2 Ricardian Model

In developing the Ricardian model of trade, we will work with an example similar to that used by Ricardo; instead of wine and cloth, however, the two goods will be wheat and cloth. Wheat and other grains (including barley, rice, and so on) are major exports of the United States and Europe, while many types of cloth are imported into these countries. In our example, the home country (we will call it just “Home”) will end up with this trade pattern, exporting wheat and importing cloth.

The Home Country

To simplify our example, we will ignore the role of land and capital and suppose that both goods are produced with labor alone. In Home, one worker can produce 4 bushels of wheat or 2 yards of cloth. This production can be expressed in terms of the marginal product of labor (MPL) for each good. Recall from your study of microeconomics that the marginal product of labor is the extra output obtained by using one more unit of labor.2 In Home, one worker produces 4 bushels of wheat, so MPL_W = 4. Alternatively, one worker can produce 2 yards of cloth, so MPL_C = 2.

Home Production Possibilities Frontier Using the marginal products for producing wheat and cloth, we can graph Home’s production possibilities frontier (PPF). Suppose there are = 25 workers in the home country (the bar over the letter L indicates our assumption that the amount of labor in Home stays constant). If all these workers were employed in wheat, they could produce Q_W = MPL_W · = 4 · 25 = 100 bushels. Alternatively, if they were all employed in cloth, they could produce Q_C = MPL_C · = 2 · 25 = 50 yards. The production possibilities frontier is a straight line between these two points at the corners, as shown in Figure 2-1. The straight-line PPF, a special feature of the Ricardian model, follows from the assumption that the marginal products of labor are constant. That is, regardless of how much wheat or cloth is already being produced, one extra hour of labor yields an additional 4 bushels of wheat or 2 yards of cloth. There are no diminishing returns in the Ricardian model because it ignores the role of land and capital.

Given this property, the slope of the PPF in Figure 2-1 can be calculated as the ratio of the quantity of cloth produced to the quantity of wheat produced at the corners, as follows:

Ignoring the minus sign, the slope equals the ratio of marginal products of the two goods. The slope is also the opportunity cost of wheat, the amount of cloth that must be given up to obtain one more unit of wheat.3 To see this, suppose that Q_W is increased by 1 bushel. It takes one worker to produce 4 bushels of wheat, so increasing Q_W by 1 bushel means that one-quarter of a worker’s time must be withdrawn from the cloth industry and shifted into wheat production. This shift would reduce cloth output by yard, the amount of cloth that could have been produced by one-quarter of a worker’s time. Thus, yard of cloth is the opportunity cost of obtaining 1 more bushel of wheat and is the slope of the PPF.

Home Indifference Curve With this production possibilities frontier, what combination of wheat and cloth will Home actually produce? The answer depends on the country’s demand for each of the two goods. There are several ways to represent demand in the Home economy, but we will start by using indifference curves. Each indifference curve shows the combinations of two goods, such as wheat and cloth, that a person or economy can consume and be equally satisfied.

In Figure 2-2, the consumer is indifferent between points A and B, for example. Both of these points lie on an indifference curve U₁ associated with a given level of satisfaction, or utility. Point C lies on a higher indifference curve U₂, indicating that it gives a higher level of utility, whereas point D lies on a lower indifference curve U₀, indicating that it gives a lower level of utility. It is common to use indifference curves to reflect the utility that an individual consumer receives from various consumption points. In Figure 2-2, we go a step further, however, and apply this idea to an entire country. That is, the indifference curves in Figure 2-2 show the preferences of an entire country. The combinations of wheat and cloth on U₀ give consumers in the country lower utility than the combinations on indifference curve U₁, which in turn gives lower utility than the combinations of wheat and cloth on U₂.

Home Equilibrium In the absence of international trade, the production possibilities frontier acts like a budget constraint for the country, and with perfectly competitive markets, the economy will produce at the point of highest utility subject to the limits imposed by its PPF. The point of highest utility is at point A in Figure 2-2, where Home consumes 25 yards of cloth and 50 bushels of wheat. This bundle of goods gives Home the highest level of utility possible (indifference curve U₁) given the limits of its PPF. Notice that Home could produce at other points such as point D, but this point would give a lower level of utility than point A (i.e., point D would offer lower utility because U₀ is lower than U₁). Other consumption points, such as C, would give higher levels of utility than point A but cannot be obtained in the absence of international trade because they lie outside of Home’s PPF.

We will refer to point A as the “no-trade” or the “pre-trade” equilibrium for Home.4 What we really mean by this phrase is “no international trade.” The Home country is able to reach point A by having its own firms produce wheat and cloth and sell these goods to its own consumers. We are assuming that there are many firms in each of the wheat and cloth industries, so the firms act under perfect competition and take the market prices for wheat and cloth as given. The idea that perfectly competitive markets lead to the highest level of well-being for consumers—as illustrated by the highest level of utility at point A—is an example of the “invisible hand” that Adam Smith (1723–1790) wrote about in his famous book The Wealth of Nations. Like an invisible hand, competitive markets lead firms to produce the amount of goods that results in the highest level of well-being for consumers.

Opportunity Cost and Prices Whereas the slope of the PPF reflects the opportunity cost of producing one more bushel of wheat, under perfect competition the opportunity cost of wheat should also equal the relative price of wheat, as follows from the economic principle that price reflects the opportunity cost of a good. We can now check that this equality between the opportunity cost and the relative price of wheat holds at point A.

Wages We solve for the prices of wheat and cloth using an indirect approach, by first reviewing how wages are determined. In competitive labor markets, firms hire workers up to the point at which the cost of one more hour of labor (the wage) equals the value of one more hour of production. In turn, the value of one more hour of labor equals the amount of goods produced in that hour (the marginal product of labor) times the price of the good (P_W for the price of wheat and P_C for the price of cloth). That is to say, in the wheat industry, labor will be hired up to the point at which the wage equals P_W · MPL_W, and in the cloth industry labor will be hired up to the point at which the wage equals P_C · MPL_C.

If we assume that labor is perfectly free to move between these two industries and that workers will choose to work in the industry for which the wage is highest, then wages must be equalized across the two industries. If the wages were not the same in the two industries, laborers in the low-wage industry would have an incentive to move to the high-wage industry; this would, in turn, lead to an abundance of workers and a decrease in the wage in the high-wage industry and a scarcity of workers and an increase in the wage in the low-wage industry. This movement of labor would continue until wages are equalized between the two industries.

We can use the equality of the wage across industries to obtain the following equation:

By rearranging terms, we see that

The right-hand side of this equation is the slope of the production possibilities frontier (the opportunity cost of obtaining one more bushel of wheat) and the left-hand side of the equation is the relative price of wheat, as we will explain in the next paragraph. This equation says that the relative price of wheat (on the left) and opportunity cost of wheat (on the right) must be equal in the no-trade equilibrium at point A.

To understand why we measure the relative price of wheat as the ratio P_W/P_C, suppose that a bushel of wheat costs $3 and a yard of cloth costs $6. Then $3/$6 = , which shows that the relative price of wheat is , that is, of a yard of cloth (or half of $6) must be given up to obtain 1 bushel of wheat (the price of which is $3). A price ratio like P_W/P_C always denotes the relative price of the good in the numerator (wheat, in this case), measured in terms of how much of the good in the denominator (cloth) must be given up. In Figure 2-2, the slope of the PPF equals the relative price of wheat, the good on the horizontal axis.

The Foreign Country

Now let’s introduce another country, Foreign, into the model. We will assume that Foreign’s technology is inferior to Home’s so that it has an absolute disadvantage in producing both wheat and cloth as compared with Home. Nevertheless, once we introduce international trade, we will still find that Foreign will trade with Home.

Foreign Production Possibilities Frontier Suppose that one Foreign worker can produce 1 bushel of wheat ( = 1), or 1 yard of cloth ( = 1), whereas recall that a Home worker can produce 4 bushels of wheat or 2 yards of cloth. Suppose that there are = 100 workers available in the Foreign country. If all these workers were employed in wheat, they could produce · = 100 bushels, and if they were all employed in cloth, they could produce · = 100 yards. Foreign’s production possibilities frontier (PPF) is thus a straight line between these two points, with a slope of −1, as shown in Figure 2-3.

You might find it helpful to think of the Home country in our example as the United States or Europe and the Foreign country as the “rest of the world.” Empirical evidence supports the idea that the United States and Europe have the leading technologies in many goods and an absolute advantage in the production of both wheat and cloth. Nevertheless, they import much of their clothing and textiles from abroad, especially from Asia and Latin America. Why does the United States or Europe import these goods from abroad when they have superior technology at home? To answer this question, we want to focus on the comparative advantage of Home and Foreign in producing the two goods.

Comparative Advantage In Foreign, it takes one worker to produce 1 bushel of wheat or 1 yard of cloth. Therefore, the opportunity cost of producing 1 yard of cloth is 1 bushel of wheat. In Home, one worker produces 2 yards of cloth or 4 bushels of wheat. Therefore, Home’s opportunity cost of a bushel of wheat is a yard of cloth, and its opportunity cost of a yard of cloth is 2 bushels of wheat. Based on this comparison, Foreign has a comparative advantage in producing cloth because its opportunity cost of cloth (which is 1 bushel of wheat) is lower than Home’s opportunity cost of cloth (which is 2 bushels of wheat). Conversely, Home has a comparative advantage in producing wheat because Home’s opportunity cost of wheat (which is yard of cloth) is lower than Foreign’s (1 yard of cloth). In general, a country has a comparative advantage in a good when it has a lower opportunity cost of producing it than does the other country. Notice that Foreign has a comparative advantage in cloth even though it has an absolute disadvantage in both goods.

As before, we can represent Foreign’s preferences for wheat and cloth with indifference curves like those shown in Figure 2-4. With competitive markets, the economy will produce at the point of highest utility for the country, point A^*, which is the no-trade equilibrium in Foreign. The slope of the PPF, which equals the opportunity cost of wheat, also equals the relative price of wheat.5 Therefore, in Figure 2-4, Foreign’s no-trade relative price of wheat is = 1. Notice that this relative price exceeds Home’s no-trade relative price of wheat, which is P_W/P_C = . This difference in these relative prices reflects the comparative advantage that Home has in the production of wheat.6