Ricardian Models: Foreign Trade

Notes on The Principles of Political Economy and Taxation

14 Jul 2019
modified: 28 Sep 2019

Ricardo considers a number of facets of foreign trade in his The Principles, but his best known theory under this topic is the Law of Comparative Advantage. This theory asserts that under conditions of relatively free trade, nations can achieve greater wealth by focusing more resources toward commodities with lower production costs than on those commodities with greater production costs. When trading partners focus production efforts on different commodities with cost efficiencies ideosyncratic to their own nation, all trading nations can benefit from exchanging their own less costly commodities for the most cost efficient commodities of other nations. Importantly, Ricardo demonstrates that these benefits for two countries prevail even when the costs of the most efficient commodities of one country exceed the production cost of the same commodity inefficiently produced in a second country.

Define valuation of corn and wine as follows:

• $v_c^{E}$ : valuation of unit quantity of corn in England.
• $v_w^{E}$ : valuation of unit quantity of wine in England.
• $v_c^{P}$ : valuation of unit quantity of corn in Portugal.
• $v_w^{P}$ : valuation of unit quantity of wine in Portugal.
1. Assume that the amount of labor required to produce a unit quantity of wine exceeds the amount of labor required to produce a unity quantity of corn in England; according the Ricardo’s labor theory of value, the valuations of these commodities in the English market adheres to the inequality, $v_c^{E} < v_w^{E}$

2. Assume amount of labor required to produce a unit quantity of corn exceeds the amount of labor required to produce a unity quantity of wine in Portugal; the labor theory of value similarly predicts the valuations of these commodities in the Portuguese market follows the inequality, $v_w^{P} < v_c^{P}$.

When the rank order of valuations for two commodities is inverted between two countries (as in assumption 1 and 2), the countries are said to benefit from a comparative advantage in the production of commodities requiring less relative labor. Under assumption 1 and 2, England benefits from a comparative advantage in the production of corn, while Portugal benefits from a comparative advantage in the production of wine. The comparative advantage of these nations holds independently of whether either country holds an absolute advantage in the production of these commodities; ie., whether both corn and wine are cheaper to produce in England than in Portugal, or vice versa.

To understand the role of comparitive advantage in foreign trade, assume the following valuations of corn and wine produced in England and Portugal:

English valuations of corn and wine produced in England:

• $v_c^{E} = \$5$•$v_w^{E} = \$6$

Thus, $\frac{v_c^{E}}{v_w^{E}} = \frac{5}{6}$ represents the proportion of a unit quantity of wine given in a market exchange for a unit quantity of corn in England.

Portuguese valuations of corn and wine produced in Portugal:

• $v_c^{P} = \$9$•$v_w^{P} = \$8$

Thus, $\frac{v_w^{P}}{v_c^{P}} = \frac{8}{9}$ represents the proportion of a unit quantity of corn given in a market exchange for a unit quantity of wine in Portugal.

With these relative valuations, England has a comparative advantage in the production of corn relative to wine, while Portugal has a comparative advantage in the production of wine relative to corn. England benefits from trade with Portugal if the Portuguese will value English corn at more than $\frac{5}{6}$ the value of Portuguese wine: $\frac{v_c^{E}}{v_w^{P}} > \frac{5}{6}$. And Portugal benefits from trade with England if the English will value Portuguese wine at more than $\frac{8}{9}$ the value of English corn: $\frac{v_w^{P}}{v_c^{E}} > \frac{8}{9}$

Then both countries benefit from an exchange where England gives more than $\frac{8}{9}$ but less than $\frac{6}{5}$ of a unit quantity of English corn for a unit quantity of Portuguese wine; or equivalently, both countries benefit if England gives more than 40 but less than 54 units of English corn for 45 units of Portugese wine:

$\begin{eqnarray} \frac{8}{9} < \frac{v_w^{P}}{v_c^{E}} < \frac{6}{5} \quad &\Rightarrow& \quad \frac{40}{45}v_c^{E} < v_w^{P} < \frac{54}{45}v_c^{E} \\[2ex] &\Rightarrow& \quad 40 v_c^{E} < 45 v_w^{P} < 54 v_c^{E} \end{eqnarray}\tag{1}$

Note that in the example above, England shows an absolute advantage in the production of both corn and wine: England produces both commodities with less labor, and hence, more cheaply than Portugal. And yet, Portugal’s comparative advantage in producing wine, along with England’s comparative advantage in producing cloth renders trade more advantageous for both countries than for either country to produce both commodities for themselves. Importantly, however,this result only holds when capital is restricted from moving freely between the two countries.

Foreign Trade as Barter

When two countries produce two commodities, each with a comparative advantage in the production of one of these commodities, a foreign trade by barter exchange can develop. A barter exchange is particularly advantageous not only because each country can specialize in those commodities most efficiently produced according to the idiosyncratic circumstances of national soil, geography, etc; but also because a trade by barter avoids the physical transportation of gold or silver to foreign nations. To achieve a foreign trade of goods without a physical exchange of money, importers and exporters used bills of exchange (BOE). A bill of exchange designated a payer - usually the seller of the bill; and a payee - initially, the purchaser of the bill, but more generally, the bearer of the bill if the initial purchaser sells the bill to a third party. To see how these financial instruments obviated the need for a physical relocation of gold or silver, the diagram below represents a situation in which England holds a comparative advantage in the production of cloth, while Portugal holds a comparative advantage in the production of wine.

The flow of money and goods can be understood as a sequence of exchanges as follows:

1. A Portuguese wine exporter sells a bill of exchange to a third party in exchange for Portuguese currency (eg., \$ as escudo or euro).
2. A Portuguese cloth importer uses revenues from cloth sales to purchase this bill of exchange from a third party and uses it to pay a cloth exporter for English cloth.
3. The cloth exporter then sells the bill of exchange to a wine importer in exchange for English currency (eg., £ as British pounds) in order to purchase more cloth from cloth producers.
4. The wine importer then uses this bill of exchange to pay wine exporters for Portuguese wine.

These several transactions effectively transfer cloth and wine between nations and return the original bill of exchange to Portugal, without the need to move currencies between nations.

Foreign Trade using Currency

When one nation lacks a complimentary comparative advantage between two commodities, or when one nation’s foreign policy effectively prohibits importation or exporation of commodities, then an exporting nation that enjoys an absolute advantage will still benefit from producing commodities cheaply in the home country and selling them at a profit in a foreign country. In these cases, the purchasing nation must bear the cost with the physical transportation of gold or silver. In this circumstance, there are two important points of consideration.

1. The producing nation will exchange commodities while accruing gold or silver; the purchasing nation will gain in foreign goods while divesting from gold or silver.
2. The higher transaction costs will prevent fewer commodities from moving between the countries.

In this situation, an exporting nation with absolute advantage will continue to pursue trade with its counter-party as long as the valuation of gold or silver exceeds the relative valuation of the commodities given in exchange for them; and similarly, the importing nation will continue to purchase commodities from exporting counter-parties as long as the relative valuation of commodities exceeds the valuation of gold or silver exchanged for them.