Question

Describe how equilibrium real GDP is established in the Keynesian model

Short answer

The expression to maintain the equilibrium in the economy is given as : $\mathrm{Y}=\frac{1}{(1-\beta )}[\alpha +{\mathrm{I}}^{\text{'}}+{\mathrm{G}}^{\text{'}}+N\text{'}X.$

The diagram is given as :

Step-by-step solution

Introduction

The main purpose of the Keynesian model is to establish the relationship between the income and expenditure in an economy. The basic constituents are given as consumption expenditure, the investments of the consumer, the governmental expenditures and the net expenditure on the export-import of the economy.

Explain Consumption Expenditure

Let us describe the different aspects of the development of equilibrium real GDP in the Keynesian model.

The Consumption Expenditure :

The main expression for the consumption is given as :

$C=\alpha +\beta Y$

Here in the above expression,

$\alpha$is defined as Autonomous Consumption

$\beta$is defined as the Marginal Propensity to Consume and

$Y$is defined as Disposable Income

Explain Investment Expenditure

The Investment Expenditure :

Investment Expenditure is defined as the expense that every firm in an economy bears for investing in the consumers and also on the goods in an economy.

The expression of investment is given as : $\mathrm{I}={\mathrm{I}}^{\text{'}}$

Explain Governmental Expenditure

The Governmental Expenditure is defined as the expenditure that the government needs to bear for the public and other projects occurring in an economy.

The expression is given as :

$\mathrm{G}=G\text{'}$

Explain the net export - import

The Net Export - Import is defined as the expenditure that happens because of the net export or import in an economy.

The expression is given as :

$NX=EX-IM.$

Develop the aggregate expression

The final expression for the expression is given as :

$\mathrm{Y}=\mathrm{C}+\mathrm{I}+\mathrm{G}+\mathrm{NX}$

Now,

the final expression will be coming as : $AE=\alpha +\beta Y+{\mathrm{I}}^{\text{'}}+{\mathrm{G}}^{\text{'}}+\mathrm{NX}.$

Now as we know that from the expression the outcome or as we can say the income will be similar to the overall expenditure, we can write the equation as :

$Y=AE$

So,

$\mathrm{Y}=\alpha +\beta \mathrm{Y}+{\mathrm{I}}^{\text{'}}+G^{\text{'}}+\mathrm{NX}.$

Solve the variable

The expression we obtain for the variable is given as :

$\mathrm{Y}=\frac{1}{(1-\beta )}[\alpha +\mathrm{I}+\mathrm{G}+\mathrm{NX}\text{.}$
Where, $\frac{1}{(1-\beta )}$Multiplier, it is the factor by which the return deriving from an expenditure exceeds the expenditure itself.

The graph can be drawn as :