Home » Models and Theory » Ricardian model: The Simple Ricardian Model

Published: января 15, 2013

# Ricardian model: The Simple Ricardian Model

Ricardian model

Ricardian model: Extensions of the Simple Ricardian Model

Ricardian model: The Role of the Ricardian Model in Understanding the World Economy

The simple Ricardian model depicts a world of two countries, A and B, each using a single factor of production, labor L, to produce two goods, X and Y. Technologies display constant returns to scale,meaning that a fixed amount of labor, ac g is needed to produce a unit of output of each good, g ¼ X,Y, in each country, c ¼ A,B, regardless of how much is produced in total. All markets are perfectly competitive, so that goods are priced at cost in countries that produce them, pc g ¼wcac g, where wc is the competitive wage in country c. Labor is available in fixed supply in each country, Lc ; it is immobile between countries but perfectly mobile within each. The Ricardian model typically leaves demands for goods much less fully specified than supplies, though a modern formulation may specify for each country a utility function, Uc ¼Uc (Cc x , Cc y ), which the representative consumer maximizes subject to a budget constraint. Utility functions may, or may not, be assumed in addition to be identical across countries, or to possess other regularity properties, althoughmost properties of the model’s solution do not require any of these assumptions.

The most basic use of the model compares the equilibriums in autarky (that is, complete self-sufficiency without trade) with those of free and frictionless trade. In autarky, since both goods must be produced in each country, prices are given immediately by the costs stated above, and further analysis is needed only if one wants to know quantities produced and consumed. If so, the linear technology implies a linear production possibility frontier (PPF) that also serves as the budget line for consumers in autarky. The autarky equilibrium is as shown in figure 1, where ~ indicates autarky and Q represents production.

Comparison of the two countries in autarky depends primarily on their relative costs of producing the two goods, which in this model defines their comparative advantage. For concreteness, assume that country A has comparative advantage in good X : aAX =aAY Q~B X =Q~B Y .

With free and frictionless trade, pricesmust be the same in both countries.Two kinds of equilibriumare possible, depending on the supplies and demands for goods in the two countries.One kind of equilibrium has world relative prices, denoted here by, strictly between the relative prices of the two countries in autarky: ~pAX =~pAY < pX =pY < ~pBX =~pBY . In that case, each country must specialize in producing only the good forwhich its relative cost is lower than theworld relative price, thus the good in which it has comparative advantage. Each must necessarily export that good.

With such complete specialization, outputs of the goods are determined by labor endowments and productivities, so equality of world supply and demandmust be achieved fromthe demand side. That is, world prices are determined such that the two countries’ demands sumto the quantity produced in one of them. These demands derive from the expanded budget constraints of each country’s consumers, reflecting the value at world prices of the single good that the country produces. Consumers cannow,unless theywish to consume only that single good, consume more of both goods than they did in autarky. Whether they choose to do so depends on the extent to which they substitute toward the cheaper good now imported fromabroad, but in any case they reach a higher indifference curve and are better off. All of this is shown in figure 2. For this to be an equilibrium, the quantity of each good exported by one country must equal the quantity imported by the other, so the heavy arrows showing net trade in each panel of the figure must be equal and opposite.

Such an equilibrium with specialization will arise only if the two countries’ capacities to produce their respective comparative-advantage goods correspond sufficiently closely toworld demands for the goods. If this is not the case if one country’s labor endowment is too low and/or its labor requirement for producing its comparative-advantage good is too high for it to satisfy world demand then while that country will specialize, the other country (call it the larger one, although that is not strictly necessary) will not. Instead of world relative prices settling between the two autarky levels as described earlier, prices will exactly equal the autarky prices of the larger country, and that country will produce both goods. At those prices, producers in the larger country will be indifferent among all output combinations on the PPF, and output in the large country will be determined instead by the need to fill whatever demand is not satisfied by the smaller country.

Such an equilibriumis shown in figure 3,where in comparison to figure 2 countryB’s labor endowment hasbeenmade smaller and bothcountries’ preference for good Y has been increased. As a result, country B is too small tomeetworld demand for good Y, even at country A’s autarky prices. Therefore the free trade equilibriumhas countryAconsumingwhere it did in autarky, while its production, QA, moves down along its PPF so that, again, its trade vector can be equal and opposite to that of country B.Note that, in this trading equilibrium, the larger country neither gains nor loses from trade.

The following are some of the implications of this simple model, some of which have been illustrated above, while others can be derived rather simply: