Allocation under Trade

Readers familiar with prevailing microeconomics may have to struggle to recognize that the Ricardian trade model (and its subsequent refinements) and the Walrasian model of general equilibrium are not models of trade, but of allocation under subsistence.

To turn them into genuine trade models, one must introduce agreements on market prices, bring in genuine money as a means of payment, and allow intermediaries to lead the social decisions on settling prices and payments. The following sections introduce the changes in several steps.

4.5.1 Pure Profit Opportunities

Exchange in a market offers an opportunity to earn a pure profit. This happens because there are other people who ascribe relatively high utility to the product the individual is able to produce, compared to a given good. For example, suppose that in isolation, Crusoe is observed to produce at a point where 2 baskets of fruits have the same utility to him as 2 bags of grain. Optimally, his resource allocation is such that he can produce either 2 bags of grain or 2 baskets of fruits with the same inputs (dL, dH).

However, stranger Defoe wants to consume fruits with a much stronger desire and is willing to offer 4 bags of grain for 2 baskets of fruits. Thus Crusoe is able to get 4 bags of grain in exchange for 2 baskets of fruits, rather than merely produce 2 bags of grain. The pure profit from exchange is 2 bags of grains.

The paradox arises from the idea that Crusoe would continue to produce more fruits and buy more grains until all further opportunities for profit are exhausted. This thinking is mistaken, because it forgets the constraints on Crusoe's factor endowments, as well as the constraints on Defoe's income. Here is a simple graphic reminder of the issue.

In Figure-14, Crusoe produces at point A under subsistence, but at point B under trade. He sells Fx=(F_b-F_a) and buys Gm=(G_c-G_b). The shadow price ratio under subsistence is given by the slope of the dotted price line. The market price ratio is given by the slope of the solid price line.

At the market price ratio, fruits are dearer and hence grains are cheaper, so that Crusoe sells fruits and buys grains.

Crusoe's net profit is given by the extra grains he can get for a given quantity of fruits under trade than under subsistence. Thus by sacrificing Fx_{of fruits, he can get as much as [(G}

c-Ga)+(Ga-Gb)] under trade, while

he could get only (G_a-G_b) under subsistence. Hence (G_c-G_a) is his net profit compared to autarky. In short, measured in G, Crusoe's marginal cost is (G_a-G_b), but marginal revenue is [(G_a-G_b)+(G_c-G_a)].

The allocation model sets the market price equal to the shadow price without imposing the budget constraints on both buyers. Crusoe cannot keep on selling more fruits to reach a point where no more pure profit opportunity remains, just as Defoe cannot keep on buying more fruits, because he too has a limited income.

An allocation model implicitly imposes an endowment constraint which defines the income at shadow prices. It is understood that the agent makes full use of all available income or endowment. But when two agents are involved, the allocation model forgets to define a global endowment or income constraint.

The exchange model imposes the global income constraint in the form of the equivalence principle. This is explained in the following chapters.

4.5.2 Expanded Production Opportunities

Trade allows people to make use of hitherto useless resources and thereby expand the potential and actual output. The allocation model cannot grasp this crucial material impact of trade on the expansion of production opportunities.

To see the theoretical issue in concrete terms, let us consider the rather striking fact that the planet's stock of natural resources has remained the same for all practical purposes. But compared to 10,000 years ago, far more of the resources are being used now. The greater part of the increased use of previously unused resource is made possible by trade. One can think about population growth as the other factor.

How does the expansion occur? Consider Crusoe's fruit output under subsistence. His island may very well be full of fruit-bearing trees. But he cannot possibly use up all the resources, because he has a limit of consumption. His time is scarce and his work is costly (painful). He will gather fruits until the marginal utility of the last basket of fruit is equal to the marginal cost or disutility of the last minute of work. He is not willing to work any harder to gather more fruits.

However, now suppose that Defoe wants some fruits from Crusoe. It is not optimal for Crusoe to produce more fruits if he has to consume them, but it is worthwhile for him to do so if he can consume more grains. The key here once again is to remember that Crusoe can also produce grains, but his grain output per minute is much lower than what he can get from Defoe in exchange of his work to gather fruits per minute.

This seems like a reallocation only because we have used a two good example. Most people cannot produce most goods at any cost. To buy more, they just work more to produce what they can produce.

In the allocation model, Crusoe is more productive in gathering fruits than growing grains. This means that at Defoe's request, Crusoe may work harder than before and produce more fruits, and expand his consumption of grains. He just turns hitherto useless fruit trees into useful factors of production. They may still not show up in his PPF, because he may still have unused trees at the margin. But his labor is definitely increased.

One can check the facts of increased use of labor through successive epochs of economic transitions from forager to pastoral to agrarian to industrial to post-industrial economies.

In an exchange model, a decomposition of output shows that the output is the minimum under subsistence. Much of what is traded would simply not be produced if not for trade. Thus, it would be hard to imagine Stigler lecturing himself with so much devotion if there were no students to pay for his lectures, and to enable him to get things he would

otherwise not be able to produce at all.

This is also the root of unemployment in a market economy. People are specialized to produce certain goods and services. Today, they are usually without access to the natural resources that subsistence producers used to have before agrarian economies privatized land. If they cannot sell what they produce, they cannot produce much at all.

In short, it is not just a gain in efficiency, but also an expansion in the size of resources brought under use. The efficiency gain is explained below.

4.5.3 Competitive Market Constraints

Ceaseless competition in the market involves ever changing constraints and opportunities. It compels the entrepreneur to stay alert and try to adjust to the changes in the market.

A review of the Ricardian trade model may expose the problem. Let us look at Crusoe's PPF once again. At the extreme ends, the PPF reveals some feature of factor endowment that is apt to escape notice. In the vicinity of the PPF touching the vertical axis F, the curve is nearly horizontal, implying that a small reduction in F may allow a large increase in G. This means that there are some resources which are more suited to produce G than F, for example, fertile croplands are more suited to produce grains than fruits. At the other extreme, the curve is nearly vertical, where a small decrease in G allows a large increase in F, again because there are some resources that are better suited to produce fruits than grains.

The PPF of course is derived from combining technology and endowment. If one likes, one may use a difference in technology to split Crusoe's resources into 'two countries', say Fruitland and Grainland. In Fruitland, the resources and technologies make it easier to produce fruit than grain. It is the opposite in Grainland.

Having split the resources into two countries, it is easy to set up a joint allocation problem. That will give rise to the Ricardian model of joint allocation that is more commonly known as the trade model.

The Ricardian model implicitly assumes that both countries (Fruitland and Grainland) are owned by the World's owner (Crusoe), whose business it is to consider the efficient or optimal allocation. If indeed the world's sole owner wants to maximize value of output, the optimal allocation is to let Fruitland produce the fruits and Grainland produce the grains according to comparative cost.

Why is it not a trade model? In a trade model, the agents do not grant mutual monopoly. In the Ricardian model, Fruitland confers monopoly of grain production to Grainland, and in return is granted the monopoly of fruit production. In actual trade, the different countries or agents are

independent. They have no rational basis to worry about comparative cost advantage at all. Competing agents abide by what Smith called absolute advantage.

Genuine trade does not abide by comparative advantage, but by absolute advantage. The more competent producer is able to produce at lower cost, or provide better products at the same price. The greater the absolute advantage, the higher the margin of profit. Indeed, the producers who are at the bottom of absolute advantage run the risk of being driven out of the market, regardless of the comparative advantage.

Comparative cost is an idea appropriate for a joint allocation model, and not for an exchange model. This idea can be very misleading when one studies economic development. Compare the illiterate lowly paid rural peasant to the literate and highly paid urban lawyer. According to comparative advantage, the peasant would remain a peasant, doing low- paid work in a stagnating sector, while the lawyer would keep increasing his relative income in an ever-growing sector.

But Smith would encourage the peasant to become a lawyer to compete for absolute advantage. That is exactly how economic development has to happen: by turning less productive factors into more productive ones, that is, by turning comparative advantage into absolute advantage.

A joint allocation model generates what is known as factor price equalization theorem (See Samuelson 1948,1949). It does not describe competitive trade. Competition means that there is no evidence to show factor price equalization.

4.5.4 Price Constraints

The logic of allocation forces the model to take the shadow price and suppose that it is the market price. The problem of course is that the other people in the market do not have the same preferences. Hence a single price ratio at which all different individuals reach allocation equilibrium is not a real possibility. The culprit is the difference in income constraint. For example, the market as a collective entity may reach a market clearing price ratio such that a certain quantity of food has exactly the same value as a theater ticket. At this exchange rate, a hungry man may just lack the income to buy both in quantities enough to make them of equal marginal utility. His income and his consumption of food may be so low and the marginal utility of the food so high that he will certainly not consider giving equal importance to the theater ticket.

In short, the market offers producers an opportunity to sell at a price significantly above the marginal cost, because buyers do not have

enough income to buy to the point where the marginal profit is zero. The producer also runs out of factor endowments long before the output reaches the point where the marginal profit is zero. At last, one may find some evidence of scarcity in the presence of what may be called scarcity rent by an allocation model.

The opposite happens when the producer is relatively incompetent and incurs a marginal cost so high that buyers are not willing to offer a price high enough to match the cost. It is also possible that there is persistent oversupply.

Adjustments in prices and quantities are supposed to eliminate the imbalances between demands and supplies. This requires intermediaries to carry out the adjustments. The discovery of the opportunities of pure profits from organizing the adjustments, the creativity to actually design and implement the transactions, and the charisma to obtain legitimacy of the new transactions are all dependent on entrepreneurial perceptions. These adjustments are not automatic, because the entrepreneurs may suffer from ignorance, and lack creativity and charisma until an accidental discovery or creativity changes the situation.

4.5.5 Payment Constraints

Perhaps the most sweeping change in analysis comes from the payment problem that arises with trade, but is absent under subsistence. The problem is that the seller of something requires a payment in a kind of good which gives him higher utility than the good he sells. The values are the same, but the utilities differ as the kinds of payments differ.

Say's Law fails under trade, because even when the values of the two goods are equal (making demand equal to supply), their utilities are not equal. Hence the seller may refuse to accept a particular payment, and insist on being paid in a different kind of good of the same value. Money is necessary to transfer claim over real goods of definite kinds.

5. EXCHANGE

Consistent economics is a study of exchange. It uses a formal tool of consistency analysis to understand exchange. However, it is useful to have a sense of the concrete reality that the abstract formal model seeks to capture.