 to 0X2, and production of good Y has fallen from 0Y1 to 0Y2.

• Thus, production in the home country will move to point E'. For the country's consumption, in tracing consumption geometrically, the key point is that the relative price line tangent at E' is also the country's trading line, or consumption-possibilities frontier (CPF).

• With production at E', the country can exchange units of good X for units of good Y at the new prevailing prices, (PX/PY)2.

• Thus, the country can settle anywhere on this line by exchanging some of its X production for good Y in the world market.

Consumer Theory: tells us that consumers will choose a consumption point where an indifference curve is tangent to the relevant price line:

• With trade, this point is C', and the well-being of the country's consumers is maximised at C', and the new consumption quantities are 0X3 of good X and 0Y3 of good Y. 

• Thus, with trade and the new relative prices, production and consumption adjust until:

MRT = MCX/MCY  = PX/PY = MUX/MUY = MRS

• Note that point C' is beyond the PPF.

Like the classical model discussed in Chapter 3, international trade permits consumers to consume a bundle that lies beyond the production capabilities of their own country. Without trade, consumption possibilities were confined to the PPF, and the PPF was also the CPF. 

With trade, the CPF differs from the PPF and permits consumption combinations that simply cannot be reached by domestic production alone. The CPF is represented by the international price line, since the home country could choose to settle at any point along this line. Access to the new CPF can benefit the country because consumption possibilities can be attained that previously were not possible. The gains from trade in Figure 3 above are reflected in the fact that the new CPF allows the country to reach a higher community indifference curve, CI2.

Trade has thus enabled the country to attain a higher level of welfare that was not possible under autarky. The trade itself also is evident in Figure 3 above because the production of good X is 0X2 and consumption of good X is 0X3, the difference between they two quantities represents the exports of good X by this country. Similarly, because 0Y2 is production of good Y and 0X3 is consumption, the difference between these two quantities measures the imports of good Y by the country.

Further, the trade pattern is summarised conventionally in the trade triangle, FC'E'. This triangle for the home country has the following economic interpretation:

1. The base of this right triangle (FE') represents the exports of the country as FE' = x3x2.

2. The height of the vertical side of the triangle (FC') represents the imports of the country as FC' = y2y3

3. The hypotenuse (C'E') of the triangle represents the trading line, and (the negative of) its slope indicates the world price ratio or terms of trade.

The Consumption and Production Gains from Trade

As discussed, the home country has gained from trade. Economists sometime divide the total gains from trade into two conceptually distinct parts:

1. Consumption gain/Gains from exchange: refers to the fact that the exposure to new relative prices, even without changes in production, enhances the welfare of the country. 

• This gain can be seen in Figure 4 above where points E, E', and C' are analogous to E, E', and C' in Figure 3 above, as are the autarky prices (PX/PY)1 and the trading prices (PX/PY)2. 

• When the country has no international trade, it is located at point E. 

• Now, suppose that the country is introduced to the trading prices (PX/PY)2 but that, for the moment, production does not change from point E. A line representing the new price ratio is then drawn through point E; production remains at E, and the new, steep price line with slope (PX/PY)2 is the trading line.

• With this trading line, consumers can do better than at point E, so they move to a tangency between the new prices and an indifference curve. 

• If consumers remained at E, the price of good X is divided by the price of good Y would be greater than the marginal utility of good X divided by the marginal utility of good Y. In other words, the marginal utility of good Y per dollar spent on Y would exceed the marginal utility of good X per dollar spent on X.

• The consumers would hence change their consumption bundle toward consuming more of good Y and less of good X. Maximising welfare with this production constraint thus places consumers at point C.

• As point C is on a community indifference curve CI'1 that is higher than indifference curve CI1 in autarky, the country has gained from trade even though production has not changed. The gain reflects the fact that, with new prices, consumers are switching to greater consumption of import good Y, now priced lower, and away from export good X, now priced higher.

• Thus, even if a country has an absolutely rigid production structure where no factors of production could move between industries, there are still gains from trade.

2. Production gain/Gains from specialisation: a further welfare gain occurs because production changes rather than remains fixed at E in Figure 4 below. 

• With the new relative prices, there is an incentive to produce more of a good X and less of good Y since X is now relatively more profitable to produce than is Y, and the production switch from E to E' is in accordance with comparative advantage. Moving production toward the comparative-advantage good thus increases welfare, permitting consumers to move from point C to point C'.

The total gains from trade attained by moving from point E to point C' (and correspondingly from CI1 to CI2) can be divided conceptually into two parts:

1. The consumption gain, involving movement from point E to point C (and correspondingly from CI1 to CI'1).

2. The production gain, involving movement from point C to C' ( and correspondingly from CI'1 to CI2).

Trade in the Partner Country

If we assume a two-country world, the analysis for the trading partner is analogous to that employed for the home country, although the trade pattern is reversed. Figure 5(a) is the basic graph. The discussion of it can be brief because no new principles are involved. For purpose of contrast, panel (b) illustrates the home country situation discussed earlier.

In Figure 5(a), the trading partner's equilibrium in autarky is at point e, where the country faces autarky prices (PX/PY)3. 

• The partner is producing quantity 0x4 of good X and  0y4 of good Y, and the welfare level for the country is indicated by indifference curve W1. With international trade, international relative prices (PX/PY)2 will be less than autarky prices (PX/PY)3.

• Thus, this partner country has a comparative advantage in good Y and a comparative disadvantage in good X. 

• Because of the new relative prices available through international trade, producers in the partner country have an incentive to produce more of good Y and less of good X. 

• The production point moves from e to e′, where there is a tangency of the PPF with (PX/PY)2 and where production of good X is 0x5 and production of good Y is 0y5. 

• From point e′, the country can move along the trading line until consumers are in equilibrium, represented by a point of tangency of the price line (PX/PY)2 to an indifference curve. 

• The consumption equilibrium is point c′ with trade, with consumption being 0x6 of good X and 0y6 of good Y. 

As in the case of the home country, the difference between production and consumption of any good reflects the volume and pattern of trade:

• Because production of good X is 0x5 and consumption of good X is 0x6, the country imports x5x6 of good X.

• Because production of good Y is 0y5 and consumption of good Y is 0y6, the country thus exports y6y5 of good Y. 

Trade triangle fe′c′ represents the same phenomenon as earlier, but in this case:

•  Horizontal side fc′ indicates imports and vertical side fe′ represents exports. 

• Note that in a two-country world, the partner-country trade triangle fe′c′ is congruent to home country trade triangle FC′E′. This must be so because, by definition, the exports of the home country are the imports of the partner country, and the imports of the home country are the exports of the partner country. 

• In addition, the trading prices (PX/PY)2 are the same for each country. 

• It is obvious that the partner country also gains from trade. With trade, the country’s consumers are able to reach indifference curve W2, whereas in autarky the consumers could reach only lower indifference curve W1. The “gains from trade” for this country could also be split into the “production gain” and the “consumption gain” as was done for the home country, but this is an exercise left for the reader.

Minimum Conditions for Trade

The discussion in the previous section demonstrated that there is a basis for trade whenever the relative prices of goods in autarky of the two potential trading partners are different. It is important to address briefly conditions under which this could come about. 

• If the generation of relative price differences in autarky seems highly unlikely, then the total potential gains from trade would be limited and trade theory largely irrelevant. 

• On the other hand, if there seems to be a considerably broad set of circumstances that could generate relative price differences, there would be a strong underlying basis for believing that potential gains from trade are present. 

Theoretically, there are two principal sources of relative price variation between two countries

1. Differences in supply conditions

2. Differences in demand conditions

To establish minimum conditions for generating relative price differences in autarky, we look first at the role of demand, assuming identical production conditions. Second, we address the role of supply under identical demand conditions.

Trade between Countries with Identical PPFs

This case could not possibly have been handled in the Classical analysis. In Ricardian analysis, if the production conditions were the same for the trading partners in all commodities (i.e., identical PPFs), then the pre-trade price ratios in the two countries would be the same; there would be no incentive for trade and of course no gains from trade. 

According to neoclassical theory, two countries with identical production conditions can benefit from trade. Different demand conditions in the two countries in the presence of increasing opportunity costs characterise this situation. 

Increasing opportunity costs are critical for the result, but the recognition of how different demand conditions influence trade is also necessary to update the Classical analysis. Figure 6 illustrates this special case. 

• The two countries have identical production conditions, so we need to draw only one PPF because it can represent either country. The different tastes in the two countries are shown by different indifference maps. 

• Suppose that country 1 has a relatively strong preference for good Y; this preference is indicated by curves S1 and S2, which are positioned close to the Y axis. 

• Country 2 has a relative preference for the X good, so its curves W1 and W2 are positioned close to the X axis. 

• The autarky equilibrium points are point E for country 1 and point e for country 2. 

• Given these autarky positions, it is evident that the autarky price ratio in country 1 is (PX/PY)1 and that the autarky price ratio in country 2 is (PX/PY)2.

Because (PX/PY)1 is less than (PX/PY)2, country 1 has the comparative advantage in good X, and country 2 has the comparative advantage in good Y. 

• The price ratios show that the preference for good Y in country 1 has bid up PY relative to PX and that the preference for good X in country 2 has bid up PX relative to PY. 

• With the opening of trade between the two countries, country 1 will export X and expand the production of X in order to do so and it will decrease production of good Y as good Y is now imported. 

Similarly, country 2 will have an incentive to expand production of and to export good Y and an incentive to contract production of and to import good X. 

The countries will trade at a price ratio (not shown) somewhere between the autarky price ratios, a price ratio that is tangent to the identical PPFs at a point between E and e. 

Both countries will be able to attain higher indifference curves. The common sense of the mutual gain from trade is that each country is now able to consume more of the good for which it has the greater relative preference. 

Thus, trade between identical economies with different demand patterns can be a source of gain and can be interpreted easily by neoclassical trade theory, while the Classical model cannot explain why trade would take place because, with identical constant-opportunity-cost PPFs, relative prices in the two countries would not differ. 

Trade between Countries with Identical Demand Conditions

We now turn to the situation in which two countries have the same demand conditions but different production conditions. 

• Production conditions may differ because:

• Different technologies are employed in two countries with the same relative amounts of the two factors, capital and labour.

• Because similar technologies exist in both countries but the relative availability of factors differs.

• Because the two countries have a combination of different technologies and different relative factor availabilities. 

Let us assume for the present discussion that production conditions differ between the two countries because the technologies are different. Each country is employing a different technology, so there will be different production possibilities and different PPFs (see Figure 7). 

Assuming that the relative amounts of factors are similar between the two countries:

• PPF1 demonstrates a technology that is relatively more efficient in the production of good X.

• PPF2 a technology that is relatively more efficient in the production of good Y.

As demand conditions assumed to be identical in both countries an identical community indifference map can be used to represent tastes and preferences. The existence of different production conditions is sufficient to produce different domestic price ratios in autarky, even in the presence of identical demand conditions. 

• Country 1, which is relatively more efficient in producing good X, will find itself producing and consuming relatively more of this product in autarky, for example, at point E. 

• Similarly, country 2, which has the technological advantage in good Y, will find itself producing and consuming more of good Y in equilibrium (point e). 

• As relative prices are different in autarky, there is a basis for trade because (PX/PY)1 <  (PX/PY)2. 

• Country 1 will export good X and import good Y at terms of trade (not shown) that are between the two autarky price ratios, and it will increase production of good X and decrease production of good Y.

• Country 2 will do the reverse—it will expand production of and export good Y and will contract production of and import good X. 

• Each country can then attain a higher indifference curve. 

We conclude that a second possible minimal condition for gains from international trade is a difference in supply conditions, even with identical demand in the two countries. 

Conclusions 

We have seen that relative prices in autarky reflect underlying supply and demand conditions, thus depending jointly on:

• The relative amounts and quality of available resources

• The characteristics of the production technologies employed

• The nature of demand in a country. 

Different relative prices can therefore exist between countries as long as one or more of these factors are different. Such a minimal condition suggests that the likelihood of a basis for trade between the many countries of the world is great. 

It also makes it clear that the underlying basis for trade can change:

• As technology changes

• As factors grow within countries

• As factors move between countries

• As individual country demand patterns change in response to economic development

• As the increased exposure to different products and cultures. 

Some Important Assumptions in the Analysis

This section briefly discusses three important assumptions used in the previous analysis that may need to be taken into account when examining the “real world.” The intent is to introduce an element of caution rather than doubt concerning neoclassical theory. Indeed, few principles are so universally accepted by economists as comparative advantage and the gains from international trade. 

Costless Factor Mobility

One important assumption is that factors of production can shift readily and without cost along the PPF as relative prices change and trade opportunities present themselves. In practice, however, it may not be possible to adjust immediately to the changed relative prices. 

• Movement from the autarky production point to the trade production point may first involve a movement inside the PPF as workers and equipment are no longer used in the import-competing industry but have yet to be fully absorbed in the export industry. 

• Perhaps labor must be retrained

• Factors must be moved from one section of the country to another

• Depreciation allowances for plant and equipment must accumulate before capital can be reinvested elsewhere. Only after time passes will the export industry be able to employ the unused factors and move the economy to the PPF. 

These kinds of mobility problems are assumed away in the theory presented earlier. When factor movement does occur slowly or experiences an adjustment cost so that the production point does not slide easily along the PPF but moves inside it, many economists argue that some type of government assistance is required. Many countries have set up such assistance programs. For example, beginning in 1962 and continuing to the present, the United States has had a recently controversial program of trade adjustment assistance in place (although the nature and funding of the program have varied over the years) to help in the transition following tariff reductions through trade negotiations. 

Full Employment of Factors of Production

This assumption is related to the problem of adjustment, but it merits separate treatment because of its application to a more general context. 

The assumption that all of a country’s factors of production are fully employed (or experience a given level of unemployment page 96 owing to institutional characteristics, e.g., a “natural level of unemployment”), combined with their efficient use in the competitive market, means that the country is operating on the PPF. 

Thus, because of this assumption, we have not previously analysed situations where trade moved the country from somewhere inside the PPF to a point on the PPF. 

The “full-employment” assumption is a general one in microeconomic theory as well as in trade theory. In micro, it is assumed that the macroeconomic question of unemployment has been solved. The solution to the problem of unemployment might lie, for example, with effective monetary and fiscal policies. 

Given this solution, the subject of microeconomics looks at questions of efficiency and welfare. Of course, realistically, countries do not always attain full employment, as has been evident in recent years. The full-employment assumption allows the analyst to focus on efficiency and welfare, as distinct from the problems of unemployment and idle capacity. 

Clearly, a country can have unemployment whether it is in autarky or is engaged in trade. However, it should be emphasised that even if a country has unemployment in autarky and is operating inside its PPF, trade permits it to move to a higher indifference curve. The opening of the country to trade will lead to different prices facing consumers and producers than was the case with autarky. Gains from exchange and specialisation still occur. 

The Indifference Curve Map Can Show Welfare Changes

In Chapter 5, the possibility that community indifference curves might intersect was raised. 

If intersections occur, there might be a problem in interpreting welfare changes when a country moves from autarky to trade. In this chapter, however, no intersecting community indifference curves have so far been drawn. It is useful to comment on this disparity. 

A number of somewhat restrictive assumptions can be used to construct non-intersecting community indifference curves. These assumptions can guarantee that welfare changes can be interpreted as they have been in this chapter (see Tower, 1979). 

The explanation of the conditions necessary for concluding that welfare will improve when autarky gives way to trade is straightforward. Two general conditions are pertinent: 

1. Individuals within the economy have reasonably similar tastes. By assuming that redistribution is not large and that people have similar tastes, we thus minimise the possibility of not being able to tell whether actual welfare has changed. 

2. The opening of the economy to trade does not radically alter the distribution of income. The underlying rationale for these conditions is that, without them, our earlier analysis would suggest that community indifference curves could intersect. 

However, even with these general conditions, we cannot be sure that the direction of the actual welfare change can be meaningfully ascertained, as the phrases “have reasonably similar tastes” and “radically alter the distribution of income” do not lend themselves to precise interpretation. Because of this uncertainty, advanced trade theory has gone well beyond the use of indifference curves to other modes of demonstrating the gains from trade. 

The compensation principle summarises the general conclusion of these extensions. The advanced literature demonstrates that potential gains from trade exist in the sense that, within the country, the people who gain from trade can compensate the losers and still be better off. 

This must mean, therefore, that there is a larger “pie” to split up after trade has been introduced. If the compensation is paid, then society is better off because the gainers have benefited even after compensating the losers. 

Everyone is at least as well off as in autarky, and some people are better off. Thus, trade can yield higher welfare than autarky, but the reverse is never true. 

If the compensation is not actually paid, then society is described as being only “potentially” better off. It is potential because some people could be made better off and everyone else no worse off, but this would not happen without the transfer. Further consideration of this principle using our familiar community indifference curves is given in the appendix to this chapter.

Change in Income Distrubution and Welfare with Increased Trade

With the opening of trade, the relative price of export goods increases and the relative price of import substitute goods decreases. 

• On the supply side, this will lead to an expansion of production of export goods and a contraction of production of import-substitute goods. Consequently, there will be an increase in the demand for inputs used in export production and a reduction in demand for inputs used in the domestic production of the import good. In the adjustment process, the price of certain factors or inputs will likely increase and the price of others will likely decline, leading to a change in income distribution. 

• Estimates of such supply-side impacts will be discussed in Chapters 8 and 9. 

• However, a study by Spilimbergo, Londoño, and Székely (1999) examined 34 countries from 1965 to 1992 and concluded that reductions in trade barriers decreased income inequality in capital-abundant countries but increased income inequality in skill-abundant countries. 

• In another study, Andrew Berg and Anne Krueger (2002) hypothesised that trade liberalisation can benefit the poorer segments of a country’s population at least as much as liberalisation benefits the average person. This hypothesised result occurs because, among other phenomena, greater openness of a country can reduce the power of domestic monopolies. Nevertheless, after surveying existing literature examining the relationship of openness and income distribution across many countries at a point in time, they concluded that no systematic relationship between the liberalisation and the poor can be made. 

Studies of any given country over time might lead to more definite results, however. In addition, distribution effects occur in consumption. Because the price of export goods is rising with trade and that of import goods is falling, individuals who spend relatively more of their income on export goods will find their real income relatively smaller compared to that of individuals who spend relatively more on import goods, other things being equal. 

To give an example of the magnitude of possible consumption-related income distribution effects, Susan Hickok (1985) estimated the impact of the higher domestic prices caused by U.S. import restrictions on automobiles, sugar, and clothing in 1984. 

• The protection-induced increases in expenditure on these products were equivalent to an income tax surcharge of:

• 66% for low-income earners ($7,000−$9,350 annually)

• 33% for those in the $14,050−$16,400 range, 20% for those earning $23,400−$28,050

• 5% for individuals earning $58,500 and above.

Because these products absorb a higher percentage of individual expenditures of low-income earners than of high-income earners, increasing international trade by removing those tariff and quota barriers would clearly have had the effect that low-income groups would benefit relatively more than high-income groups. 

Some recent work has tried to measure the welfare gains from trade using aggregate data on the relative size of trade to a country’s economy and the responsiveness of trade to changing costs.

Marc J. Melitz and Stephen J. Redding (2014): note that calculated welfare gains in these studies are relatively small and cite a study (Eaton and Kortum, 2002) of 19 developed countries that indicated that the loss in welfare of going from trade to autarky varied from 0.2 to 10.3%. 

*Melitz and Redding suggest, however, that trade in intermediate inputs can increase productivity in domestic industries and hence increase country well-being, and this channel and its associated gains are not incorporated into welfare studies. 

Work by Ariel Burstein and Javier Cravino (2015) in a similar vein supports the notion that estimates of gains from trade must include the productivity-enhancing impacts of that trade.

The anecdote is famous. A mathematician, Stan Ulam, once challenged Paul Samuelson to name one proposition in the social sciences that is both true and nontrivial:

• His reply was: “Ricardo’s theory of comparative advantage”; see Samuelson (1995, p. 22). Truth, however, in Samuelson’s reply refers to the fact that Ricardo’s theory of comparative advantage is mathematically correct, not that it is empirically valid. 

• The goal of our paper is to assess the empirical performance of Ricardo’s ideas. To bring Ricardo’s ideas to the data, one must overcome a key empirical challenge. 

• Suppose, as Ricardo’s theory of comparative advantage predicts, that different factors of production specialise in different economic activities based on their relative productivity differences. Then, following Ricardo’s famous example, if English workers are relatively better at producing cloth than wine compared to Portuguese workers, England will produce cloth, Portugal will produce wine, and at least one of these two countries will be completely specialised in one of these two sectors. 

Accordingly, the key explanatory variable in Ricardo’s theory, relative productivity, cannot be directly observed. This identification problem is emphasised by Deardorff (1984, p. 476) in his review of empirical work on the Ricardian model of trade: 

• Problems arise, however, most having to do with the observability of [productivity by industry and country]. The problem is implicit in the Ricardian model itself because the model implies complete specialisation in equilibrium:

  • This in turn means that the differences in labor requirements cannot be observed, since imported goods will almost never be produced in the importing country. 

  • A similar identification problem arises in the labor literature in which the self-selection of individuals based on comparative advantage is often referred to as the Roy model. 

  • As Heckman and Honoré (1990) have shown, if general distributions of worker skills are allowed, the Roy model—and hence Ricardo’s theory of comparative advantage—has no empirical content. 

  • Econometrically speaking, the Ricardian model is not non-parametrically identified. How can one solve this identification problem? 

    • One possibility consists in making untestable functional form assumptions about the distribution of productivity across different factors of productions and economic activities. These assumptions can then be used to relate productivity levels that are observable to those that are not. 

    • In a labor context, a common strategy is to assume that workers’ skills are log-normally distributed. 

    • In a trade context, building on the work of Eaton and Kortum (2002), Costinot, Donaldson, and Komunjer (forthcoming) have shown how the predictions of the Ricardian model can be tested by assuming that productivity levels are independently drawn from Fréchet distributions across countries and industries. 

This paper proposes an alternative empirical strategy that does not rely on identification by functional form:

• Our basic idea, as in Costinot and Donaldson (2011), is to focus on agriculture, a sector of the economy in which scientific knowledge of how essential inputs such as water, soil, and climatic conditions map into outputs is uniquely well understood. 

• As a consequence of this knowledge, agronomists are able to predict how productive a given parcel of land, which will we refer to as a “field,” would be were it to be used to grow any one of a set of crops. In this particular context, the econometrician therefore knows the productivity of a field in all economic activities, not just those in which it is currently employed. 

• Our strategy can be described as follows:

  • We first establish how, according to Ricardo’s theory of comparative advantage, total output of various crops should vary across countries as a function of:

1. The vector of productivity of the fields that countries are endowed with, and

2. The producer prices that determine the allocation of fields across crops

•  We then combine these theoretical predictions with productivity and price data from the Food and Agriculture Organization (FAO). 

• Our dataset consists of 17 major agricultural crops and 55 major agricultural countries. 

• Using this information, we can compute predicted output levels for all crops and countries in our sample and ask: "How do predicted output levels compare with those that are observed in the data?" 

• Our empirical results show that the output levels predicted by Ricardo’s theory of comparative advantage agree reasonably well with actual data on worldwide agricultural production. 

• Despite all of the real-world considerations from which Ricardo’s theory abstracts, a regression of log output on log predicted output has a (precisely estimated) slope of 0.21. This result is robust to a series of alternative samples and specifications. The rest of the article is organised as follows:

  • Section I derives predicted output levels in an economy where factor allocation is determined by Ricardian comparative advantage. 

  • Section II describes the data that we use to construct measures of both predicted and actual output. 

  • Section III compares predicted and observed output levels

  • Section IV offers some concluding remarks.

Ricardian Predictions

The basic environment is the same as in Costinot (2009). We consider a world economy comprising:

• c = 1,…,C countries

• g = 1,…,G goods

• f = 1,…,F factors of production. 

In our empirical analysis:

• A good will be a crop

• Factor of production will be a parcel of land or “field” Factors of production are immobile across countries and perfectly mobile across sectors. 

• Lcf ≥ 0 denotes the inelastic supply of factor f in country c

• Factors of production are perfect substitutes within each country and sector but vary in their productivity A[cf g] ≥ 0. 

A[cf g] is represented in the correct form in the equation below

• Total output of good g in country c is given by:

• L[cf g] is the quantity of factor f allocated to good g in country c

L(cf g] is represented in the correct form in the equation above

• The variation in A[cf g] is the source of Ricardian comparative advantage. 

• If two factors f1 and f2 located in country c are such that

for two goods g1 and g2, then field f2 has a comparative advantage in good g2.

• Throughout this article, we focus on the supply-side of this economy by taking producer prices p[c g] ≥ 0 as given. 

p(c g] is represented in the correct form in the equation below

• We assume that the allocation of factors of production to each sector in each country is efficient and solves:

• Since there are constant returns to scale, a competitive equilibrium with a large number of profit-maximising firms would lead to an efficient allocation. 

• Because of the linearity of aggregate output, the solution of the previous maximisation problem is easy to characterise. 

• As in a simple Ricardian model of trade with two goods and two countries, each factor should be employed in the sector that maximises A[cf g] p[c g], independently of where other factors are being employed. 

• Assuming that the efficient allocation is unique, we can express total output of good g in country c at the efficient allocation as:

• 𝓕[c g] is the set of factors allocated to good g in country c  :

Equations (1) and (2) capture Ricardo’s idea that relative rather than absolute productivity differences determine factor allocation and, in turn, the pattern of international specialisation.

The Data

To assess the empirical performance of Ricardo’s ideas we need data on actual output levels as well as data to compute predicted output levels.

• Q˜[c g] is the data on actual output levels

• Q[c g] is the data to compute predicted output levels

According to equations (1) and (2) Q[c g] can be computed using:

• Data on productivity, A[cf g], for all factors of production f

• Endowments of different factors, Lcf 

• Producer prices, p[c g]. 

We describe our construction of such measures here. Since the predictions of Ricardo’s theory of comparative advantage are fundamentally cross-sectional in nature, we work with the data from 1989 only; the year in which the greatest overlap in the required measures is available. 

We use data on both agricultural output (Q˜[c g] ) and producer prices ( p[c g] ) by country and crop from FAOSTAT. 

• Output is equal to quantity harvested and is reported in metric tons. 

• Producer prices are equal to prices received by farmers net of taxes and subsidies and are reported in local currency units per tonne. 

• Imperfect data reporting to the FAO means that some output and price observations are missing. 

• We first work with a sample of crops and countries that is designed to minimise the number of unreported observations. 

• This sample comprises 55 countries and 17 crops. 

• In the remaining sample, whenever output data are missing we assume that there is no production of that crop in that country. Similarly, whenever price data are unreported for a given observation, both quantity produced and area harvested are also reported as zero in the FAO data. In these instances, we therefore replace the missing price entry with a zero.

•  Our data on productivity (A[cf g] ) come from version 3.0 of the Global Agro-Ecological Zones (GAEZ) project run by the International Institute for Applied Systems Analysis (IIASA) and the FAO (IIASA/FAO 2012). 

• We describe this data in detail in Costinot and Donaldson (2011) but provide a brief description here; see also Nunn and Qian (2011). 

• The GAEZ project aims to make agronomic predictions about the yield that would obtain for a given crop at a given location for all of the world’s major crops and all locations on Earth:

  • Data on natural inputs (such as soil characteristics, water availability, topography and climate) for each location are fed into an agronomic model of crop production with distinct parameters for each variety of each crop. These models condition on a level of variable inputs, and GAEZ makes available the output from various scenarios in which different levels of variable inputs are applied. 

  • We use the scenario that corresponds to a “mixed” level of inputs, where the farmer is assumed to be able to apply inputs differentially across subplots within his or her location, and in which irrigation is available. 

  • It is important to stress that the thousands of parameters that enter the GAEZ model are estimated from countless field and lab experiments, not from statistical relationships between observed country-level output data (such as that from FAOSTAT which we use here to construct Q˜ [c g] ) and natural inputs. 

  • The spatial resolution of GAEZ outputs is governed by the resolution of the natural input whose resolution is most coarse, the climate data. As a result the GAEZ productivity predictions are available for each five–arc-minute grid cell on Earth. The land area of such a cell varies by latitude but is 9.2 by 8.5 km at the Tropics. 

  • The median country in our dataset contains 4,817 grid cells, but a large country such as the United States comprises 157,797 cells. Since the grid cell is the finest unit of spatial heterogeneity in our dataset we take each grid cell to be a distinct factor of production f and the land area of each grid cell to be the associated endowment, Lcf. 

  • Hence, our measure of the productivity of factor f if it were to produce crop g in country c, A[cf g] , corresponds to the GAEZ project’s predicted “total production capacity (metric tons/ ha).” We match countries (at their 1989 borders) to grid cells using GIS files on country borders from the Global Administrative Areas database. 

  • A sample of the GAEZ predictions can be seen in Figure 1, below. Here we plot, for each grid cell on Earth, the predicted relative productivity in wheat compared to sugar cane (the two most important crops by weight in our sample). 

  • As can be seen, there exists a great deal of heterogeneity in relative productivity throughout the world, even among just two of our 17 crops. 

  • In the next section we explore the implications of this heterogeneity—heterogeneity that is at the core of Ricardo’s theory of comparative advantage—for determining the pattern of international specialisation across crops.

Empirical Results

We are now ready to bring Ricardo’s ideas to the data. 

To overcome the identification problem highlighted by Deardorff (1984) and Heckman and Honore (1990), we take advantage of the GAEZ data, together with the other data described in Section II, to predict the amount of output (Q[c g]  ) that country c should produce in crop g according to Ricardo’s theory of comparative advantage, i.e., according to equations (1) and (2). We then compare these predicted output levels to those that are observed in the data (Q˜[c g]  ). 

In the spirit of the “slope tests” in the Heckscher-Ohlin-Vanek literature, see Davis and Weinstein (2001), we implement this comparison by simply regressing, across countries and crops, data on actual output on measures of predicted output. 

Like Davis and Weinstein (2001), we assess the empirical performance of Ricardo’s ideas by studying whether:

1. The slope coefficient in this regression is close to unity; and

2. The coefficient is precisely estimated. 

Compared to these authors, however, we have little confidence in our model’s ability to predict absolute levels of output. 

The reason is simple: the model presented in Section II assumes that the only goods produced (using land) in each country are the 17 crops for which GAEZ productivity data are available. In reality there are many other uses of land, so the aggregate amount of land used to grow the 17 crops in our study is considerably lower than that assumed in our analysis. 

To circumvent this problem, we simply estimate our regressions in logs. 

Since the core aspect of Ricardian comparative advantage lies in how relative productivity predicts relative quantities, we believe that a comparison of logarithmic slopes captures the essence of what the model described in Section I can hope to predict in this context. 

Our empirical results are presented in Table 1:

• All regressions include a constant and use standard errors that are adjusted for clustering by country to account for potential within-country (across crop) correlation in data reporting and model misspecification. 

• Column 1 contains our baseline regression. The estimated slope coefficient is 0.212 and the standard error is small (0.057). While the slope coefficient falls short of its theoretical value (one), it remains positive and statistically significant. 

The fact that Ricardo’s theory of comparative advantage does not fit the data perfectly should not be surprising:

1. First, our empirical exercise focuses on land productivity and abstracts from all other determinants of comparative costs (such as factor prices that differ across countries and factor intensities that differ across crops) that are likely to drive agricultural specialisation throughout the world.

2.  Second, the fit of our regressions does not only depend on the ability of Ricardo’s theory to predict relative output levels conditional on relative productivity levels, but also on the ability of agronomists at the GAEZ project to predict productivity levels in each of 17 crops at five arc-minute grid cells throughout the world conditional on the (counterfactual) assumption that all countries share a common agricultural technology.

3. Third, while the spatial resolution of the GAEZ predictions is considerably finer than the typical approach to cross-country data in the trade literature (in which countries are homogeneous points), five arc-minute grid cells are still very coarse in an absolute sense. This means that there is likely to be a great deal of potential within-country heterogeneity that is being smoothed over by the GAEZ agronomic modelling. 

Yet despite these limitations of our analysis, Ricardo’s theory of comparative advantage still has significant explanatory power in the data, as column 1 illustrates.

Columns 2 and 3 explore the robustness of our baseline estimate in column 1 to the inclusion of crop and country fixed effects, respectively. The rationale for these alternative specifications is that there may be crop- or country-specific tendencies for misreporting or model error. 

Such errors may be economic in nature if, say, some countries had higher international price distortions, or agronomic in nature if, say, the GAEZ model predictions were relatively more accurate for some crops than others. 

Including such fixed effects can reduce the slope coefficient to as low as 0.096, in column 3, but these estimates are still statistically significantly different from zero. 

Thus, the results in columns 2 and 3 show that Ricardo’s theory of comparative advantage continues to have explanatory power whether focusing on the across-country variation, as in column 2, or the across-crop variation, as in column 3. 

Finally, columns 4 and 5 investigate the extent to which our estimates are driven by particular components of the sample. 

Column 4 estimates the slope only among the 28 countries that are at or above the median in terms of agricultural production (by weight). 

Column 5 estimates the slope only on the 9 crops that are the most important (by weight) in global production. 

In both cases the estimated slope coefficient is similar (within one standard error) to our baseline estimate in column 1.