# 2.3: Ricardian Model Assumptions

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Learning Objectives

1. Learn the structure and assumptions that describe the Ricardian model of comparative advantage.

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

Perfect competition in all markets means that the following conditions are assumed to hold.

1. Many firms produce output in each industry such that each firm is too small for its output decisions to affect the market price. This implies that when choosing output to maximize profit, each firm takes the price as given or exogenous.
2. Firms choose output to maximize profit. The rule used by perfectly competitive firms is to choose the output level that equalizes the price ($$P$$) with the marginal cost ($$MC$$). That is, set $$P = MC$$.
3. Output is homogeneous across all firms. This means that goods are identical in all their characteristics such that a consumer would find products from different firms indistinguishable. We could also say that goods from different firms are perfect substitutes for all consumers.
4. There is free entry and exit of firms in response to profits. Positive profit sends a signal to the rest of the economy and new firms enter the industry. Negative profit (losses) leads existing firms to exit, one by one, out of the industry. As a result, in the long run economic profit is driven to zero in the industry.
5. Information is perfect. For example, all firms have the necessary information to maximize profit and to identify the positive profit and negative profit industries.

## Two Countries

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

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.

## One Factor of Production

Labor is the one factor of production used to produce each of the goods. The factor is homogeneous and can freely move between industries.

## Utility Maximization and Demand

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 $$U = C_{C}C_{W}$$, where $$C_C$$ and $$C_W$$ 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.

## General Equilibrium

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.

## Production

The production functions in Table $$\PageIndex{1}$$ and Table $$\PageIndex{2}$$ represent industry production, not firm production. The industry consists of many small firms in light of the assumption of perfect competition.

Table $$\PageIndex{1}$$: Production of Cheese
United States France
$$Q_{C} = \frac{L_C}{a_{LC}} \frac{[hrs]}{[hrs / lbs]}$$ $$Q_{C}^{*} = \frac{L_C^*}{a_{LC}^{*}}$$

where

• $$Q_C$$ = quantity of cheese produced in the United States
• $$L_C$$ = amount of labor applied to cheese production in the United States
• $$a_{LC}$$ = 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.
Table $$\PageIndex{2}$$: Production of Wine
United States France

$$Q_{W} = \frac{L_W}{a_{LW}} \frac{[hrs]}{[hrs / gal]}$$

$$Q_{W}^{*} = \frac{L_W^*}{a_{LW}^{*}}$$

where

• $$Q_W$$ = quantity of wine produced in the United States
• $$L_W$$ = amount of labor applied to wine production in the United States
• $$a_{LW}$$ = 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.

The unit labor requirements define the technology of production in two countries. Differences in these labor costs across countries represent differences in technology.

## Resource Constraint

The resource constraint in this model is also a labor constraint since labor is the only factor of production (see Table $$\PageIndex{3}$$).

Table $$\PageIndex{3}$$: Labor Constraints
United States France
$$L_C + L_W = L$$ $$L_C^* + L_W^* = L^*$$

where

• L = the labor endowment in the United States (the total number of hours the workforce is willing to provide)

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.

## Factor Mobility

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.

## Transportation Costs

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.

## Exogenous and Endogenous Variables

In describing any model, it is always useful to keep track of which variables are exogenous and which are endogenous. Exogenous variables 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 ($$L, a_{LC}, a_{LW}$$) are exogenous. The corresponding starred variables are exogenous in the other country.

Endogenous variables 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 ($$L_C, L_W, Q_C, Q_W$$) are endogenous. Likewise, the corresponding starred variables are endogenous in the other country.

KEY TAKEAWAYS

• The Ricardian model incorporates the standard assumptions of perfect competition.
• The simple Ricardian model assumes two countries producing two goods and using one factor of production.
• The goods are assumed to be identical, or homogeneous, within and across countries.
• The workers are assumed to be identical in the productive capacities within, but not across, countries.
• Workers can move freely and costlessly between industries but cannot move to another country.

Exercise $$\PageIndex{1}$$

1. Jeopardy Questions. As in the popular television game show, you are given an answer to a question and you must respond with the question. For example, if the answer is “a tax on imports,” then the correct question is “What is a tariff?”
1. The type of variable whose value is determined as a part of the solution to the model.
2. The type of variable whose value is determined outside the model and is presumed to be known by the model participants.
3. The rule used by perfectly competitive firms to determine the profit-maximizing level of output.
4. What a perfectly competitive firm may do if it experiences substantially negative profit.
5. The kind of equilibrium in a model in which multiple markets satisfy the equality of supply and demand simultaneously.
2. Suppose that the unit labor requirements for wine and cheese are $$a_{LC}$$ = 6 hrs./lb. and $$a_{LW}$$ = 4 hrs./gal., respectively, and that labor hours applied to cheese and wine production are 60 and 80, respectively. What is total output of cheese and wine?
3. Suppose that the unit labor requirements for wine and cheese are $$a_{LC}$$ = 3 hrs./lb. and $$a_{LW}$$ = 2 hrs./gal., respectively, and that labor hours applied to cheese and wine production are 60 and 80, respectively. What would the total output of wine be if all the labor hours were shifted to produce wine?

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