# 4.4: Immobile Factor Model Overview and Assumptions

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Learning Objectives

1. Learn how the immobile factor model differs from the Ricardian model.
2. Learn the assumptions of a standard immobile factor trade model.

## Overview

The immobile factor model highlights the effects of factor immobility between industries within a country when a country moves to free trade. The model is the standard Ricardian model with one variation in its assumptions. Whereas in the Ricardian model, labor can move costlessly between industries, in the immobile factor model, we assume that the cost of moving a factor is prohibitive. This implies that labor, the only factor, remains stuck in its original industry as the country moves from autarky to free trade.

The assumption of labor immobility allows us to assess the short-run impact of movements to free trade where the short run is defined as the period of time when all factors of production are incapable of moving between sectors. The main result of the model is that free trade will cause a redistribution of income such that some workers gain from trade, while others lose from trade.

## Assumptions

The immobile factor model assumptions are identical to the Ricardian model assumptions with one exception. In this model, we assume that $$L_C$$ and $$L_W$$ are exogenous. This means that there is a fixed supply of cheese workers and wine workers. Cheese workers know how to make cheese but cannot be used productively in the wine industry, and wine workers cannot be used productively in the cheese industry. This assumption differs from the Ricardian model, which assumed that labor was freely mobile across industries. In the Ricardian model, a cheese worker who moved to the wine industry would be immediately as productive as a longtime wine worker.

Neither assumption—free and costless mobility nor complete immobility—is entirely realistic. Instead, they represent two extreme situations. The Ricardian assumption can be interpreted as a long-run scenario. Given enough time, all factors can be moved and become productive in other industries. The immobile factor assumption represents an extreme short-run scenario. In the very short run, it is difficult for any factor to be moved and become productive in another industry. By understanding the effects of these two extremes, we can better understand what effects to expect in the real world, characterized by incomplete and variable factor mobility.

What follows is a description of the standard assumptions in the immobile factor model. We assume perfect competition prevails in all markets.

### Number of Countries

The model assumes two countries to simplify the model analysis. Let one country be the United States, the other France. Note that anything related exclusively to France in the model will be marked with an asterisk.

### Number of Goods

The model assumes there are two goods 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.

### Number of Factors

The model assumes there are two factors of production used to produce wine and cheese. Wine production requires wine workers, while cheese production requires cheese workers. Although each of these factors is a kind of labor, they are different types because their productivities differ across industries.

### Consumer Behavior

Factor owners are also the consumers of the goods. We assume the factor owners have a well-defined utility function defined over the two goods. Consumers maximize utility to allocate income between the two goods.

### A General Equilibrium

The immobile factor model is a general equilibrium model. The income earned by the factor is used to purchase the two goods. The industries’ revenue in turn is used to pay for the factor services. The prices of the outputs and the factor are determined such that supply and demand are equalized in all markets simultaneously.

### Demand

We will assume that aggregate demand is homothetic in this model. This implies that the marginal rate of substitution between the two goods is constant along a ray from the origin. We will assume further that aggregate demand is identical in both of the trading countries.Note that this assumption is a technical detail that affects how the trading equilibrium is depicted but is not very important in understanding the main results.

### Supply

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
$$Q_C = \frac{ \bar L_C [hrs]}{a_{LC} [hrs/lb]}$$ $$Q_C^* = \frac{ \bar L_C^*}{a_{LC}^*}$$

where

• $$Q_C$$ = quantity of cheese produced in the United States
• $$\bar L_C$$= fixed 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 production process in France.
Table $$\PageIndex{2}$$: Production of Wine
United States France
$$Q_W = \frac{ \bar L_W [hrs]}{a_{LW} [hrs/gal]}$$ $$Q_W^* = \frac{ \bar L_W^*}{a_{LW}^*}$$

where

• $$Q_W$$ = quantity of wine produced in the United States
• $$\bar L_W$$ = fixed 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 production process in France.

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

key takeaway

• The immobile factor model is a two-country, two-good, two-factor, perfectly competitive general equilibrium model that is identical to the Ricardian model except that labor cannot move across industries.

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 assumption that distinguishes the immobile factor model from the Ricardian model.
2. The term describing the period of time encompassed by the immobile factor model.
3. The firms’ objective in the immobile factor model.
4. The consumers’ objective in the immobile factor model.
5. The term for the entire collection of assumptions made in the immobile factor model.

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