The subject-matter of the theory of income distribution is the study of the determination of the shares of the factors of production in the total output produced in the economy over a given time period.
If, for simplicity, we assume that there are two factors of production, labour and capital, their shares are defined as follows:
[share of labour] = w. L / X
[share of capital] = r. K / X
where w = wage rate
r = rental of capital
L = quantity of labour employed
K = quantity of capital employed
X = value of output produced in the economy.
The factor shares depend on the state of technology which defines the production function, and on the relative factor prices. We saw that the production function defines the technically efficient combinations of factors for the production of various levels of output. These combinations define factor intensities, which are measured by the capital-labour ratio (K/L). The factor intensity in the production of any commodity depends on the substitutability of factors. A measure of the degree of substitution of factors is the elasticity of substitution defined as
σ = % change of K/L / % change of MRTSL.K / d(K/L)/(K/L) = d(MRTS)/(MRTS)
In saw that the choice by a firm of one among all the technically efficient combinations of factors depends on the relative prices of these factors. The equilibrium of the firm is defined by the tangency of isoquants and isocost lines, that is, by equating the slope of the isoquants (MRTSL K) to the slope of the isocost lines (w/r).
MRTSL.k = w/r
To the above determinants of income distribution we must add technological progress. Technical progress usually changes the factor intensity in the production of the various goods. For example, if the technological progress is of the capital-deepening type, there will be some substitution of capital for labour, which will lead to an increase in the share of capital to the total product of the economy.
In summary we may write
There is a strong interrelationship between the three determinants of income distribution, arising from the fact that technology and technical progress affect the factors’ demand and supply which determine their prices.