The Market Motivation to Trade

Suppose two countries, the United States and France, are initially in autarky. Assume the United States has a comparative advantage in cheese production relative to France. This implies

aLCaLW<aLC∗aLW∗.

This, in turn, implies

( P C P W )Aut< ( P C ∗ P W ∗ )Aut.

This means that the autarky price of cheese in France (in terms of wine) is greater than the autarky price of cheese in the United States. In other words, you can buy more wine with a pound of cheese in the French market than you can in the U.S. market.

Similarly, by rearranging the above inequality,

( P W P C )Aut> ( P W ∗ P C ∗ )Aut,

which means that the autarky price of wine is higher in the United States (in terms of cheese) than it is in France. In other words, a gallon of wine can be exchanged for more cheese in the United States than it will yield in the French market.

Next, suppose the barriers to trade that induced autarky are suddenly lifted and the United States and France are allowed to trade freely. For simplicity, we assume there are no transportation costs to move the products across borders.

Differences in price ratios between countries and the desire to make more profit are sufficient to generate international trade. To explain why, it is useful to incorporate some friction in the trading process and to tell a dynamic story about how a new free trade equilibrium is reached.

First, note that the higher price of cheese in France means that cheese workers in the United States could get more wine for their cheese in France than in the United States. Suppose one by one over time cheese workers begin to take advantage of the opportunity for trade and begin to sell their cheese in the French market. We assume that some workers are more internationally adroit and thus move first. The motivation here is profit. Workers want to get more for the goods they are selling. As the U.S. cheese workers appear in the French market, the supply of cheese increases. This also represents exports of cheese from the United States to France. The increased supply will reduce the price of cheese in the French market, meaning that over time, the quantity of wine obtained for a pound of cheese will fall. Thus P_C∗/P_W∗ falls once trade is opened.

Next, consider French wine workers immediately after trade opens. Since the price of wine is higher in the United States, French wine workers will one by one over time begin to sell their wine in the U.S. market. This represents exports of wine from France to the United States. The increased supply of wine to the United States lowers its price on the U.S. market. Thus each gallon of wine will trade for less and less cheese. This means P_W/P_C falls, which also means that its reciprocal, P_C/P_W, rises.

These shifts in supply will continue as long as the prices for the goods continue to differ between the two markets. Once the prices are equalized, there will be no incentive to trade any additional amount. Equalized prices mean that a pound of cheese will trade for the same number of gallons of wine in both markets. The free trade prices will be those prices that equalize total supply of each good in the world with total demand for each good.

As a result of trade, the price ratio, or terms of trade, will lie in between the two countries’ autarky price ratios. In other words, the following inequality will result:

( P C P W )Aut< ( P C P W )FT< ( P C ∗ P W ∗ )Aut.

Whether the free trade price ratio will be closer to the U.S. or France’s autarky price ratio will depend on the relative demands of cheese to wine in the two countries. These demands in turn will depend on the size of the countries. If the United States is a much larger country, in that it has a larger workforce, it will have a larger demand for both wine and cheese. When trade opens, the addition of France’s supply and demand will have a relatively small effect on the U.S. price. Thus the free trade price ratio will be closer to the U.S. autarky price ratio.

The Market Motivation for Specialization

Once the prices begin to change because of trade, they will also affect the profitability of producing the two goods. In the United States, the price of cheese, its export good, will rise in moving to trade, while the price of wine, its import good, will fall. As shown above, the final price ratio in the United States (cheese to wine) in free trade will be greater than the autarky price ratio, so that

( P C P W )FT>( P C P W )Aut.

Because the autarky price ratio equals the opportunity cost of cheese production, it follows that

( P C P W )FT>aLCaLW.

Note that this inequality will be true as soon as the price deviates from the autarky price and long before the free trade prices are reached. This also means that shortly after trade begins, the price of cheese (measured in terms of wine) exceeds the cost of producing cheese (also measured in terms of wine). Normally, when we measure the price and cost in dollar terms, when the price per unit exceeds the cost per unit, then positive profit is realized. The same is true when we measure the price and cost in terms of wine. Thus as soon as trade begins to change prices, cheese production becomes more profitable in the United States. And because we assume people are profit seeking, they will therefore seek to expand cheese production. But where will they find the workers to do so? There is only one place: wine workers. To expand cheese production, the country will have to give up wine production. But why do that?

Well, when the price of cheese in terms of wine exceeds the opportunity cost of cheese, it is also true, via cross multiplication, that

aLWaLC >( P W P C )FT.

This means that the cost of producing wine (in terms of cheese) exceeds the price of wine (also in terms of cheese). Because cost is greater than price, profit is negative in the wine industry in the United States. That means wine producers have an incentive to shut down. And when they do, those workers can be moved into the cheese industry, where profit seekers wish to expand.

Thus, as long as individuals are profit seeking, the price differences that arise in autarky will be sufficient to induce export and specialization in the comparative advantage good. There is no need to use the complicated opportunity cost formula to first identify the comparative advantage good and no need to tell anyone what to do. Instead, the free market mechanism—Adam Smith’s invisible hand—is all that it takes.