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Specific Factors and

Income Distribution

2.2. The Ricardo-Viner Model: the specific-factors model. International Economics - Alejandro C. García Cintado

1

The specific factors model allows trade to affect income distribution.

Assumptions of the model:

o Two goods, cloth and food. o Three factors of production: labor ( L ), capital ( K ) and land ( T for terrain). o Perfect competition prevails in all markets.

The Specific Factors Model

How much of each good does the economy produce? The production function for cloth gives the quantity of cloth that can be produced given any input of capital and labor: QC = QC ( K , L (^) C ) (4-1)

o QC is the output of cloth o K is the capital stock o LC is the labor force employed in cloth

The Specific Factors Model

(cont.)

The production function for food gives the quantity of food that can be produced given any input of land and labor:

QF = QF ( T , L (^) F ) (4-2)

o QF is the output of food o T is the supply of land o LF is the labor force employed in food

The Specific Factors Model

(cont.)

Fig. 4-1: The Production Function

for Cloth

The shape of the production function reflects the law of diminishing marginal returns. o Adding one worker to the production process (without increasing the amount of capital) means that each worker has less capital to work with. o Therefore, each additional unit of labor adds less output than the last.

Figure 4-2 shows the marginal product of labor, which is the increase in output that corresponds to an extra unit of labor.

Production Possibilities (cont.)

For the economy as a whole, the total labor employed in cloth and food must equal the total labor supply:

LC + LF = L (4-3)

Use these equations to derive the production possibilities frontier of the economy.

Production Possibilities (cont.)

Production Possibilities (cont.)

Use a four-quadrant diagram to construct production possibilities frontier in Figure 4-3.

o Lower left quadrant indicates the allocation of labor. o Lower right quadrant shows the production function for cloth from Figure 4-1. o Upper left quadrant shows the corresponding production function for food. o Upper right quadrant indicates the combinations of cloth and food that can be produced.

Production Possibilities

(cont.)

Why is the production possibilities frontier curved? o Diminishing returns to labor in each sector cause the opportunity cost to rise when an economy produces more of a good. o Opportunity cost of cloth in terms of food is the slope of the production possibilities frontier – the slope becomes steeper as an economy produces more cloth.

Production Possibilities (cont.)

Opportunity cost of producing one more yard of cloth is MPL (^) F / MPLC pounds of food. o To produce one more yard of cloth, you need 1/ MPLC hours of labor. o To free up one hour of labor, you must reduce output of food by MPL (^) F pounds. o To produce less food and more cloth, employ less in food and more in cloth. o The marginal product of labor in food rises and the marginal product of labor in cloth falls, so MPL (^) F / MPLC rises.

The demand curve for labor in the cloth sector:

MPL (^) C x PC = w (4-4)

o The wage equals the value of the marginal product of labor in manufacturing.

The demand curve for labor in the food sector:

MPL (^) F x PF = w (4-5)

o The wage equals the value of the marginal product of labor in food.

Prices, Wages, and Labor Allocation

(cont.)

Figure 4-4 represents labor demand in the two sectors. The demand for labor in the cloth sector is MPLC from Figure 4-2 multiplied by PC. The demand for labor in the food sector is measured from the right. The horizontal axis represents the total labor supply L.

Prices, Wages, and Labor

Allocation (cont.)

Fig. 4-4: The Allocation of Labor

At the production point, the production possibility frontier must be tangent to a line whose slope is minus the price of cloth divided by that of food. Relationship between relative prices and output:

• MPLF / MPLC = - P (^) C / P (^) F (4-6)

Prices, Wages, and Labor

Allocation

(cont.)