IS-LM Model

IS-LM Model…

• Keynes developed the theories on product market equilibrium and money market equilibrium separately.

• J.R. Hicks integrated Keynesian theories of product and money markets to show how equilibrium of both the sectors coincide at the same level of income and interest rate.

• Hicks’ model is known as the IS-LM model.

IS-LM Model…

• IS-LM model was proposed by Hicks (in 1937) in the paper “Mr Keynes and the Classics: A Suggested Interpretation”; and enhanced by Alvin Hansen (hence it is also called the Hicks-Hansen model).

• IS represents the product market equilibrium condition, i.e., investment (I) = saving (S).

• LM represents the money market equilibrium condition (L=M), where L stands for liquidity preference or demand for money (Md ) and M stands for money supply (Ms).

IS-LM Model…

• IS-LM model can be explained under the following three headings:

1. Derivation of IS curve2. Derivation of LM curve3. General Equilibrium

Derivation of IS Curve

• IS curve shows the equilibrium in goods market. It is derived by the help of saving and investment functions.

• IS curve is the curve which shows the relationship between the rate of interest and the equilibrium level of income, i.e., S = I at different rates of interest.

• Derivation of IS curve rests on two facts:

Derivation of IS Curve…

(i) Saving is a positive function of income: S=f(Y), f’(Y)>0 (It means that saving rises with rise in level of national income and vice-versa. In other words, slope of saving function is positive, i.e., MPS is positive).

(ii) Investment is an inverse function of rate of interest:I=g(r), g’ (r) <0 (It means that investment rises with fall in rate of interest and vice-versa. In other words, slope of investment function is negative).

Derivation of IS Curve…

• For product market equilibrium : Saving (S) = Investment (I)• By using this relationship, we can derive IS-

Curve

Derivation of IS Curve…

B: Saving Investment Equality

S=I

I

S

A: Saving FunctionY

S

Y1 Y2

S2

S1

S2

S1

I1 I2

C: Investment Function

I

r

r1

r2

I1 I2

D: Goods Market Equilibrium

IS-Curve

Y

r

Y1 Y2

r1

r2

IS

Derivation of IS Curve…• Panel (A) shows the positive relation of consumption and

national income. Saving function has been derived in panel (A). We know that consumption function is: C = a + bY. Again, we know that S = Y - C (for two-sector economy)

It can be developed as S = -a + (1-b) Y. It shows the positive relation of saving with income.

• Panel (B) indicates the saving-investment equality. It is shown by 45° line. We know that product market is equilibrium at S = I.

• Panel (C) represents the inverse relation of investment to rate of interest. Slope of investment curve is negative.

• Finally, IS curve is derived in panel (D). Each point in IS curve shows the product market equilibrium.

Derivation of IS Curve…

• We can derive IS curve by using algebraic method.• For two-sector economy, C = a + bY, and I = IF - hr,

where - h = ∆I/∆r• AD = C + I, and AS = Y• For equilibrium, AS = ADOr, Y = C + IOr , Y = (a + bY) + (IF - hr)Or, Y = (1/1-b) { a + IF - hr}• Using this function , we will get the IS schedule.

Derivation of IS Curve…

Numerical example: C = 10 + 0.5 YI = 200 -2000rNow, AS = Y and AD = C + IFor equilibrium, AS = AD or, Y = C + IOr, Y = (10 + 0.5 Y) + (200 – 2000r) Or, Y = 420 – 4000r, which is the required IS function.

Putting various values of r, we can find different values of Y. Thereafter, we can derive IS curve plotting Y along horizontal axis and r along vertical axis.

(Draw IS curve yourself.)

Derivation of LM CurveLM curve shows the equilibrium in money market. It is derived by the help of money- demand and money -supply functions.•In Keynesian theory of money demand, there are two parts of money demand (Md ):

(i) Mt = transaction demand = transaction

demand + precautionary demand (ii) Msp= speculative demand Mt depends on the level of income and there is positive relationship between income and transaction demand for money. It can be written as:

Mt=kY, where k > 0

Derivation of LM Curve…

The speculative demand for money has inverse relationship with rate of interest.

Msp=h(r) , h’(r) <0Total money demand function is:

Md= Mt + Msp

Md = kY + h (r)The supply of money Ms is determined

outside the model-it is exogenous.For equilibrium:

Md = Ms

Derivation of LM Curve…

LM

A: Transaction Demand

Y

Mt

Y1 Y2

Mt2

Mt1

B: Supply of MoneyMsp

Mt

Mt2

Mt1

Msp2 Msp1

Msp2 Msp1

C: Speculative Demand

Msp

r

r2

r1

r2

r1

D: Money Market Equilibrium

LM-Curve

Y

r

Y1 Y2

Derivation of LM Curve…• Panel (A) represents the positive

relation of Mt with income. ……..

• Panel (B) shows money supply . Total money supply (M) = Mt + MSP. ……..

• Panel (C) of the diagram shows the inverse relation of speculative demand for money with interest-rate. …..

• Finally, LM curve is derived in panel (D). ……

Derivation of LM Curve…• We can derive LM curve by using algebraic method.For money market equilibrium,Md = MS, where Md = Mt + MSP, where Mt = k Y, (K˃ 0).

MSP = L(r) = LF - mr (negative relation between MSP and r)

Md = kY + (LF - mr)

For equilibrium, Md = MS

Or, kY + (LF - mr) = MS

Or, Y = (1/k) {MS - LF + mr}

• Using this function , we will get the LM schedule.

Derivation of LM Curve…• Numerical Example:Suppose, MS = 150, Mt = 0.5 Y

MSP = 150 -1500r

For equilibrium, Md = Ms

or, Mt + MSP = Ms

Or, 0.5Y + 150 – 1500r = 150Or, Y = 3000rWe get various values for different values of r.Plotting these values in the graph, we get the LM

function

General Equilibrium

We now have two partial equilibriums; one in the money market for given levels of income and other in the product market for given levels of interest rates. We can determine the general equilibrium in both markets by determining where IS and LM curves intersect.The graph (in the next slide) suggests that only one interest rate and one level of gross domestic product satisfies the equilibrium conditions in both markets simultaneously.

General Equilibrium

LM

YE

rE

IS0

General Equilibrium…

Numerical example:We have already gotY = 420 – 4000r (IS function)Y = 3000r (LM function)Solving IS and LM functions, we getY = 180 and r = 0.06 = 6% It means that whole the economy (both of

product and money markets) will attain equilibrium (with income 180) at the interest rate 6%.

Monetary Policy Actions

How does monetary and fiscal policy affect the IS and LM curves? •Expansionary (contractionary) monetary policy will shift the LM curve to the right (left).•Expansionary (contractionary) fiscal policy will shift the IS curve to the right (left).

Monetary Policy Actions…

Monetary policy actions shift the LM curve. Expansionary monetary policy will shift the LM curve to the right, lowering interest rates and stimulating aggregate demand through investment, jobs and consumption. Contractionary monetary policy will have exactly the opposite effects.

Monetary Policy Actions …

r

Y

Expansionary

Monetary policy

Expansionary

Monetary policy

LM

IS0

LM*

Fiscal Policy Actions…..

Fiscal policy actions shift the IS curve. Expansionary fiscal policy will shift the IS curve to the right, stimulating aggregate demand through increased after tax income and government spending, but increasing interest rates. Contractionary fiscal policy will have exactly the opposite effects.

Fiscal Policy Actions …

r

Y

Expansionary

Fiscal policy

Expansionary

Fiscal policy

LM

IS0

IS*

Numerical Problems

Question 1: Derive the LM function from the following money-sector model:

Suppose, MS = 150, Mt = 0.5 Y

MSP = 100 -1500r

Numerical Problems…

Question 2: Following functions are given for an economy:

C = 1 + 0.8Y, S = -1 + 0.2Y, I = 1.2 -5r,MS = 1.2, Md= 0.2Y – 4r

(i) Derive IS function.(ii) Derive LM function.(iii)Determine income and interest rate at

general equilibrium.

Thank You