Equilibrium Income and Output Determination in Two Sector Economy

Keynes has identified two agents: the household and business firms in two sector economy. The model assumes that there is no intervention of government and no foreign trade exists.Besides this, the two sector model has a few more assumptions that it satisfies.

Assumptions

i. Prices, wages, and interest rates are constant. 

ii. Output is determined by the total expenditure of the economy.

iii.
Profits earned by the firms are distributed in the form of dividends rather than saving.

State of Equilibrium:Keynes stated that the equilibrium in national income is determined when aggregate demand/expenditure is equal to aggregate supply.

Aggregate Demand/Expenditure

The aggregate demand/expenditure in the two sector economy is the sum total of the consumption made by household sector (C) and investment expenditures made by business firms (I). Symbolically, AE for two sector economy is expressed as:

AE=C+I

The factors that affect household consumption include income and non-income determinants. Generally, household consumption expenditure is affected by the current level of income. The non-income determinants include real interest rates, consumer’s wealth, and consumers’ expectation of future prices and incomes.

Keynes assumed that in the short run, current income is the most important factor that affects household consumption which  can be mathematically expressed as

C= Ca + λ Y

Where, C = Total annual consumption expenditure;

             Ca=Autonomous Consumption

Λ= Marginal propensity to consume (MPC), 0< λ<1;

Y= Total income/output

Investment Expenditure

Investment expenditures are the firms’ expenses occurred during the production of goods and services. These include expenditures on capital goods like plants, equipment, etc. Investments may be both planned or intended or unplanned or unintended.In determining the income equilibrium, investment is assumed to be autonomous. Investments are made based on the firms’ future profitability, regardless of changes in interest rates. Autonomous investment can be expressed as:

I= Ia

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Equilibrium Income and Output: Graphs

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The determination of income/output determination in a two sector economy is illustrated in the figures below:

Figure: Two sector equilibrium with Y= AE

The significance of the 45 line is that it consists of points which are at equal distance from the axes.The vertical line shows aggregate expenditure and the horizontal line is aggregate output.Equilibrium is the point where aggregate expenditure line Y=AE intersects with the 45-degree line. In the figure, the line AE= C+I intersects the 45-degree line at point E where AE=Y and the equilibrium level of output/income is OYe. Any points to the right of E shows excess of supply that exceeds the desired level of expenditure i.e. Y> AE=C+I. Similarly, any point left of E shows excess of demand where AE=C+I

Or, Y= AE

Or, Y= C + I

Substituting C= Ca + λY and I=Ia in Y=C + I, we get,

Y= Ca + λY + Ia

Or, Y = Ca + λY + Ia

Or, Y- λY = Ca + Ia

Or, Y (1-λ) = Ca + Ia

That is, equilibrium income/output,

Thus, the equilibrium income and output (Ye) is equal to the sum of autonomous expenditures (Ca + Ia) times the multiplier 1/ (1 – MPC).

 Adopted from:"Income and Output Determination: Two Sector Economy," in Businesstopia, January 26, 2018, https://www.businesstopia.net/economics/macro/income-output-determination-two-sector-economy.

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