The document provides an overview of the IS-LM model, which explains how the goods market and money market reach equilibrium in an economy. It defines the IS curve as the locus of interest rate-income combinations where investment equals savings. The LM curve similarly shows combinations where money demand equals supply. The intersection of the IS and LM curves indicates the general equilibrium point where both markets clear simultaneously. The summary analyzes how shifts in fiscal or monetary policy can cause the IS and/or LM curves to shift, changing the equilibrium interest rate and level of income in the economy.

1. General Equilibrium of Product
and money market
(IS LM Model)
By: L.R. Lohani

2. Introduction
• The IS-LM model was developed by J.R. Hicks
and A. Hansen. The IS-LM model explains how
Product market (goods market or Real market)
and Money market attain equilibrium in an
economy. This model describes the
interdependence between real sector and
monetary sector. It is also known as the
General equilibrium theory.

3. Concept of IS curve
• The concept of IS curve is developed by J.R.
Hicks in order to explain the product market
equilibrium. In the word IS, ‘I’ refers to the
Investment and ‘S’ refers to the saving.
• IS curve is the locus of various combinations
of rate of interest (r) and level of income (Y)
along which there is equality between I and S
(i.e. I=S) such that product market
equilibrium.

4. Assumptions
1) Investment is an inverse function of ‘r’,
i.e. I= f(r), f’<0
2) Saving is positive function of ‘Y’,
i.e. S=f(Y), f’>0
3) The product market attains equilibrium when S=I
Mathematical Derivation
According to Keynes,
AD= C+I ..........(i)
AS= C+S...........(ii)
The economy enjoys equilibrium when AD=AS
i.e. C+I=C+S
I=S...........(iii)

5. As we know,
S= -a+ (1-b)Y ............(iv)
Where,
-a= autonomous dissaving
1-b= MPS (marginal propensity to save)
Y= level of income
Similarly, Investment function is the combination of
autonomous investment and induced investment
i.e. I= Ia-i.r ..............(v)
Where, Ia= autonomous investment
i= marginal propensity to invest (MPI)
r= rate of interest

6. Product market enjoys equilibrium when,
S=I
-a+(1-b) Y = Ia- i.r
(1-b) Y = a+ Ia- i.r
................(vi)
The equation (vi) shows the inverse relation
between rate of interest and level of income.
Slope of IS curve,

8. • In the figure, panel A shows the inverse relationship
between interest rate and investment. Panel B shows
the equality between S and I. Panel C shows the saving
function and panel D gives the IS curve or product
market equilibrium.
• Let initial interest rate is r0 in panel A. At this interest
rate investment is I0. The level of saving should be S0
for equilibrium which is shown in the panel B. the level
of saving S0 is possible when income level is Y0 which is
shown in panel C. The combination between r0 and Y0
gives point e0 in panel D which is market clearing
situation.

9. • If interest rate lowers down to the r1level the
level of investment increases to I1(panel A).
The level of saving should be S1 for goods
market equilibrium (panel B). This is possible
only when income level increases to Y1 (panel
C). The combination between r1and Y1 gives
another market clearing situation denoted by
e1in panel D. When these points e0 and e1 are
joined, the downward sloping IS curve is
derived.

10. Concept of LM curve
The concept of LM curve was developed by A.
Hansen in order to explain the money market
equilibrium. In the word LM, ‘L’ refers to the
liquidity preference (money demand) and ‘M’
refers to the money supply.
LM curve is the locus of various combinations of
rate of interest ‘r’ and level of income ‘Y’ along
which Md=Ms such that money market is in
equilibrium

11. Assumptions
1) Supply of money is exogenously determined. Ms=M......(i)
2) Money is demanded for 3 motives i.e. Transaction Motive,
Precautionary Motive and Speculative Motive (By Keynes).
Md=Lt+Lp+Lsp
Md= K(Y) +L(r).........(ii)
Where, K(Y)= Sum of transaction and precautionary demand for money
L(r)= Speculative demand for money
For simplicity, we assume a straight line demand function for speculative
demandfor money.
i.e. L(r) = L-l.i
Where, L and l are constant and i is interest rate
Now equation (ii) becomes
Md= KY+(L-l.i).........(iii)

12. 3) The money market stands equilibrium when,
Ms =Md
M= KY+(L-l.i)
KY = M- (L- l.i)
Y= 1/K (M-L+l.i)………(iv)
The above equation gives the money market
equilibrium at different level of income and
interest rate, which is called LM function.

14. • In the figure, Panel (A) shows the
downward sloping speculative demand for
money (Lsp curve). At the rate of r0, the
speculative demand for money is Lsp0. With
the given money supply, the transaction
demand for money will be Lt0, which is shown
in panel B. If Lt0 is the transaction demand for
money, the level of income will be Y0 which is
shown in Panel C. The combination of r0 and
Y0 clears the money market shown by point e0
in panel D.

15. • In the same way, if rate of interest lower down to r1,
more money will be speculated. The increase in
speculative demand for money implies decrease in
money for transaction purpose with no change in
money supply. The decrease in money demand for
transaction implies lower income level Y1. The
combination r1 of Y1 and represents another market
clearing equilibrium shown e1 by in panel D. When
these two points e0 and e1 are joined, the upward
sloping LM curve is derived.
However, the slope of LM curve depends on the
nature of speculative money demand function.

16. General Equilibrium/ IS-LM
equilibrium
• The particular equilibrium point of both
market (product market and money market)
gives the general equilibrium conditions. It
means all points of IS curve and LM curve are
not stable. The combination between certain
level of income and a particular rate of
interest can clear both market.

18. • The figure shows that the general equilibrium
of economy takes place at point e. at this
point, the combination between re and Ye
makes both market in simultaneous
equilibrium.
• Any other combinationother than re and Ye
doesn’t make equilibrium of both markets i.e.
either product market or money market or
both markets.

20. • In the first figure, r is same as r1 at A and B. but Y2>Y1 at
A, I<S.
So, to the right of IS curve I<S.
• Similarly, r is same as r2 at C and D, But Y1<Y2 at C, I>S.
So, to the left of IS curve I>S.
• In the second figure, Y is same as Y2 at A and D but r1<r2
at D, Md>Ms
So, to the right of LM curve, Md>Ms
• similarly , Y is same as Y1 at B and C but r2>r1 at B,
Md<Ms
So, to the left of LM curve, Md<Ms

22. Region Goods Market MoneyMarket
I I<S Md<Ms
II I<S Md>Ms
III I>S Md>Ms
IV I>S Md<Ms

23. Due to these disequilibriumconditions in the
economy, the economy move along until it
reaches the stable equilibrium point e, as
shownin the figure.

24. Numerical Questions
1. a. Suppose consumption and investment
functions are given as; C = 200+0.8 Y and I =
200-2000i. Then find the equilibrium level of
income at interest rates 10%, 9% and 7%.
b. Derive the LM function from the following
monetary sector model; MT = 0.5 Y, MSP =
110-1600i and MS = 200 million. Give
economic interpretation of the LM curve.

25. 2. Let consumption function (C) = 10 + 0.5Y ;
investment function (I) = 200-2000i; Money
supply (MS) = Rs. 150 million MT= 0.5 Y, MSP =
150-1500i
a. Derive IS equation using S-I approach.
b. Derive LM equation.
c. Compute output and rate of interest at general
equilibrium.
d. What will be the new output and rate of interest
at general equilibrium when money supply
increases by 50 million?

26. 3. Let product market and money market models
given as follows C= 100+0.75Yd , I= 120-0.5i, MS
= 120, Md = 0.2Y-500i, Lump sum tax (T) = 20
a. Compute equilibrium level of income and rate of
interest at general equilibrium.
b. What will be the effect on equilibrium level of
income and rate of interest when central bank
increases money supply by Rs 30 trillion?

27. 4. Supposethe product market model is given
as C= 100+0.8 Y, I = 110 – 5i and the money
market model is found as MS = 45, Md = 0.5Y-
4i, where he symbols have their usual
meaning. Find:
a. IS and LM functions.
b. Determine equilibrium income (Y) and
interest rate (i).

28. Shifts in IS and LM functions:
change in general equilibrium

29. Shifts in the IS curve
According to Keynes, IS curve shifts to the right
due to following reasons.
When,
• C, I, G, or NX increases
• Saving decreases
• Tax decreases
And vice versa.

30. IS1
IS2
IS3
LM
Income
Rate
of
interest
Y0 Y1 Y2
R0
R1
R2
E0
E1
E2

31. Shifts in the LM curve
• The LM curve, the equilibrium points in the
money market, shifts for two reasons: changes in
money demand and changes in the money
supply.
• If the money supply increases, ceteris paribus, the
interest rate is lower at each level of Y or in other
words, the LM curve shifts right and vice versa.
• Similarly, when money demand increase with the
constantsupply of money.

32. Contd.
• For example: when central bank follows an
expansionary monetary policy, it would
increase liquidity in the market due to which
increases for both i.e. transaction and
speculative purpose. This shifts the LM curve
to the right. Similarly, when central bank
adopts contractionary monetary policy, the
LM curve shifts leftward.

33. Y0 Y1 Y2
R2
R1
R0
Income
IS
LM1
LM0
LM2
E2
E0
E1
Rate
of
interest

34. Simultaneous shifts in the IS and LM
functions
• Based on above explanations, it can be concluded
that when IS curve shifts to the right due to
increase in investment or decrease in saving, both
the rate of interest and level of income tends to
rise and vice versa given the LM curve.
• On the other hand, when LM curve shifts to the
right due to an increase in money supply or
decrease in demand for money, rate of interest
tends to fall and level of income tends to rise
given the IS curve.

37. Derivation of IS curve with fiscal policy
1. IS model with lump sum tax
Assumptions
• The government expenditure and lump sum tax both
determined by exogenous factors so they are constant.
• The government adopt balance budget (G=T)
Product market will be equilibrium when AD=AS
i.e. C+I+G = C+S+T…………..(i)
Where C= a+ bYd, I= Ia -hi, T= Ta, G= Ga and S= -a+(1-b) (Y-T)
Then equation I becomes

38. 2. IS model with tax function
This model can be derived on the basis of
followingassumptions.
i. The government expenditure is determined
autonomouslyand remains constant.
ii. Taxesmean only income tax at a flat rate
iii. tax function is given as T= Ta +t.Y
Then the income function becomes

39. Numerical
1. The following data are given for an economy
Consumption (C) = 40+0.75Yd ,
Investment (I) = 140-10i
GovernmentExpenditure (G) = 100
Lump Sum Tax (T)= 80
Money demand (Md) = 0.2Y-5i
Money Supply (MS) = 85
wherethe symbols have their usual meaning
a. Find out the equilibrium income and interest rate
b. Suppose the government increases its expenditure on
education and health services by Rs 65 crores, what
would be its effect on equilibrium income and interest
rate?

40. 2. Consider the following features of Nepalese Economy
C= 1009+0.8Yd, I= 200-1080i, G= Rs. 100 billions, T= 50+0.2Y, Ms=
250 billions, Md= 100+0.5Y -2500i
a. Determine equilibrium equation for the product market.
b. Derive IS and LM functions.
c. Find the shift in the IS schedule if deficit financed (ΔG= 72
billion) and comment your results.
d. Find the shift in the IS schedule if tax rate is increased by 5%
and comment your results.
e. Find the shift in the IS schedule if ΔG= 72 billion and tax by 5%
and comment your results.
f. Find the shift in the LM schedule if ΔMs= Rs. 50 billion and
comment your results.
g. Find the equation for the general equilibrium, equilibrium
income and rate of interest at t=0.20, G =Rs 100 billions and
Ms= Rs 250 billions.
h. Find the equilibrium income and rate of interest at Δt =0.05, ΔG
= Rs. 72 billion and ΔMs = Rs 50 billion and comment your
results.