Chapter 4: Specific Factors And Income Distribution
The specific factors model assumes an economy that produce two goods and that can allocate its
labor supply between the two sectors, unlike the Ricardian model the specific factors model allows
for the existence of factors of production besides labor. Whereas labor is a mobile factor that can
move between sectors, these other factors are assumed to be specific. That is, they can be used only
in the production of particular goods.
Imagine an economy that can produce two goods, cloth and food. The country has three factors of
production: labor (L), capital (K), and land (T for terrain). Capital and land are both specific factors
that can be used only in the production of one good. Cloth is produced using capital and labor, and
food is produced using land and labor. The relationship of how much of the factors are used in a
sector is summarized by a production function:
QC =QC ( K , LC ) where Q C is the economy’s output of cloth, K is the economy’s capital stock,
and LC is the labor force employed in cloth.
Q F=Q F (T , LF ) where Q F is the economy’s output of food, T is the economy’s supply of
land, and LF is the labor force devoted to food production.
The labor employed must equal the total labor supply: LC + LF =L
, To analyze the economy’s production possibilities, we need only to ask how the economy’s mix of
output changes as labor is shifted from one sector to the other. This can be done graphically, first by
representing the production functions, and then by putting them together to derive the production
possibility frontier. The slope of Q C ( K , LC ) represents the marginal product of labor, that is, the
addition to output generated by adding one more person hour. If labor input is increased without
increasing capital, there will normally be diminishing returns: Because adding a worker means that
each worker has less capital to work with, each successive increment of labor will add less to
production than the last.
If we shift one person-hour of labor from food to
cloth, however, this extra input will increase output in that sector by the marginal product of labor in
cloth, MPLC . To increase cloth output by one unit, then, we must increase labor input by 1/ MPLC
hours. To increase output of cloth by one unit, then, the economy must reduce output of food by
MPLF / MPLC.
Slopeof production possibilities curve=−MPLF /MPLC
The slope of PP, which measures the opportunity cost of cloth in terms of food – that is, the number
of units of food output that must be sacrificed to increase cloth output by one unit.
The demand for labor in each sector depends on the price of output and the wage rate. If w is the
wage rate of labor, employers will therefore hire workers up to the point where
MPLC × PC =w
MPLF × PF =w
The wage rate must be the same in both sectors because of the assumption that labor is freely
mobile between sectors. The sum of labor demanded in the cloth and food sectors just equals the
total labor supply L.
The specific factors model assumes an economy that produce two goods and that can allocate its
labor supply between the two sectors, unlike the Ricardian model the specific factors model allows
for the existence of factors of production besides labor. Whereas labor is a mobile factor that can
move between sectors, these other factors are assumed to be specific. That is, they can be used only
in the production of particular goods.
Imagine an economy that can produce two goods, cloth and food. The country has three factors of
production: labor (L), capital (K), and land (T for terrain). Capital and land are both specific factors
that can be used only in the production of one good. Cloth is produced using capital and labor, and
food is produced using land and labor. The relationship of how much of the factors are used in a
sector is summarized by a production function:
QC =QC ( K , LC ) where Q C is the economy’s output of cloth, K is the economy’s capital stock,
and LC is the labor force employed in cloth.
Q F=Q F (T , LF ) where Q F is the economy’s output of food, T is the economy’s supply of
land, and LF is the labor force devoted to food production.
The labor employed must equal the total labor supply: LC + LF =L
, To analyze the economy’s production possibilities, we need only to ask how the economy’s mix of
output changes as labor is shifted from one sector to the other. This can be done graphically, first by
representing the production functions, and then by putting them together to derive the production
possibility frontier. The slope of Q C ( K , LC ) represents the marginal product of labor, that is, the
addition to output generated by adding one more person hour. If labor input is increased without
increasing capital, there will normally be diminishing returns: Because adding a worker means that
each worker has less capital to work with, each successive increment of labor will add less to
production than the last.
If we shift one person-hour of labor from food to
cloth, however, this extra input will increase output in that sector by the marginal product of labor in
cloth, MPLC . To increase cloth output by one unit, then, we must increase labor input by 1/ MPLC
hours. To increase output of cloth by one unit, then, the economy must reduce output of food by
MPLF / MPLC.
Slopeof production possibilities curve=−MPLF /MPLC
The slope of PP, which measures the opportunity cost of cloth in terms of food – that is, the number
of units of food output that must be sacrificed to increase cloth output by one unit.
The demand for labor in each sector depends on the price of output and the wage rate. If w is the
wage rate of labor, employers will therefore hire workers up to the point where
MPLC × PC =w
MPLF × PF =w
The wage rate must be the same in both sectors because of the assumption that labor is freely
mobile between sectors. The sum of labor demanded in the cloth and food sectors just equals the
total labor supply L.
