keynesian_02 ver 3

8/10/2019 Keynesian_02 Ver 3

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Keynesian System - IIMoney, Interest and income


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C a b Y T ( )

0C a bY bT btY

0( )C a b Y T tY

0Y a bY bT btY I G

C

Y

b bt

a I G bT

1

1

0( )

The Government Spending and Tax Multipliers Algebraically

The Case in Which Tax Revenues Depend on Incomes

Through substitution we get

Solving for Y:


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1

1 b bt

The Government Spending and Tax Multipliers Algebraically

The Case in Which Tax Revenues Depend on Incomes

This means that a $1 increase in Gor I(holding aand T0constant) will

increase the equilibrium level of Yby

Holding a, I, and Gconstant, a fixed or lump-sum tax cut (a cut in T0) will

increase the equilibrium level of income by

btb

b

1


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Money in the Keynesian System

Money affect income via interest rate:

Money Supply increases interest rate decreases aggregatedemand increases national income increases.

Chain1: Money Supply increases interest rate decreases

Chain 2: interest rate decreases aggregate demand increases


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Interest rate and Aggregate demand

Investment demand = f (interest rate).

Investment projects will be pursued only when expected profitability> the cost of the project.

All the components of Investment; business investment, residentialconstruction, consumer durables etc. will respond to the changes ininterest rate.


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Effect of a decrease in the interest rate


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Effect of a decrease in the interest rate

A decline in the interest rate from r0to r1shift the aggregate demandcurve to E1

Interest sensitivity of aggregate demand decides how effective is themonetary policy which works through the interest rate channel.

Interest rate sensitivity of various components of aggregate demandhas to be analyzed.


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Keynesian Theory of interest rate

Chain1: Money Supply increases interest rate decreases.

So, quantity of money plays a key role in the determination ofinterest rate in the economy.

Assumptions: Financial assets includes money and non-money assets (Bonds)

Bonds are perpetuities.


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Determination of Interest rate


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Determination of Interest rate

Interest rate is determined at the point where the supply of money =

demand for money.

Supply of money is determined by the Central bank through variouspolicy tools

Demand for money is determined in the economy due to followingfactors;

Transaction demand

Precautionary demand

Speculative demand


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Demand for Money

Transaction demand for money: Money acts as a medium ofexchange.

Md = f (Yd )

Money is demanded only for transaction purpose only.

Precautionary Motive:

Md = f(Yd)

Money demanded for unexpected events


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Demand for Money

Speculative demand for money:

Md= f(r) , where r is the interest rate.

Money is demanded for speculation; buying and selling bonds orbond transaction.


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Speculative demand for Money

Why people hold money above that needed for transaction andprecautionary motives when bond pay interest rate and money doesnot?

The answer to the above question explained by the motives for

speculative demand for money. It is understood that there is uncertainty of interest rate movement

and this uncertainty of interest rate results the relationship betweeninterest rate and bond price also uncertain.


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If interest rate are expected to move such a way as to cause capital

losses which outweigh the positive interest earnings on the bond, thenpeople prefer to hold money.

Earning / return on bonds = r expected capital gain/loss

Interest rate and bond prices are inversely related to each other.

Interest rate bond price

Interest rate bond price


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Suppose one Rs. 1000 bond pays the holder Rs.50 per year as coupon. (r= 5%)

How much would this bond be worth today?

This depends on the current market interest rate.

If current market interest rate rc= 5%, the bond sold at Rs.1000. (bond

price)

If current market interest rate rc= 10%, the bond sold at Rs.500 (50/500= 0.10 (10%))


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Hence, when the interest rate increases from 5% to 10%, bonds will besold at a capital loss of 500.

If interest rate decreases to 2%, bond price will be 2,500.

Thus a decline in the interest rate result in a capital gain of existing

bonds.


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Return on money = 0

Expected return on bonds = r + expected capital gain.

Expected return on bonds = r - expected capital loss.

Hence, expectations about future interest rate movement is crucial.


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Expectation about interest rate andspeculative demand for money

Every investor has a conception of normal interest rate (rn).

When rc> rn investor expect the interest rate to fall.

When rc< rn investor expect the interest rate to increase.


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Concept of Normal interest rate.

Every individual has a concept of normal interest rate in their mind. ith individual has rni as the normal interest rate.

If the current interest rate above rni,you expect the interest rate to fall tonormal.

When you expect the interest rate to fall, you will have capital gain if you

are holding bonds.


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Concept of Normal interest rate.

Hence, you prefer to hold bonds between the range (rni to )

When the current interest rate is below the normal rate, the investorexpect it to increase to the normal.

Hence, they will experience a capital loss of holding bonds.

Hence, they will hold money between the range (0 to rni ).


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Speculative Demand Keynes assumes that different people have different views on the

normal interest rate The curve is flattens out at a very low interest rate, reflecting at a lower

rate there is a general expectation of capital loss on bond that outweighspositive interest earnings.

At this rate, increment to wealth would be held in the form of money.

No further drops in the interest rate is required to attract speculativedemand for money.


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The IS-LM modelEquilibrium in the goods and money markets

Understanding public policy


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The IS-LM model

The IS-LM model translates the General Theoryof Keynes into neoclassical terms (often calledthe neoclassic synthesis)

It was proposed by John Hicks in 1937 in a papercalled Mr Keynes and the "Classics": ASuggested Interpretation and enhanced by AlvinHansen (hence it is also called the Hicks-

Hansen model).


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The IS-LM model

The model examines the combined equilibriumof two markets :

The goods market, which is at equilibrium when investments equalsavings, hence IS.

The money market, which is at equilibrium when the demand forliquidity equals money supply, hence LM.

Examining the joint equilibrium in these two markets allows us todetermine two variables : output Yand the interest rate i.


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The IS-LM model

The model rests on two fundamental assumptions All prices (including wages) are fixed.

There exists excess production capacity in the economy

This is a complete change in perspective comparedto classical economics:

The level of demand determines the level of output and employment.

There can be an equilibrium level of involuntary unemployment.


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The IS-LM modelThe IS-LMmodel has become the standard

modelin macroeconomics.

Its essential contribution (linked to that of Keynes)

is this potential equilibrium unemployment: Such a situation is impossible in earlier neoclassic models, as the price of

labour (like all prices) is assumed to adjust naturally until supply and

demand for labour are balanced.


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This is whyIS-LM remains central to modern

macroeconomics, and has been extended to

explain more markets/ variables:

TheAS-AD (Aggregate Supply-Aggregate Demand) model adds inflation

into the problem

The Mundell-Flemingmodel deals with international trade adds Balance of

Payment into the problem.


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The IS-LM model

The IS curve

The LM curve

Macroeconomic equilibrium and policy


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The IS curve

The IS curve shows all the combinations of interestrates iand outputs Yfor which the goods market is inequilibrium

It is based on the goods market equilibrium we have examined in the KeynesianSystemI (chap.5)

However, a simplifying assumption we made initiallywas that investment Iwas exogenous

We know that investment actually depends negatively on the level of interest


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The IS curve

The Investment function

Is the sum of private investment (endogenous) and publicinvestment (exogenous)

Here, the interest rate has a real interpretation: it is themarginal profitability of investment

Ig

i

gI I i G T

Ig= I(i) + (G-T)


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The IS curve

The Savings function Is obtained from the aggregate demand equation,

subtracting investment and consumption:S=Y-C-T

S= -C0+(1-b)(Y-T)

S

Y

S = -C0+ (1 - b)(Y-T)

mps: 0< 1-b)


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The IS curve

i

i i

Y

Ig

S

i Y

45IS

S = -C0+ (1 - b)(Y-T)

Ig= I(i) + (G-T)


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IS Curve

IS curve is the locus of all the points representing equilibrium in thegoods/ commodity market.

It shows various combinations of I and Y where goods marketequilibrium is attained.

The IS curve slopes downwards as at lower interest rate, the level of

investment is high. For equilibrium, Income has to be higher to induce higher saving to be

equal to higher investments.


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Factors that determine the Slope of theIS schedule.

(a) If the investment function is inelastic, a given change in i, resultsa small change in investment, which requires a small change insaving. Given the saving function, it requires a small change inincome (Y). Hence the IS curve is steeper.

If the investment function is elastic, the IS curve is Flatter.


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Factors that determine the Slope of theIS schedule.

(b)Higher is the marginal propensity to save (MPS), IS curve will besteeper.

Lower is the marginal propensity to save (MPS), IS curve will be Flatter.


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The IS curve

i

i i

Y

Ig

S

i Y

45IS

Higher propensity

to consume

IS flattens out


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Factors that explains the Shift in the ISSchedule

IS curve will shift when any or all autonomous expenditures changes(G, T and I)


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The IS curve

i

i i

Y

Ig S

i Y

45IS

Reduction inpublic spending

IS shifts to theleft


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Changes in the Govt. Expenditures andimpact on the IS Schedule

Before changes in the G, the equilibrium was

I + G = S + T

Now, I + G1= S1+ T

So, G = S

S = (1b) Y

Or Y = 1/ (1-b) G at initial rate of interest. (i)


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Changes in Tax and impact on the ISSchedule

Tax increases, saving decreases by (1-b) MPS

Hence product market equilibrium is;

I + G = S1+ T1

As I and G are unchanged, S1 and T1are such that S = T or S + T =

0


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Changes in Tax and impact on the ISSchedule

S = (1b) (YT)

= (1b) Y(1b) T

As S + T = 0;

(1b)

Y(1b)

T +

T = 0 (1b) Y + b T = 0

(1b) Y = - b T

Y = (- b) /(1b) T


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IS Schedule

(1) IS curve slopes downward to the right

(2) IS will be relatively flat if interest elasticity of investment is highand MPC is high.

(3) IS will shift to the right by (1/1-b)when govt. expenditure will

increase

(4) IS will shift to the left byb / (1-b) when tax increases.


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The IS-LM model

The IS curve

The LM curve



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The LM curve

The LM curve shows all the combinations of interestrates iand outputs Yfor which the money market isin equilibrium

It is based on the money market equilibrium we haveexamined last two weeks

This time the interest rate ihas a monetary

interpretation: It is the opportunity cost of money, in other words thepayment made for renouncing liquidity (preference forliquidity)

The LM curve


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The LM curve

Liquidity preference: Given a level of output Y, the level of

interest iadjusts so that the demand for money (given by the

liquidity function L) equals the exogenous supply:

M = Money supple (exogenous)

P = Level of prices (exogenous by assumption)

iYLP

M,

The LM curve


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The LM curve

Simplifying assumption: The liquidity function, which gives the demand forreal money balances, can be decomposed depending on the type ofdemand

There are two motives for demanding real money balances:

The transaction and precautionary motiveL1(Y): The money demanded inorder to be able to transact in the future (function of the level of output)

The speculation motive L2(i): The money demanded for purposes of

speculation (opportunity cost of the interest rate). When interest is high,people dont want to hold money, whereas when the rates are low, moneydemanded increases.

iLYLiYL 21,


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The LM curve

L1(Y)

Real Money Balances demanded for

the transaction and precautionarymotive (L1) are an increasing function

of output Y

Y

L1(Y)


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The LM curve

i

Real Money Balances demanded for thespeculation motive (L2)are a decreasing

function of the rate of interest.

Under a given (low) level of interest, the

money demanded becomes infinite: agents do

not want to hold assets, and any money

available is hoarded.

Liquidity Trap

L2(i)

L2(i)


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The LM curve

L1Money supply M is fixed and exgogenous. The moneymarket equilibrium requires that the sum of money

demands add up to the supply of money

(M/P) = L1(Y) + L2(i)

L2

Given one demand for money, say L2(i), then the

other is given, by:

L1(Y) = (M/P) - L2(i)

(M/P) = L1(Y) + L2(i)

45


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The LM curvei i

Y

Y

L1(Y) L1(Y)

L2(Y)

L2(Y)

LM

45

L1(Y)

L2(i)


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LM curve is the locus of points representing equilibrium in the moneymarket.

Money market equilibrium means money demand should be equal tomoney supply.

The LM curve slopes upward because as the interest rate increases, thespeculative demand for money decreases.

Given the supply of money the money demand for transaction andprecautionary should increase.


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Money demand for that will increase if income increases.

Hence, the points of equilibrium in the money market consistent withincreasing interest rate and increasing income.


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Factor that determine the slope of the LMcurve.

Steeper money demand schedule reflect the interest elasticity of moneydemand is low, hence, LM curve will be steep

Flat money demand schedule reflect the interest elasticity will be high,hence LM curve will be flat.


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Shift in the LM curve

Change in the money supply

Change in the money demand.

LM will shift downward (upward) to right (left) with increase(decrease) in money supply.

LM will shift upward (downward) to the left with increase (decrease)in money demand at given level of income and interest rate.


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The LM curvei i

Y

Y

L1(Y) L1(Y)

L2(Y)

L2(Y)

LM

LM

4545

Fall in money

supply

Pushes LM left

L1(Y)

L2(i)

LM


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LM curve

LM schedule giving the combinations of Y and r that represent moneymarket equilibrium

LM curve slopes upward

LM will be relatively flat if interest elasticity of money demand is veryhigh.

LM will shift downward (upward) to right (left) with increase (decrease)

in money supply. LM will shift upward (downward) to the left with increase (decrease) in

money demand at given level of income and interest rate.


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The IS-LM model

The IS curve

The LM curve



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IS

LM


Income, Output Y

Interestrate

i

Y*

i*

The intersection of IS and LM

represents the simultaneous

equilibrium on the goods and

the money market

For a given value ofgovernment spending G, taxes

T, money supply M and prices

P


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IS-LM can be used to assess the impact ofexogenous shocks on the endogenous variables ofthe model (interest rates and output)

One can also evaluate the effectiveness of thepolicy mix, i.e. the combination of: Fiscal policy: changes to government spending and taxes

Monetary policy: changes to money supply


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Fiscal policy affects the equilibrium in the goodsmarket, viachanges in G and T. Weve seen that this influences the IS curve.

The shift in IS affects both endogenous variables(output and interest rate) In the previous chapter, we assumed that investment was

exogenous (There was no interest rate in the basic model)

Idid not change when Gor Twere changed

This is no longer the case with IS-LM : there is a crowdingout effect



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q p y

1. An increase in spending G pushes IS tothe right

The difference between Ykand YIS-LM is

the crowding out effect

2. By an amount:G

c

1

1

IS

LM

Y1

i1

Income, Output Y

Interestrate

i

i2

YIS-LM YK

But as Y increases (multiplier effect), so

does money demand. The interest rate

must increase to compensate, which

discourages investment


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keynesian_02 ver 3

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