The Ricardian model shows the possibility that an industry in a developed country could compete against an industry in a less-developed country (LDC) even though the LDC industry pays its workers much lower wages.
The modern version of the Ricardian model assumes that there are two countries producing two goods using one factor of production, usually labor. The model is a general equilibrium model in which all markets (i.e., goods and factors) are perfectly competitive. The goods produced are assumed to be homogeneous across countries and firms within an industry. Goods can be costlessly shipped between countries (i.e., there are no transportation costs). Labor is homogeneous within a country but may have different productivities across countries. This implies that the production technology is assumed to differ across countries. Labor is costlessly mobile across industries within a country but is immobile across countries. Full employment of labor is also assumed. Consumers (the laborers) are assumed to maximize utility subject to an income constraint.
Below you will find a more complete description of each assumption along with a mathematical formulation of the model.
Perfect competition in all markets means that the following conditions are assumed to hold.
The case of two countries is used to simplify the model analysis. Let one country be the United States and the other France. Note that anything related exclusively to France in the model will be marked with an asterisk. The two countries are assumed to differ only with respect to the production technology.
Two goods are produced by both countries. We assume a barter economy. This means that no money is used to make transactions. Instead, for trade to occur, goods must be traded for other goods. Thus we need at least two goods in the model. Let the two produced goods be wine and cheese.
Labor is the one factor of production used to produce each of the goods. The factor is homogeneous and can freely move between industries.
In David Ricardo’s original presentation of the model, he focused exclusively on the supply side. Only later did John Stuart Mill introduce demand into the model. Since much can be learned with Ricardo’s incomplete model, we proceed initially without formally specifying demand or utility functions. Later in the chapter we will use the aggregate utility specification to depict an equilibrium in the model.
When needed, we will assume that aggregate utility can be represented by a function of the form U = CCCW, where CC and CW are the aggregate quantities of cheese and wine consumed in the country, respectively. This function is chosen because it has properties that make it easy to depict an equilibrium. The most important feature is that the function is homothetic, which implies that the country consumes wine and cheese in the same fixed proportion at given prices regardless of income. If two countries share the same homothetic preferences, then when the countries share the same prices, as they will in free trade, they will also consume wine and cheese in the same proportion.
The Ricardian model is a general equilibrium model. This means that it describes a complete circular flow of money in exchange for goods and services. Thus the sale of goods and services generates revenue to the firms that in turn is used to pay for the factor services (wages to workers in this case) used in production. The factor income (wages) is used, in turn, to buy the goods and services produced by the firms. This generates revenue to the firms and the cycle repeats again. A “general equilibrium” arises when prices of goods, services, and factors are such as to equalize supply and demand in all markets simultaneously.
The production functions in Table 2.4 "Production of Cheese" and Table 2.5 "Production of Wine" represent industry production, not firm production. The industry consists of many small firms in light of the assumption of perfect competition.
Table 2.4 Production of Cheese
| United States | France |
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where QC = quantity of cheese produced in the United States LC = amount of labor applied to cheese production in the United States aLC = unit labor requirement in cheese production in the United States (hours of labor necessary to produce one unit of cheese) ∗All starred variables are defined in the same way but refer to the process in France. |
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Table 2.5 Production of Wine
| United States | France |
|---|---|
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where QW = quantity of wine produced in the United States LW = amount of labor applied to wine production in the United States aLW = unit labor requirement in wine production in the United States (hours of labor necessary to produce one unit of wine) ∗All starred variables are defined in the same way but refer to the process in France. |
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The unit labor requirementsThe quantity of labor needed to produce one unit of a good. define the technology of production in two countries. Differences in these labor costs across countries represent differences in technology.
The resource constraint in this model is also a labor constraint since labor is the only factor of production (see Table 2.6 "Labor Constraints").
Table 2.6 Labor Constraints
| United States | France |
|---|---|
| LC + LW = L | LC∗ + LW∗ = L∗ |
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where L = the labor endowment in the United States (the total number of hours the workforce is willing to provide) |
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When the resource constraint holds with equality, it implies that the resource is fully employed. A more general specification of the model would require only that the sum of labor applied in both industries be less than or equal to the labor endowment. However, the assumptions of the model will guarantee that production uses all available resources, and so we can use the less general specification with the equal sign.
The one factor of production, labor, is assumed to be immobile across countries. Thus labor cannot move from one country to another in search of higher wages. However, labor is assumed to be freely and costlessly mobile between industries within a country. This means that workers working in the one industry can be moved to the other industry without any cost incurred by the firms or the workers. The significance of this assumption is demonstrated in the immobile factor model in Chapter 4 "Factor Mobility and Income Redistribution".
The model assumes that goods can be transported between countries at no cost. This assumption simplifies the exposition of the model. If transport costs are included, it can be shown that the key results of the model may still be obtained.
In describing any model, it is always useful to keep track of which variables are exogenous and which are endogenous. Exogenous variablesA variable whose value is determined external to the model and whose value is known to the agents in the model. In the Ricardian model, the unit labor requirements and the labor endowment are exogenous. are those variables in a model that are determined by processes that are not described within the model itself. When describing and solving a model, exogenous variables are taken as fixed parameters whose values are known. They are variables over which the agents within the model have no control. In the Ricardian model, the parameters (L, aLC, aLW) are exogenous. The corresponding starred variables are exogenous in the other country.
Endogenous variablesA variable whose value is determined as an outcome of, or solution to, the model. In the Ricardian model, the allocation of workers to production, the quantities of the goods produced, and the terms of trade are endogenous. are those variables determined when the model is solved. Thus finding the solution to a model means solving for the values of the endogenous variables. Agents in the model can control or influence the endogenous variables through their actions. In the Ricardian model, the variables (LC, LW, QC, QW) are endogenous. Likewise, the corresponding starred variables are endogenous in the other country.
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