Question

Starting with the Keynesian cross, explain how to derive the IS curve

Answer 1

The idea behind Keynesian cross is that level of planned expenditure in the economy which is the amount consumers (households), firms, and government plan to spend on goods and services as per their requirements. . When this planned expenditure is higher than firms producing goods expected, then will start depleting their inventory stocks of goods, and this will stimulate/Increase more production, then they will start hiring more workers and produce more, so income will rise. When the planned expenditure is lower than the firms producing goods expected, then they start building up their inventory stocks with unsold goods, which will cause them to step back on production, lay workers off, and income will fall.

In the above equation, C has been replaced by its components, a (autonomous consumpton), and b (marginal propensity to consume). The Keynesian Cross takes I and G and T to be exogenous, they are fixed amounts when you draw the line of planned expenditure (demand), if you change them you have to shift the whole line up or down.We can express this by expressing the closed economy Keynesian model of AD in terms of ‘demand’ which we will call Z.

And we know that there is a Inverse relation ship between Real Interest rates and Planned Investments.

1. If Real Interest rates went up,then the Planned Investment went down
2. If Real Interest rates went down,Planned Investments went up

Let us a have a basic Keynesian Cross

Planned Expenditure=Y^p=C(Y-T)+I^p(r)+G+NX

where C=Aggregate Consumption

Y-T is Disposable Income=Aggregate Income-Aggregate Taxes

I^p=Planned Investment , a function of real Interest rate

G=Government Expenditures

NX=Net Exportslet as assume if Interest rate changes from r1 to r2 and r2<r1 then we know that Planned Investment will increase.it can be shown as under

Here if Interest rate changes then the Planned Investment changes that is Interest rate decreased and in accordance Planned Investment Increased and resulting in the rise in shift of curve

And we can say clearly that if Interest rate is decreased then Planned Investment increases along with Equilibrium GDP and vice versa

Now with the above logic we can have the Investment Savings (IS) Curve

Now here r = Interest Rate and Y=income.

as we came to know that if rates of interest increases then investment decreases results in sapping out GDP and vice-versa