# expression for equilibrium national income

It implies that ΔY is 1/1-b times of ΔI and 1/I-b is termed as multiplier (m).In mathematical terms, the multiplier is defined as the ratio of change in national income that occurs due to change in investment. In such a case, the rate of multiplier would be one. meaning export less import (net export) ; however if the external sector is added to the Keynesian equation the resultant equation is the open economy using Keynesian model.Which variables differentiate a closed economy from an open economy under the National income determination?An open economy is represented by the equations belowY = C + I + G + X – M                                                (1.1)Equation (1.4) explains tax revenue. Therefore, consumption (C) acts as the major determinant or function of income (Y).Where, a = constant (representing consumption when income is zero)By substituting the value of consumption in the equation of AD, we get:In Table-1, the column of income represents the aggregate supply and the column of aggregate demand represents expenditure.

$\begin{array}{lcl}\text{C}&=&\20+0.9\left(\text{Y}-\text{T}\right)\\&=&\20+0.9\left(\300-\60\right)\\&=&\236\end{array}$$\begin{array}{lr}\text{After-tax income}&\240\\\text{Imports of 0.2 or 20% of Y}-\text{T}&\times0.2\\\text{Imports}&\48\end{array}$$\begin{array}{rcl}\text{Y}&=&\text{AE}\\&=&\text{C}+\text{I}+\text{G}+\text{X}-\text{M}\\&=&\20+0.9\left(\text{Y}-\text{T}\right)+\70+\80+\50-0.2\left(\text{Y}-\text{T}\right)\\&=&\220+0.0\left(\text{Y}-\text{T}\right)-0.2\left(\text{Y}-\text{T}\right)\end{array}$Since T is 0.2 of national income, substitute T with 0.2 Y so that:$\begin{array}{rcl}\text{Y}&=&\220+0.9\left(\text{Y}-0.2\text{Y}\right)-0.2\left(\text{Y}-0.2\text{Y}\right)\\&=&\220+0.9\text{Y}-0.18\text{Y}-0.2\text{Y}+0.04\text{Y}\\&=&\220+0.56\text{Y}\end{array}$$\begin{array}{rcl}\text{Y}&=&\220+0.56\text{Y}\\\text{Y}-0.56\text{Y}&=&\220\\0.44\text{Y}&=&\220\\\frac{0.44\text{Y}}{0.44}&=&\frac{\200}{0.44}\\\text{Y}&=&\500\end{array}$ The Keynesian AS curve is drawn based on an assumption that total income is equal to total expenditure. For example, in Figure-6, the shift in the equilibrium position from EIn case of static multiplier, when the equilibrium position shifts from one point to another, the aggregate MPC does not show any change.

If there is any type of increase or decrease in the aggregate supply/demand, then they themselves fluctuate in a manner, so that they reach back at the equilibrium point.Saving-investment approach refers to the method in which the saving (S) and investment (I) are used for the determination of national income. Here 1/1 – b is called the multiplier. 100 then the aggregate demand is Rs.