X. Keynesian model of a closed economy

John Maynard Keynes

• 1883-1946• Cambridge, UK• Thinker – economics,

logic, probability• Practitioner –

Treasury during WWI, advisor to the War Cabinet at WWII, crucial role at the birth of IMF/WB

X.1 General Theory - basic concepts

X.1.1 Consumption

• Consumption: function of disposable income only

• Marginal propensity to consume, MPC, is positive and less than one:

• Savings function

• Marginal propensity to save, MPS

and

YDCC

SYD CYD C YD S = S YD

0 SYD 1

1SC YDYD

MPC = CYD , 1C0 YD

MPS = SYD ,

X.1.2 Marginal efficiency of investment

• Ch. II : investment as a decreasing function of real interest, I=I(r), Ir<0

• Keynes called this relationship marginal efficiency of capital, later labeled marginal efficiency of investment, MEI

• Keynes assumption: MEI reflects expected return, these expectations very volatile, investment unstable and more than on interest, depends on many exogenous factors (low interest elasticity of investment)

• After Keynes – more sophisticated investment functions, for the time being I=I(r), Ir→ 0

X.1.3 Multiplier (1)

• Theoretical question: how does the equilibrium change, if there is - ceteris paribus – change in one of the exogenous variables (e.g. level of investment)?

• Practical question during Great Depression: if there is an improvement in investors’ expectations about the future (i.e. there is an increase in autonomous investment), what is the impact on product (and employment) increase?

Multiplier (2)

• Famous textbook explanation for a simple economy

C = C(Y), Y = C + I, I exogenous

and for impact of change in investment

• Differentiation of equilibrium condition:

• The term is (given the assumption on MPC) higher than one and reflects (approximately) impact of change in investment on the product

• Alternative interpretation: sum of expenditures’ increments after initial increase of AD

YY C1

1

dI

dY and , dIdYCdY

1 1 CY 1 SY

dIC1

1...CC1dI...dICdICdIdY

Y

2YY

2YY

X.1.4 Labour market, involuntary unemployment

• Classical labour market (L II): demand, supply, flexible nominal wage, equilibrium

• Keynes:– Does not dispute classical demand for labour– Refuses the construction of the labour supply

• Workers do not adjust to real, but to nominal wage• Nominal wage much less flexible:

– general political reasons after WWI (workers not ready to accept wage cuts)

– during Great Depression it was possible to hire labour even without increasing nominal wage

– On the labour market: possibility of an equilibrium with involuntary unemployment

X.1.5 Liquidity preference and interest

• Keynes abandoned QTM• Disregarding investment volatility – interest is

a key variable for Keynes, but– It is not determined in interaction between

investment and savings– It is given by equilibrium between supply and

demand on the money market

• Different role of interest – not as a reward for postponed consumption, but reward for giving up the possibility to hold liquid assets (money)

Why people demand money?Three different reason to demand money1. Transaction demand (see QTM): people demand money

to cover their transactions – increasing function of income

2. Precautionary demand (not much importance): people demand money to have enough cash - increasing function of income

3. Speculative demand (principle difference from Fisher’s version of QTM): people decide whether hold money (that provides zero interest) or any type of interest bearing asset (for simplicity called bond)

Note: there is an inverse relation between interest and price of bond: the larger is interest, the lower is the price and vice versa (see any basic textbook on Finance or Macroeconomics)

Liquidity preference

• Speculative demand – decreasing function of interest• Primarily, people hold liquidity (money). They give up

this possibility (i.e. transfer their wealth into interest bearing bonds), only when it brings additional yield:– In general, the higher the interest, the higher the

yield, hence higher interest lower demand for money (and higher demand for bonds)

– Keynes: uncertainty and risk - if interest expected to increase, than price of bond decreases and people prefer to hold money (why to hold bonds when their price will fall)

Demand for money• Keynes labeled total demand for money as liquidity

preference

• Particular case: at very low rates of interest nobody wants to invest into bonds (everybody expects the interest to increase, so price of bond to decrease) and people hold only money (money demand is infinitely interest elastic – graphically horizontal)

• Demand for money: r),L(Y1

,

MD

PL Y, r

L Y 0, L r 0

r

M/P

r),L(Y2

21 YY

X.2 Equilibrium in the Keynesian system

X.2.1 Goods market and effective demand

Effective demand and supply determination

• Aggregate demand AD:– consumption mainly given by disposable income, but has

important autonomous component; relatively stable– investment, determined by expected return, very volatile,

“animal spirits”– Governmental expenditures exogenous

• Refusal of Say’s law: – effective demand ≡ AD, supported by purchasing power

(money), i.e. the demand, the agents really want to spend money for

– such (effective) AD does not have to be equal to AD that would be necessary to “buy out” the full employment output

– opposite causality compared to Say’s law: demand determines supply (and production, employment)

Quantitative adjustmentShort-term (or depression situation): prices (and wages) fixed• If consumption depends on disposable income only• If investment depends less on interest, but mainly on exogenous

factors (expectations, uncertainty, etc.)• If government expenditures exogenousthen• Price is not a decisive factor in determining supply and demand• In equilibrating processes, producers generate output according

effective AD– adjustment of quantities, not of prices– quantities, i.e. output, consumption, savings, investments, etc. adjust, not

prices• Another essential novelty compared to classical model where

– Output determined on labor market that adjusted to wage (price of labor)

– Composition of demand determined by interest (price of money)

Equilibrium on goods market• Equilibrium condition Y=AD, so

or! Remember basic macroeconomic identities !

• Solution equilibrium output• Quantitative adjustment – during the

equilibrating processes, quantities, not prices, adjust– AD>AS real investment higher than planned

decrease of production– AD<AS vice-versa

• Graphical illustration – Paul Samuelson

GrITYCY BDrI TYS

Paul A. Samuelson

• 1915 –

• MIT

• Neoclassical synthesis

• Teacher, professor

• Textbook – Economics, invented “Keynesian cross”

• Foundation of Economic Analysis (1947)

• Linear Programming and Economic Analysis

• Nobel Price Award 1970

                                           

Y

Y,AD

Y

S,I

45

S T

AD

BDI

Y0

E

E

Y0

Y2

Y2

Y1

1Y

unintendedinvestment > 0

unintendedinvestment < 0

Output multiplier

• For a moment, assume interest r fixed• Equilibrium on the goods market:

• Differentiating equilibrium condition and after arrangement (with dr = 0)

• Multiplier of a change in exogenous variable (G)

G rI YTY C Y

dY 1

1 CY T 1 TY dG dG

=1 1-CY-T 1-TY

Y

Y,AD

S,I

45o

E0

Y0

Y0

1GrITYCAD

E1

1GrI

TTYS Y1

Y1

E0

E1

Y

0GrITYCAD

0GrI

X.2.2 Money market

Interest and equilibrium on the money market

• Nominal supply of money exogenous, controlled by Central Bank

• Supply of real money:• Equilibrium and interest determination:

– Interest too high ↔ excess supply of money → people buy bonds (higher demand for bonds) → price of bond → r

– Interest too low ↔ excess demand for money → people sell bonds (higher supply of bonds) → PB → r

• Implication – by changing the supply of nominal money, Central Bank can influence the level of interest

PMS

MS

PL Y, r

M

P

r

L Y, r

E

M0

P

r0

r1

r2

P

MS

Interest and money market

• Equilibrium on money market – supply of money equals demand

• Principal difference from classical model: interest is determined on money market and results from– Liquidity preference

– Supply of money by central authorities

• Reminder: classical model – interest is a result of society’s thrift (savings) and investment demand

Consequences for labor market• If output determined on the goods market, than

employment corresponds to that level of output• It does not have to be a full employment output –

such an output is only a special case → main reason why Keynes called his book “General Theory”

• If workers do not react to real wage → supply of labor is missing in Keynesian model and nominal wage becomes (in particular moment of time) and exogenous variable

• Equilibrium as a state of rest ↔ equilibrium with involuntary unemployment

X.3 IS-LM

John R. Hicks

• 1904-1989

• LSE, Oxford

• Value and Capital

• Austrian school

• Theories of economic growth

• Nobel price (1972)

• ISLM model: “Mr.Keynes and the Classics”, Econometrica, 1937

                                           

X.3.1 IS curve

• Equilibrium on the goods market:

• One equation for two unknowns• Graphically: set (locus) of points (Y,r),

maintaining goods market in equilibrium• Differentiating this equilibrium condition

and after arrangement the slope of IS is given by

G rI YTY C Y

0

I

1

I

T1C1

dY

dr

rr

YT-Y

Y

S+TS,I

GrI 0

0Y

Y

r

0Y

0r

0E GrI 1

1E

1Y

0E

1Y

1E1r IS

IS curve (1)

• Differentiation of equilibrium condition = movement along IS

• Slope of IS given by– Multiplier

– Interest elasticity of investment

• Low interest elasticity means almost vertical IS

• Keynes – low interest elasticity of investment, hence small change of investment, AD and product due to changes in r

0Ir dYdr

IS curve (2)

• Points off IS curve - disequilibrium:– “to the right and above”: – high interest, low

investment and low AD excess aggregate supply

– “to the left and bellow” – low interest, high investment and high AD excess aggregate demand

• Shift of IS changes in exogenous variables

X.3.2 LM curve• Equilibrium on money market

• Again, one equation for two unknowns

• Graphically: set (locus) of points (Y,r), maintaining money market in equilibrium

• Differentiation the equilibrium condition and arrangements give the slope of LM

r Y,L P

MS

0L

L

dY

dr

r

Y

r

P

M

r,YL 0

P

MS

0E

0P

M

Y

r

0r

0Y

0r 0E r,YL 1

1E

1Y

1E1r

1r

LM

LM curve (1)

• Differentiation of equilibrium condition = movement along LM

• Slope of LM given by– Income elasticity of demand for money– Interest elasticity of demand for money

• If interest elasticity of demand very high , then LM curve almost horizontal

liquidity trap

rL 0dYdr

LM curve (2)

• Points off LM curve – disequilibrium– “to the left and above” – high interest,

people interested in bonds (not in money) excess supply of money

– “to the right and bellow” – low interest, people not interested in bond (but in money) excess demand

• Shift of LMS curve changes in exogenous variables

X.3.3 Equilibrium in ISLM

• Solution of the system of 2 equations in 2 unknowns

• Graphical solution, adjustment processes

G rI YTY C Y

r Y,L P

MS

Y

r

IS

LMESGESM

EDGESM

EDGEDM

ESGEDM

X.3.4 Liquidity trap

• When interest so low, that demand for money becomes infinitely interest elastic (horizontal), then– Absolute liquidity preference (nobody wants to

purchase additional bonds)– Interest does not react to changes in supply of nominal

money liquidity trap• LM curve becomes for some low value of interest

also horizontal• Never observed in reality, in some situation, some

economies close (Great Depression, Japan in the 1990s)

X.3.5 Interest-inelastic investment function

• When investment reacts very slowly to even large changes in interest then even a fall to zero level interest does not have to generate aggregate demand strong enough to allow for full employment equilibrium output

• At least theoretically, the economy can stay at state of rest with zero interest and output with involuntary unemployment

• Graphically: IS curve very steep, full employment output would require ISLM intersection at negative interest rate

X.5 Policies

X.5.1 Fiscal policy in ISLM

• Changes of governmental expenditures

• Changes in tax rates

• Transfers to population (not included in the simple model here)

Increase of governmental expenditures

• Initial equilibrium in E1

• Increase: higher AD– Shift of IS, when each level of interest

corresponds to higher level of Y at given interest point A represents new equilibrium on goods market

– However, in A, disequilibrium on money market (off LM curve), EDM interest I AD Y

• New equilibrium in E2

G>0

r

Y

IS1

LM

E1

Y1

r1 IS2

A

YAY2

E2r2

Multiplier of governmental expenditures

• Differentiation of both equations:

, hence• Substituting in the first equation for dr from second

equation and after arrangement we have

• By assumptions

and

dY = CY-T 1 - TY dY + Irdr + dG

0 = LYdY + L rdr dr = - LY L r dY

dY = 1

1-CY-T 1-TY +Ir

LY

L r

dG =.dG

0 < CY-T 1 - TY <1 and Ir

LY

L r

> 0

1<<

Crowding out effect (1)

• In ISLM model, multiplier of governmental expenditures is lower than the same multiplier for the goods market only (when interest is given)

• Full model (and in reality) – higher governmental expenditures are partially offset by decrease of investment (due to the increase of interest) - G crowds out private investment

• Formally: impact of the term Ir .LY

L r

Crowding out effect (2)

• Keynes (short term): increase in governmental expenditures will have higher impact on product when– Interest elasticity of demand for money is

high (LM curve almost horizontal)– And/or interest elasticity of investment is low

(IS curve very steep)– Hence

• Classical model (long term): vertical LM increase of governmental expenditures fully crowds out private investment

Ir 0 and/or L r

L r 0

Tax policies

• Simplification: • Tax multiplier (derived equally as above)

• Policy induced change: impact of the tax change enabled first through the change of disposable income, than impact on consumption, AD and product (income); only than multiplier applies.

• Effect less certain – the reaction of consumers to a tax change might modify MPC

T Y = tY, 0 < t < 1

.

dY = -CY-TY

1-CY-T 1-t + Ir LY

L r

dt = - CY-TYdt

Balanced budget multiplier

• Keynes – allowed for budget deficit

• Reality – budget balance is always watched

• Question: what is the multiplier in case of equal change in governmental expenditure and amount of taxes, i.e. if ?

• We have

and after arrangement

• Balanced budget multiplier is equal one.

dG = d T Y

dY = CY-TdY - CY-TdG + dG

dY dG = 1

X.5.2 Monetary policy in ISLM

• Original equilibrium in E2

• Increase of money supply

• At given Y, excess supply of money higher demand for bonds, higher price of bonds and lower interest shift of LM to the right, new equilibrium on money market at point A

• However, disequilibrium at goods market (EDG) low interest increases investment, AD and product. Higher product increases demand for money increase of interest overall equilibrium at E2

MS> 0

r

Y

IS

LM1

E1

Y1

r1

LM2

ArA

E2

Y2

r2

Multiplier of monetary policy

• Again, differentiation of both equilibrium conditions, hence

• After arrangements

dG= 0 , but dMS

P ° 0

dY =

Ir

L r

1 - CY-T 1-TY + Ir

LY

L r

dM

S

P=

Ir

L r

dM

S

P>0

Efficiency of monetary policy

• The higher efficiency (impact on product growth) of monetary policy,– The lesser interest elasticity of demand for money (the steeper

is demand for money and LM curve as well)

– The higher is interest elasticity of investment (the flatter is IS curve

• If (flat LM) , than multiplier of monetary policy is equal to zero and monetary policy is entirely ineffective liquidity trap

L r

X.6 Conclusions• General Theory - reflection of Great Depression

– Output below potential level for long time

– High involuntary unemployment

– Prices and wages either stable or even falling (deflation)

– In the short term, output can be expanded without increase of wages (and prices)

– Right-angled AS (see next slide) and output (and employment) determined by the position of effective AD

• Relevancy today - model for short term– wages and prices are adjusting slowly due to rigidities on

labor market

Y

P AS

Yf

P1

Y1

AD1 AD2

Y2

Literature to Ch. X• ISLM model – any intermediate textbook on

macroeconomics– Mankiw, Ch. 9 - 11– Holman, Ch. 10

• Snowdon, B., Vane, H.: Modern Macroeconomics, Edvard Elgar, 2005, Ch.1-3 (and the literature given here – General Theory, Hicks, Pigou, etc.) - interesting additional reading