Economics » National Income » Elementary Theory of Income Determination and Equilibrium National Income

# Equilibrium National Income

## Equilibrium National Income

An open economy is represented by the structure equation (model) below:

Y = C + I + G + (X – M)…………………… (11.3)

where C = a + bYd        a > 0; 0 < b < 1…………………… (11.4)

Yd = Y – T [disposable income]………………………………. (11.5)

T = To [Lump-sum tax]………………………………………….. (11.6)

I = Io [Investment Expenditure]…………………………….. (11.7)

G = Go [Government Expenditure]………………………… (11.8)

X = Xo [Export (autonomous)]……………………………….. (11.9)

M= Mo [Import (autonomous)]…………………………….. (11.10)

### Derivation of Equilibrium National Income

Substitute into equation (11.3)

Y = a + bYd + Io + Go + (Xo – Mo)

= a + b (Y – T) + Io +Go + (Xo – Mo)

= a + bY – bTo + Io + Go + (Xo – Mo)

Y – bY = a – bTo + Io +Go + (Xo – Mo)
(1 – b)Y = a – bTo + Io + Go + (Xo – Mo)
Y = $$\cfrac{1}{1-b}$$ [a – bTo + Io +Go + (Xo – Mo)]……………………….. (11.11)
where $$\cfrac{1}{1-b}$$ is the multiplier.

Equation (11.11) gives the equilibrium national income. Note that, at this level, we are concerned with a simple national income model for an open economy. Hence, our assumptions include that tax (T), investment expenditure (I), government expenditure (G), export (X) and import (M) are fixed or given (i.e. they are said to be autonomous).

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