A Ricardian Numerical Example
by Steven Suranovic ©1997-2004
The simplest way to demonstrate that countries can gain from trade in the
Ricardian model is
of a numerical example. This is how Ricardo presented his argument originally. The example
demonstrates that both countries will gain from trade if they specialize in their comparative
good and trade some of it for the other good. We set up the example so that one country (the US)
has an absolute advantage in the production of both goods. Ricardo's surprising result was that a
country can gain from trade even if it is technologically inferior in producing every good. Adam
Smith had explained in the Wealth of Nations that trade is advantageous to both countries, but in
example each country had an absolute advantage in one of the goods. That trade could be
advantageous if each country specializes in the good in which it has the technological edge is not
surprising at all.
Suppose the exogenous variables in the two countries take the values in the following table.
By assumption the U.S. has the absolute advantage in cheese production and wine production since aLC(1) < aLC*(6) and aLW(2) < aLW*(3).
The US also has the comparative advantage in cheese production since. The cost of producing cheese in the U.S. is ½ gallon per pound of cheese. In France, it is 2 gallon per pound.
France, however, has the comparative advantage in wine production since . The cost of producing wine in France is ½ pound of cheese per gallon of wine while in the U.S., it is 2 pounds per gallon.
The production possibility frontiers for both countries are plotted on the adjoining figure. Notice that the US PPF lies outside France's PPF. Since both countries are assumed to be the same size in the example, this indicates the US absolute advantage in the production of both goods.
The absolute value of the slope of each PPF represents the opportunity cost of cheese production. Since the US PPF is flatter than France's this means that the opportunity cost of cheese production is lower in the US and thus indicates that the US has the comparative advantage in cheese production.
With full employment of labor, production will occur at some point along the PPF.
To see the effects of specialization and free trade we must compare it to a situation of no trade, or autarky. Thus we must construct an autarky equilibrium first. To determine the autarky production point requires some information about the consumer demand for the goods. Producers will produce whatever consumers demand at the prevailing prices such that supply of each good equals demand. In autarky this means that the production and consumption point for a country are the same.
For the purpose of this example we will simply make-up a plausible production/consumption point under autarky. Essentially we assume that consumer demands are such as to generate the chosen production point. The Table below shows the autarky production/consumption levels for the two countries. It also shows total world production for each of the goods.
In this diagram we depict the autarky production and consumption points for the US and France. Each point lies on the interior section of the country's production possibility frontier.
Ricardo argued that trade gains could arise if countries first specialize in their comparative advantage good and then trade with the other country. Specialization in the example means that the US produces only cheese and no wine, while France produces only wine and no cheese. These quantities are shown in the following Table. Also shown are the world totals for each of the goods.
At this point we can already see a remarkable result. When countries specialize in their comparative advantage good, world output of both wine and cheese rises. Cheese output rises from 19 to 24 pounds. Wine output rises from 6 to 8 gallons. What's more, the output increases occur without an increase in the quantity of labor used to produce them. In autarky it took 48 worker-hours to produce 19 pounds of cheese and 6 gallons of wine. With specialization, the same 48 worker-hours produce 24 cheese and 8 wine. This means that there is an increase in world productivity - more output per unit of labor. Often times this productivity improvement is referred to as an increase or improvement in world production efficiency.
The increase in world production efficiency does not benefit the countries unless they can trade with each other after specialization. Both production points were feasible under autarky but the countries demanded some of each good. Thus the countries will want some of each good after specialization and the only way to accomplish this is through trade. Now if the world can produce more of both goods through specialization, clearly there must be a way to divide the surplus between the two countries so that each country ends up with more of both goods after trade than they had in autarky.
The surplus in world production amounts to 5 extra pounds of cheese and 2 extra gallons of wine. To assure that trade is advantageous for the two countries, each must have at least as much to consume of one good and more to consume of the other. Suppose we split the wine surplus equally and give 3 extra pounds of cheese to France and 2 extra pounds to the US. Since the US consumed 16 cheese and 4 wine in autarky, they would now have 18 cheese and 5 wine after specialization and trade. France, which began with 3 cheese and 2 wine in autarky, would now have 6 cheese and 3 wine. Consumption and production after trade for the two countries is shown in the Table.
In order for consumption of both goods to be higher in both countries trade must occur. In the example, the US is consuming 5 gallons of wine and producing none so it must import the 5 gallons from France. France is consuming 6 pounds of cheese with no cheese production so it must import the 6 pounds from the US. The terms of trade is ToT = 5 gal/6 lbs or 5/6 gal/lb.
The Ricardian model numerical example assumes that countries differ in their production technologies such that one of the countries is absolutely more productive than the other in the production of each of the two goods. If these two countries specialize in their comparative advantage good then world production rises for both goods. Increased output occurs even though there is no increase in the amount of labor input in the world, thus the example demonstrates that specialization can raise world production efficiency. Because of the increase in output it is possible to construct a terms of trade between the countries such that each country consumes more of each good with specialization and trade than was possible under autarky. Thus both countries can gain from trade.The surprising result from this example is that a country which is technologically inferior to another in the production of all goods can nevertheless benefit from trade with that country.
Limitations of the Numerical Example
A numerical example can display only one possible outcome for the model. As such, all conclusions should be viewed as possibilities rather than a general result of the model. With further thought there are some problems with the example. First, it is conceivable that with a different choice for the country's autarky production/consumption points, world output might not rise for both goods upon specialization. In this case we could not be sure that both countries would gain from trade. Second, since we merely made up a terms of trade that generated the interesting conclusion, we could ask whether a favorable terms of trade is likely to arise or not. Is it possible to make up a different terms of trade such that one country enjoys all the benefits of increased production while the other is made worse off? How can we be sure that this outcome would not arise? Finally even if the country has more of both goods after trade, can we be sure that all consumers would have more of both goods? Perhaps some consumers would have more while other less.
The answer to some of these questions can be found by describing more carefully some of the features of the model. In particular, we must describe the relationship between prices and wages. Using these relationships we can explain the impact of free trade on the price ratio and the effect of trade on the distribution of income.
International Trade Theory and Policy