for Economics.

1. IS curve:
Introduction:
It was discussed earlier that according to J.M.Keynes level of NI is determined where S=I. Keeping in view
this idea, Hicks in 1937 in his article “Classicals and Mr. J.M.Keynes” presented the concept of IS curve.
According to the rate of interest. In other words Hicks established relationship between Y and I where S=I.
accordingly it is also know as investment saving curve.
Definitionof the IS curve:
IS curve is a curve which shows different combinations of rate of interest (i) and level of NI (Y) where savings
(S) are equal to investment (I).
Assumptions of the IS curve:
To derive IS curve we assume the following:
1) Two sector economy where government is excluded.
2) Y=C+I
3) C=Co+CY
4) I=Io-Vi
5) S=f (Y)
6) I=f (i)
7) S= -So+SY
Firstly IS curve is derived mathematically and numerically. Then a schedule is constructed and finally
IS curve will be derived with the help of diagrams
Y=C+I
Putting the value of C and I (assumed in assumptions)
Y= Co+CY+ Io-Vi
Solving for Y:
Y-CY = Co+Io-Vi  Y(1-c) = Co+Io-Vi
IS equation:
Y=Co+Io-Vi  Y= _I_ Co+Io-Vi
1-c 1-c
We assume the following data to get some specific IS equations:
1) C=100+0.05Y
2) I=100-10i
3) Co>0
4) Io>0
5) C<1
6) V>0
Putting them in the IS equation:
Y=__1__ 100+100-10i
1-0.5
Y= _1_ 200-10i  Y= 200-10i = 200-10i 10
0.5 5/10 5
Or Y = 400-20i  IS equation.
Now assuming different interest rates we get different values if Y where I=S.
i Y S=I

2. Taking i=5%, we have Y=400-20i  400-20 _5_ = 399.
100
C=100+0.5(399)  100+199.5 = 299.5.
S=Y-C=399-299.5 =99.5.
I=100-10i=100-10 _5_ = 100-0.5 = 99.5.
100
Thus we have
The above schedule has conformed that IS curve shows the pairs of rate of interest and Y where S=I. now with the help
of figure we construct the IS curve.
In part (1) of this fig we have shown S=F (Y). As Y , S this means that saving schedule is having positive slop. In
part (2) of this fig we have shown investment function I=f (i). This curve slops downwards showing as rate of interest
falls, investment will increases. Every point on part (3) of the fig shows the quality between saving and investments. In
part (4) of the fig we have derived IS curve. As the point K shows the combination of Oi3 (rate of interest) and OY1 (NI).
At Oi3 rate of interest, investment is OI1 (A) while at OY1 NI the savings are OS1 shown by the point G. Both savings
and investments are equal at D.
The point R shows the combination of Oi2 rate of interest and OY2NI. At Oi2 rate of interest, investment is OI2--shown
by point B. at OY2 NI savings are OS2--shown by point H. both savings and investments are equal at E.
I Y S I
5% 399 99.5 99.5

3. The point T shows the combination of Oi rate f interest and OY3 NI. At such interest rate investment is OI3 while at OY3
NI, savings are OS3---shown by point L. both investment and savings are equal at F.
Thus by joining the point K,R,T---we get IS curve which shows relationship between Interest rate and NI.
As we told earlier that IS curve represents equilibrium in good market. Accordingly there operates a mechanism through
change in the interest rate which brings equality between savings and investments. We take a point off the IS curve like Z
where rate of interest is lower. In such situation I > S – shown by point N. the increase in investment will lead to increase
NI through multiplier effect. When NI increases savings will also increase – shown by H. ultimately the equilibrium in
goos market takes place at R. hence lower i results in increases investment – increased income and increased savings. At
any point off the IS curve like U where i remains same but level of NI has gone up to OY2. Because of increased levelof
NI the savings level rises to OS2 (point H). in this situation S > I as show by point J in (3). Because of increased savings
the rate of interest will decreases. As a result investment will increases from OI1 to OI2. Through all this process we
reach the point R on IS curve and point E where S2 = I2. All this shows that market forces operat in such a way that they
bring equilibrium in goods market.
The steepness of the IS curve depends upon the amount of investmet increases with the given reduction in i. secondly on
the magnitude of investment multiplier.