# A Simple Pure Exchange Economy

## The Pure Exchange Model of Trade Module

**A Simple Pure Exchange Economy**lesson on

**Policy and Theory of International Economics**course, we are delighted to have you here.

### Learning Objectives

- Learn the definition of the terms of trade.
- Learn how the terms of trade between two goods is equivalent to the ratio of dollar prices for the two goods.

The Ricardian model shows that trade can be advantageous for countries. If we inquire deeper and ask what is meant when we say a “country” benefits in this model, we learn it means that every individual, every worker, in both countries is able to consume more goods after specialization and trade. In other words, everyone benefits from trade in the Ricardian model. Everybody wins.

Unfortunately, though, this outcome is dependent on the assumptions made in the model, and in some important ways these assumptions are extreme simplifications. One critical assumption is that the workers in each country are identical; another is the free and costless ability of workers to move from one industry to another. If we relax or change these assumptions, the win-win results may not remain. That’s what we will show in the pure exchange model and the immobile factor model.

For a variety of reasons, it is more common for trade to generate both winners and losers instead of all winners. Economists generally refer to a result in which there are both winners and losers as income redistributionOccurs when some individuals gain income while others lose or when individuals gain and lose income shares of total income. because the winners can be characterized as receiving a higher real income, while those who lose suffer from a lower real income.

The simplest example of advantageous trade arising from differences in resource endowments can be shown with a pure exchange model. In this model, we ignore the production process and assume more simply that individuals are endowed with a stock of consumption goods. We also show that trade can result in a redistribution of income. The model and story are adapted from a presentation by James Buchanan about the benefits of international trade.James Buchanan, “The Simple Logic of Free Trade,” *Proceedings of the First Annual Symposium of the Institute for International Competitiveness* (Radford, VA: Radford University, 1988), iii–x.

## A Simple Example of Trade

Suppose there are two individuals: Farmer Smith and Farmer Jones. Farmer Smith lives in an orange grove, while Farmer Jones lives in an apple orchard. For years, these two farmers have sustained themselves and their families by collecting oranges and apples on their properties: Smith eats only oranges and Jones eats only apples.

One day these two farmers go out for a walk. Farmer Smith carries ten oranges with him in case he becomes hungry. Farmer Jones carries ten apples. Suppose these farmers meet. After a short conversation, they discover that the other farmer sustains his family with a different product, and the farmers begin to discuss the possibility of a trade.

The farmers consider trade for the simple reason that each prefers to consume a variety of goods. We can probably imagine the monotony of having to eat only apples or only oranges day after day. We can also probably imagine that having both apples and oranges would be better, although we might also prefer some fried chicken, mashed potatoes, a Caesar salad, and numerous other favorite foods, but that is not included as a choice for these farmers. As such, when we imagine trade taking place, we are also assuming that each farmer has a preference for variety in consumption. In some special cases, this assumption may not be true. For example, Farmer Jones might have a distaste for oranges, or he may be allergic to them. In that special case, trade would not occur.

Assuming trade is considered by the farmers, one question worth asking is, What factors will determine the terms of tradeThe amount of one good traded per unit of another in a mutually voluntary exchange. Often expressed as a ratio of prices.? The terms of trade is defined as the quantity of one good that exchanges for a quantity of another. In this case, how many apples can be exchanged for how many oranges? It is typical to express the terms of trade as a ratio. Thus, if one apple can be exchanged for four oranges, we can write the terms of trade as follows:

$\text{TOT}=\frac{1\text{apple}}{4\text{oranges}}=\frac{1}{4}\text{apple}\text{/}\text{orange}\text{,}$where TOT refers to terms of trade. It is immaterial whether the ratio is written apples over oranges or oranges over apples, but to proceed, one or the other must be chosen.

The terms of trade is also equivalent to the ratio of prices between two goods. Suppose *P*_{A} is the price of apples (measured in dollars per apple) and *P*_{O} is the price of oranges (measured in dollars per orange). Then

To demonstrate the equivalency, consider the units of this price ratio shown in brackets above. After some manipulation, we can see that the dollars cancel and thus the price of oranges over the price of apples is measured in units of apples per orange. We can refer to this price ratio as the price of oranges in terms of apples—that is, how many apples one can get in exchange for every orange. Notice that the price of *oranges* over apples is in units of *apples* per orange. Similarly, *P*_{A}/*P*_{O} has units of oranges per apple.This model and many others we will consider are actually barter economies. This means that no money is being exchanged between the agents. Instead, one good is exchanged for another good. However, since we are accustomed to evaluating values in monetary terms, we will often write important expressions, like the terms of trade, in terms of their monetary equivalents as we have done here.

### Key Takeaways

- The terms of trade is defined as how much of one good trades for one unit of another good in the market.
- The terms of trade between two goods (e.g., apples and oranges) is equivalent to the ratio of the dollar prices of apples and oranges.

### Exercises

- If two bushels of apples can be traded for three bushels of oranges, what is the terms of trade between apples and oranges?
- If two bushels of apples can be traded for three bushels of oranges, how many bushels of oranges can be purchased with one bushel of apples?
- If the price of ice cream is $3.50 per quart and the price of cheesecake is $4.50 per slice, what is the terms of trade between cheesecake and ice cream?