IS and LM Curve of two sector and three sector model In the economy.
Unit: 11
(1) Y = C + I
(2) Md = Ms
= Dependence of product Market on Money Market
Y=C+I
- hi
hi
∆ / ∆i
Y = C(Y) + I(i)
= Dependence of Money Market on product Market
Ms - Md
Md = Mt + Msp
Mt = k(Y)
Msp = Fi
Md = k'(Y) + F(i)
= IS - LM Model
= Investment - Saving Curve (IS - Curve)
Y = C(Y) + I(i)
I = I(i)
S = Y - C(Y)
∴ I(i) = Y - C(Y) → Saving function
Investment function
I = 200 – 2,000i
S = Y – (10 + 0.5Y)
C(Y) = 10 + 0.5Y
Diagram- 1)
The IS Curve is the locus of a point showing equilibrium of a point of a product market at various
combinations of interest rate or saving & income.
It has 2 implications
1) The product market will not be in equilibrium at any point away from the IS Curve.
For Eg: At any point to the right of the IS curve S>I. Any point to the left of the IS curve S<i.
2) The IS Curve has a negative slope which implies that the level of national income is inversely
related to the interest rate
Liquidity Money Curve (LM Curve)
Ms = Md
Md = Mt + Msp
Mt = ky
Msp = L(i)
Ms = ky + L(i)
↳ Money market equilibrium
Diagram- 2)
Mt = 120,
k = 0.5
Mt = 240
Mt = 90 , Y =?
Mt = 60, Y = ?
The tm is a locus of point showing equilibrium points of the money market at different level of
interest of income and demand for money.
Diagram- 3)
IS-LM Model – Two Sectors
Diagram- 4)
Diagram- 5)
IS-Model: Driving equation for product Market.
AD = AS
AD-Y = C(Y) + I(i) ………. 1
CY = a + bY………2
I(i) = - hi………3
hi =
Now substituting 2 & 3 in 1
Y
a
Y
- hi……4
Y- Y
a
- hi
∴Y
Y
a
- hi / 1-b
1 / (1- ) (a
Diagram- 6)
- hi)
in investment with interest rate
Y
(a
- hi)…….5 1 / 1-b = multiplier
2)
C(Y) = 10 + 0.5Y
I(i) = 200 - 2000i h = 2000i
Y = 10 + 0.5Y + 200 - 2000i
1 / 1-0.5 (10 + 200 - 2000i)
= 2(210 + 2000i)
= Y = 420 - 4000i
Y = 420 - 4000i
= 1 / 0.5y (1500i) ON Divedede
Y = 3000i - LM
Y = 420 - 4000i - IS
IS - LM i = 6%
Y = 180
ON Diwedlm
Shift in the IS-Curve
Diagram- 7)
° The LM Curve is assumed to be given the shift in the IS schedule is caused by the shift in the
investment schedule due to an autonomous investment and vice-versa.
Now, how general equili riu
changes with a ∆ in invest ent S schedule
Diagram- 8)
Inverse relationship between price of bond and i.
° The funds for new investment come from reallocation of asset portfolio investors sell their bonds
to acquire funds for new investment as a result bond prices go down and interest rate rises and
speculative demand for money goes up. At the same time when investment rises. As a result savings
rise on one hand and transaction demand for money on the other. Following the shift in the IS-curve
all the variables of the model I, i, Y, Md, and move upward given the money supply. (E to A)
• When fall in the investment process (E to B) same process in vice-versa.
Diagram- 9)
Md = Mt + Msp {transaction is a function of income Mt = k(Y), (k>0) Msp function of interest
inverse relationship Msp = L(i)
Assuming Msp to be a linear function
Msp = L - li , l
∆Msp/∆i
Substituting Mt & Msp
Md = ky + (L - li)
Now,
Ms = Md
∴ Ms = ky + (L - li) (Rearrange in terms of Y)
Y = 1/k (Ms - L + li)
Y
1/ (Ms - L - li)
Ms
1 0
Mt = 0.5Y
Msp = L - li = 150 - 1500i
Md = 0.5Y + (150 - 1500i)
Y = 1/0.5 (150 - 1500i)
Rise in Msp given the i
↓se in supply of money
↓se in transaction demand for money.
For rightward vice-versa.
The Money supply, excess liquidity,
ore de and for onds, price of onds rise, i ↓se, S
investment rises, income rises, Both transaction & speculative.
Diagram- 10)
ar et
Shift in L Curve and General Equilibrium.
• When the
oney supply rises, given the level of Y it leads to excess liquidity. This excess
liquidity finds its way into the bonds and security markets as a result the bond and security prices
go up and interest rate goes down. This encourages new investment which rises in income
• Rise in Y leads to rise in the transaction demand for money on the other hand the speculative
demand for money rises due to fall in the interest rate. Thus the total demand for money rises. The
process continues till fro
E₁ to E₀.
from ①
- hi
-a
(1- ) (Y-T)
T→②
I = 200 - 2000i → ③
S = -10 + 0.5 (Y-T) → ④
-T
0→⑤
to in terms of eq ②
= 200 - 2000i + 400 = -10 + 0.5(Y- 0)
= 240 - 2000i
0. Y
∴ Y = 460 - 4000i
case of lump sum tax
10 → ⑦
0→⑥
Diagram- 11)
Diagram- 12)
• Both s and rising with govt expenditure (a, ) - case of lump tax.
C
100
0.
I+G=S+T
(Y-T) S
-100
0.2 (Y-T)
200 - 2000i
100 T
0
0.20Y
1 / (1-b)(1-t) = fiscal multiplier
850 - 5000i
200 - 2000i + 100 - (-100 + 0.05 (Y - (80 + 0.20Y))) + 80 + 0.20Y
∴ Y = 850 - 5000i ↳ IS function for 3-sector model.
Diagram- 13)
Derivation of LM
Ms = Md
Md = Mt + Msp
Mt = 0.5Y…..(1)
Msp = 100 - 2500i……(2)
From 1 & 2
Md = 0.5Y + 100 - 2500i…….(3)
∴ Ms
200
∴ Ms = Md
200 = 0.5Y + 100 - 2500i
Y = 200 + 5000i
∆Ms = 100
Ms
∆Ms
Md
Y = 400 + 5000i
Diagram- 14)
° The shift in the LM curve to makes the money sector equilibrium shift from point A to B. This
shift should not be confused with rise in real income. It simply means that an rise in the money
supply can support a higher level of income given the rate of interest depending on the factor A.
° If households decide to keep there Mt constant the equilibrium point will move from A to C it
causes a fall in the interest rate from 6 to 21. The reason if households keep there Mt constant after
the rise in money supply. They will have an excess Msp.
3-SECTOR MODEL OF IS-LM CURVE
= Derivation of IS-Curve
1. lump tax
2. taxation on income
C+I+G=C+S+T
Equilibrium in product market
C+I+G=C+S+T
I + G = S + T…….(1)
and G = T
case of lump sum tax
C = a + bYd (Yd = Y - T)
- hi
S = -a + (1-b)Yd
= -a + (1-b)(Y-T)
,T
T
 General equilibrium
YIS = 850 - 5000i
YLM= 200 + 8000i
850 - 5000i = 200 + 5000i
850 - 200 = 10000 i
= 650 / 10000 i
= 6.5 / 100
= 0.065
= 6.5%
850 - 5000 (6.5) = 200 + 5000 (6.5)
Y = 525
Diagram- 15)
Three sector model LM Curve.
MS=MD
MD = MT + MSP
MT
0. Y……….(1)
MSP = 100 – 2 00 …..(2)
From (1) and (2)
MS = 200
 MS = MD
200 = 0.5Y + 100 – 2500 I
 Y = 200 + 5,000 I
Diagram- 16)
1) The shift in the LM Curve makes the Money Sector equilibrium point shift from point A to point
B. This shift should not be confused with increases with real income.
It simply means that an increase in the money supply. Can support a higher level of income gives
the rate of interest depending on the factor K.
2) If the houses hold desired to keep their MT constant the equilibrium point will move from point
A to C (as shown in the curve); a fall in the interest rate from 6 to 12%.
The reason is if household keep their MT constant either increase in money supply they will have in
excess, speculative demand for money.
General Equilibrium from LM Curve
Diagram- 17)
YIS = 850 – 5000 I
YLM = 200 + 5,000 I
YIS = YLM
850 – 5,000 I = 200 + 5,000 I
 650 = 10,000 I
 I = 0.065 Or 6.5%
525 is equilibrium level of income