Distribution Theories

1. Income Distribution Theory
Course
a. Kelecki’s theory of distribution
b. Kaldor’s distribution theory
c. Ricardian or Classical theory of Income Distribution
Pujan Adhikari

2. Distribution Theory
• Macro theory of the Distribution Deals with how shares of the output or income
are determine.
• The systematic attempt to account for the sharing of the
national income among the owners of the factors of production. Theories have
studied how the costs of these factors and the size of their return—rent, wages,
and profits—are determined.
• Income distribution theory is concerned with the analysis of the determination
of relative shares of the factors of production in the total national income.

3. Kelicki’s “Degree of monopoly” theory of Distribution
This theory assumed that national income into wages and profit and the share
depends upon the degree of monopoly in the economy.
Kelecki has used A.P. learner’s microeconomic measurement of monopoly.
𝜇 =
𝐴𝑅 − 𝑀𝐶
𝐴𝑅
Where, 𝜇 = 𝑑𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 𝑚𝑜𝑛𝑜𝑝𝑙𝑜𝑦
𝐴𝑅 = 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑒𝑣𝑒𝑛𝑢𝑒 𝑜𝑟 𝑝𝑟𝑖𝑐𝑒
𝑀𝐶 = 𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑐𝑜𝑠𝑡(𝑚)
𝜇 =
𝑝 − 𝑚
𝑝
Aggregation gives the macroeconomic level of monopoly.

4. Assumptions
• The national income/ output is distributed into two shares. Wages and
profits
• Marginal cost includes the cost of labor and the cost of raw materials per unit
of output.
• Cost of labor includes only the wages of manual labor.
• The salaries of white color workers are included in the income or profits of
capitalist class.
• (p-m) is the gross capitalist profit per unit of output.
• Economy is in under full employment. i.e. existence of excess capacity.
• SMC equals SAC on manual labor and raw materials to a certain point
corresponding to “practical capacity’.
•

5. Explanation of model
𝝁 =
𝒑−𝒎
𝒑
………………micro degree of monopoly
𝑆𝑀𝐶 = 𝑆𝐴𝐶 = 𝑎 or, 𝝁 =
𝒑−𝒂
𝒑
𝑝𝜇 = 𝑝 − 𝑎 ……… Gross capitalist profit per unit of output of
employer.
For macroeconomic computation
If x is the total output of a firm, Total gross capitalist profit of the
employer = 𝒙𝒑𝝁 = 𝒙(𝒑 − 𝒂)
For aggregate economy, 𝒙𝒑𝝁 = 𝒙( 𝒑 − 𝒂)

6. 𝑥𝑝 is the total value of the output of all the goods produced and which is aggregate
turnover(T) of the economy.
𝒙𝒑𝝁
𝒙𝒑
=
𝒙(𝒑−𝒂)
𝒙𝒑
or,
𝒙𝒑𝝁
𝒙𝒑
=
𝒙(𝒑−𝒂)
𝑻
Weighted average of micro degree of monopoly, 𝒖 =
𝒙(𝒑−𝒂)
𝒙𝒑
=
𝑔𝑟𝑜𝑠𝑠 𝑐𝑎𝑝𝑎𝑖𝑡𝑎𝑙𝑖𝑠𝑡 𝑝𝑟𝑜𝑓𝑖𝑡
𝑎𝑔𝑔𝑟𝑒𝑔𝑎𝑡𝑒 𝑡𝑢𝑟𝑛𝑜𝑣𝑒𝑟
• Interpretation
For given level of cost of raw materials, the increase in average degree of monopoly
power 𝑢 will cause the share of gross capitalist profit or income to rise at the expense of
labor share.
This shows the distribution of national income is determined by the degree of monopoly.

7. Labor’s Share in National income and degree of monopoly
Kelecki showed the dependence of labor’s share in national income on
macro degree of monopoly in the economy.
𝒖 =
𝒙(𝒑−𝒂)
𝒙𝒑
, Substituting 𝐴 − 𝑊 for 𝑥( 𝑝 − 𝑎), where, A =
national Income , W = total wage bill in the economy
𝑢 =
𝐴−𝑊
𝑇
⟹ 𝑢.
𝑇
𝑊
=
𝐴−𝑊
𝑇
𝑇
𝑊
⟹ 𝑢.
𝑇
𝑊
=
𝐴
𝑊
− 1 ⟹ 𝑢.
𝑇
𝑊
+ 1 =
𝐴
𝑊
1
𝑢.
𝑇
𝑊
+1
=
𝑊
𝐴
Relative share of wages in the national income

8. Interpretation
1
𝑢.
𝑇
𝑊
+ 1
=
𝑊
𝐴
• The relative share of wages in the national income is inversely related to the
degree of monopoly 𝑢 and
𝑇
𝑊
.
• Rise in the degree of monopoly reduces the labor’s share in national income.
• As degree of monopoly increases ,
𝑇
𝑊
is also increased by a rise in the degree of
monopoly since this raises the price in relation to wages.
• Also,
𝑇
𝑊
can increases with the increase in the cost of raw materials in relation to
wage cost. This also reduced the share of labor in national income.

9. • Constancy of Labor’s share in National income
Case 1: in the case of capitalist countries
• Many empirical evidence has revealed that labor's share in national income has
remained more or less constant in may capitalist countries. He argues that an increase
in the concentration of capital in few hands increases the monopoly power in the
western countries. It reduces the share of labor in national income(W/A).
But these capitalists countries have been exploiting their colonial countries and
getting cheaper raw material from them. This effect reduces the T/W and increases W/A ,
so that they have been able to maintain constant share of labor in the national income. In
the other words, the effect of increase in macro degree of monopoly is offset by reducing
the T/W.
Case2: In the case of Business Cycle
• Kelecki has been able to explain the constancy of labor's share in national income even
during the course of business cycle. At the boom period, monopoly power will decline
due to the entrance of new firms.
But the prices of raw materials increases. This keeps W/A more or less constant.
Similar, during recession, the monopoly power of increases, but the cost of raw materials
is declining. This keeps the share of labor in national income constant.

10. Criticisms:
• Kelecki contributes only the degree of monopoly as the only determinant of
the level profit and distributing shares. However, in the words of Jan Pen,
the marginal costs differ in accordance with efficiency of firms and not this
differences efficiency is due to the existence of monopolistic situations.
Factors like shortage of capital, existence of cost differentials between firms
etc. also affects the level of profit and interest.
• Kelecki has ignored the power of labor union and has emphasized only the
power of the capitalists. The similar power exercise can be done as that of
capitalists.

11. Kaldor’s Theory of Income Distribution
According to Kaldor, the distribution of national income goes into shares , wages
and profits. Kaldor has called his theory as the Keynesian theory of distribution as
this theory employed Keynes’ theoretical framework.
Assumption
• A state of full employment is prevails in the economy so that national output is
given.
• National income is divided into two broad categories : wages and profit
𝑌 = 𝑤 + 𝑝
• The wages consists not only the cost of manual labor but salaries as well.
• Profits comprises the income of property owners. Profits include rents, interest
and dividends
• The marginal propensity to save of wage- earners(𝑠 𝑤) is smaller than the
marginal propensity to save of profit earner (𝑠 𝑝) and they are constant.

12. Explanation
Algebraic expression of Kaldorian theory
𝑌 = 𝑤 + 𝑝 … … 𝑖
( 𝑡𝑜𝑡𝑎𝑙 𝑖𝑛𝑐𝑜𝑚𝑒 𝑖𝑠 𝑠𝑢𝑚 𝑜𝑓 𝑎𝑔𝑔𝑟𝑒𝑔𝑎𝑡𝑒 𝑤𝑎𝑔𝑒 𝑎𝑛𝑑 𝑎𝑔𝑔𝑟𝑒𝑔𝑎𝑡𝑒 𝑝𝑟𝑜𝑓𝑖𝑡𝑠).
Equilibrium condition of Keynesian identity is,
𝐼 = 𝑆 … (ii) total saving + total investment of the economy
Total saving in the economy is the sum of aggregate savings out of wages and
aggregate savings out of profits,
𝑆 = 𝑠 𝑤 + 𝑠 𝑝 … … . (𝑖𝑖𝑖)
If 𝒔 𝒘 𝒂𝒏𝒅 𝒔 𝒑represent the average propensity to save of the wage earners
and the profit earners respectively.
𝑆 𝑤 = 𝑠 𝑤 × 𝑊 𝑎𝑛𝑑 𝑆𝑝 = 𝑠 𝑃 × 𝑃

13. 𝐼 = 𝑆 𝑤 + 𝑆 𝑝
𝐼 = 𝑠 𝑤 × 𝑊 + 𝑠 𝑃 × 𝑃 … . (𝑖𝑣)
𝐼 = 𝑠 𝑤 × 𝑌 − 𝑃 + 𝑠 𝑃 × 𝑃 ∵ 𝑊 = 𝑌 − 𝑃
𝐼 = 𝑝 𝑠 𝑃 − 𝑠 𝑤 + 𝑠 𝑤𝑌
𝐼
𝑌
=
𝑝
𝑌
𝑠 𝑃 − 𝑠 𝑤 + 𝑠 𝑤
𝑝
𝑌
𝑠 𝑃 − 𝑠 𝑤 =
𝐼
𝑌
− 𝑠 𝑤
𝒑
𝒀
=
𝟏
𝒔 𝑷−𝒔 𝒘
𝑰
𝒀
−
𝟏
𝒔 𝑷−𝒔 𝒘
𝒔 𝒘
𝒑𝒓𝒐𝒇𝒊𝒕
𝑵𝒂𝒕𝒊𝒐𝒏𝒂𝒍 𝒊𝒏𝒄𝒐𝒎𝒆
=
𝟏
𝒔 𝑷−𝒔 𝒘
𝑰
𝒀
−
𝟏
𝒔 𝑷−𝒔 𝒘
𝒔𝒘
..mathematical expression of Kaldor’s model.

14. 𝑝𝑟𝑜𝑓𝑖𝑡
𝑁𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑖𝑛𝑐𝑜𝑚𝑒
=
1
𝑠𝑃−𝑠𝑤
𝐼
𝑌
−
1
𝑠𝑃−𝑠𝑤
𝑠𝑤
Interpretation
• Given the saving propensities of the capitalists and the wage earners , the ratio
of profits to national income (P/Y) depends on the ratio of investment to
national income (I/Y).
𝑰
𝒀
↑→
𝑷
𝒀
• This model holds good only if 𝒔𝑷 > 𝒔𝒘, that is saving propensity of he capitalists
exceeds that of wage earners. The stability condition will be achieved.
• 𝑰𝒇 𝒔𝑷 < 𝒔𝒘, the system will be unstable. WHY?

15. 𝒔𝑷 < 𝒔𝒘,
𝑷𝒓𝒊𝒄𝒆 ↓→ 𝑫𝒆𝒎𝒂𝒏𝒅 ↓→ 𝒇𝒖𝒓𝒕𝒉𝒆𝒓 𝒑𝒓𝒊𝒄𝒆 ↓
• The degree of the stability of the system depends on the difference of the
marginal propensities,
1
𝑠𝑃−𝑠𝑤
, which is called “Coefficient of Sensitivity of
Income Distribution”.
• If the 𝑠𝑃 − 𝑠𝑤 is small, the coefficients will be large and small change in
𝑰
𝒀
will
cause relatively large changes in income distributions
𝑷
𝒀
.

16. Recardian or Classical Theory of Income Distribution
Assumptions
• The assumptions is divided into two sector. a. Agriculture sector b. Industrial
sector
• Ricardo divides the total income into three shares. Wages, Rents, Profits
• The law of diminishing returns operates in the agriculture sector.
• Malthusian law of population is also assumed to be applicable. Change in
population depend in whether actual wage is greater or smaller than
subsistence wage.
• Supply of land is inelastic or fixed.
• Profit is necessary incentive for capital accumulation.
• Marginal principle explains the determination of rent.
• Surplus principle explains the determination of wages.

17. Determination of wage rate
• The level of employment is determined by the wage fund but not by the wage
rate and the marginal productivity. The basic proposition of this theory is that at
any time there is a given stock of fund(wheat, wage fund) which determine the
wage rate.
• In the short-run the actual wage rate is wage fund divided
By the no. of workers and wage may be
Greater or less than subsistence level.
• 𝐴𝑐𝑡𝑢𝑎𝑙 𝑤𝑎𝑔𝑒 𝑟𝑎𝑡𝑒 =
𝑤𝑎𝑔𝑒 𝑓𝑢𝑛𝑑
𝑛𝑜.𝑜𝑓 𝑙𝑎𝑏𝑜𝑟
• In the long run, the wage rate fall down to the subsistence level.
• In fig, wage rate is determined by wage fund. Wf curve is a rectangular
hyperbola. The number of workers determines the marginal product of labor.
𝑤
𝑤0
𝑁
𝑁0
𝑤𝑎𝑔𝑒 𝑏𝑖𝑙𝑙
𝑤f

18. Rent
Rent is the difference between the product of labor on the marginal land and
product on the average land or the difference between the average and marginal
labor productivity.
In figure, vertical difference between 𝐴𝑃𝐿 and 𝑀𝑃𝐿 at the 𝑁0employment level is
the rent per labor.
Total output=BC𝑁0O
BCDA represents total rent in the economy.
𝑅
𝑀𝑃𝐿 𝐴𝑃𝐿
𝑤
𝑤0
𝑁
𝑁0
𝑤f
𝑝
𝐴
𝐵
𝐶
𝐷
𝐸
𝑂

19. Profit
Profits are the surplus of total product over wages and rents.
Profits are income left after the payments of wages and rent.
Profit= difference between marginal productivity of labor(MP) and actual wage
rate.
𝑇𝑜𝑡𝑎𝑙 𝑝𝑟𝑜 𝑓𝑖𝑡 = 𝐴𝐷𝐸𝑊0
𝑅
𝑀𝑃𝐿
𝐴𝑃𝐿
𝑤
𝑤0
𝑁
𝑁0
𝑤f
𝑝
𝐴
𝐵
𝐶
𝐷
𝐸
𝑂

20. Impact of growth on Distribution
Agriculture is taken as foundation of economy. Growth in agriculture induced by
capital accumulation affects the relative shares of rents, wages and profits.
Capital accumulation production wage fund labor demand wage rate( above
the subsistence level) (this encourages the well off labor to marry and breads.)
Population demand for goods and services employment of labor and cultivation
of inferior land price of goods and services

21. Impact
1. As the demand for agricultural production increases the price rises. As the
population increases inferior grades land are cultivated to meet the increasing
demand. Rents on the superior grades of land rise and absorb a greater share
of the output produced on these land. This reduces the share of capital and
profit.
2. profits decline and wages tend to fall to the subsistence level.
3. This process of rising rents and declining profits continues till the output from
the marginal land just covers the subsistence wage of the labor at which profit
become zero and stationary state arises.
4. A fall in the corn rate of profit in agriculture will decline money rate of profit in
industrial sector. A rise in price of agriculture product will lead to raise the cost
of subsistence level in industrial sector.