VII Keynesian revolution - theory

Remark

• Lectures VII and VIII – closed economy only

• But see Lectures XI and XII

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

VII.1 General Theory – fundamental contributions

VII.1.1 Consumption

Three postulates (1)

Three basic conjectures about savings

1. Consumption function of disposable income only

2. - marginal propensity to consume, MPC, is positive and less than one:

• Savings function

• - marginal propensity to save, MPS, and

YDCC

YDCYDCYDS 1S0 , YDSS YD

1SC YDYD

YDC1C0 YD

YDS

Three postulates (2)

3. Average propensity to consume

• Keynes assumed that APC falls with increasing income

• If this is true: danger of secular stagnation of capitalist economy (see later)

Linear consumption function satisfies all three postulates

After Keynes: large body of theory, huge empirical research – see Literature

DYCAPC

cYDCC

VII.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 as 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 our purpose here we keep simple investment function, with interest as only explanatory variable

Real vs. nominal interest• In the classical model: real interest r, in investment

function only• On money markets: nominal interest i

– In classical model so far we did not need nominal interest, as it was neither endogenous, neither exogenous variable of the model

– In particular, in QTM, neither r, neither i has any role in demand for money

• In Keynesian demand for money bellow, the decisive variable is nominal interest i

• Not to complicate the explanation, a simple assumption:– Exogenous expected inflation πe and i = r + πe (Fisher

equation)– More on Fisher equation and Fisher effect in later Lectures

• Investment function: I = I(i- πe), Ii<0, Ii→0

VII.1.3 Multiplier

Multiplier (1)

• The notion of multiplier – see already previous lecture, in general form– Here we go back to the origins of the concept

• 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)?

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

• Alternatively: 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

Keynes’ assumption on multiplier

• Assumed unrealistically high levels, approaching to 3

• If this was true, than the impact of an exogenous change very strong (see next Lecture discussion on policy implications)

VII.1.4 Labor market, involuntary unemployment

• Classical labor market: demand, supply, flexible nominal wage, equilibrium

• Keynes:– Does not dispute classical demand for labor– Refuses the construction of the labor 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 labor even without increasing nominal wage

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

Nominal wage rigidity and involuntary equilibrium

SN

N

W/PDN

N1

W1/P1

W1/P2

N2 N3 N

Y

F

N1N2

Y1

Y2

Fall of price → increase of realwage → if nominal wage rigid→ unemployment N3 – N2

If equilibrium employment N2 → equilibrium output Y2, lower than full employment output Y1

VII.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)

– Here, in speculative money demand, nominal interest i (see remark above)

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 very low 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: i),L(Y1

,

i

M/P

i),L(Y221 YY

0L , 0L iY

i)L(Y,P

MD

VII.2 Equilibrium in the Keynesian system

VII.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 adjustment

• 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• Prices are not a decisive factor in determining supply and demand

on aggregate level• 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

• 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– Required simplification: price entirely fixed

Gπ-iITYCY e BDπ-iI TYS e

Paul A. Samuelson• 1915 – 2009• MIT• Neoclassical synthesis• Teacher, professor• Textbook – Economics,

invented “Keynesian cross” (see next slide)

• Foundation of Economic Analysis (1947)

• Linear Programming and Economic Analysis

• Nobel Price Award 1970

                                           

Y

Y,AD

Y

S,I

45o

S T

AD

I+BD

Y0

E

E

Y0

Y2

Y2

Y1

1Y

unintendedinvestment > 0unintended

investment < 0

VII.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 → i

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

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

PMS

i)L(Y,P

MS

M

P

i

E

M0

P

P

MS

i)L(Y,

1i

0i

2i

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 the Keynesian model and nominal wage becomes (in particular moment of time) and exogenous variable

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

VII.3 Complete Keynesian model

VII.3.1 The model• Market with goods and services

demand and equilibrium,assuming AD=AS

supply

• Labor market demand

• Financial markets (money market)demand and equilibrium, assuming MD=MS

• Components of aggregate demandconsumption function

investment function

GICY

NK,FY

PWNN D

i)L(Y,PM

YT-YCC

)π-I(iI e

Technical features• 6 equations and 6 endogenous variables:

Y, C, I, N, P, i– Important: price P is flexible!

• 5 exogenous variables: K, M, G, W, πe

• Equilibrium as a state of rest• Demand equals supply on 2 markets: goods

and services and money• Labor market

– Nominal wage W in particular moment is given (exogenous)

– Supply schedule is missing!• The model is completely interdependent, no

dichotomy, money is not a veil

VII.3.2 ISLM

ISLM – important comment• Textbook interpretation (”orthodox” interpretation of

Keynes):– Both prices and wages are fixed– There are spare capacities in the economy, namely the more labor

can be hired without impact on the increase of wages and prices– In simple interpretation of ISLM: no need to distinguish between

nominal and real interest rates (i and r), as price P is considered fixed (i.e. πe=0); bellow we use r (but could use i as well)

• Fixed price: simplification of AD x AS relation in Keynesian model as well– Right-angled AS curve (see next slide)

• Less standard derivation bellow: starting from full model, linearizing, collapsing into just two equations and getting simultaneous solution

• For usual explanation of ISLM, see any textbook on macroeconomics, with graphical interpretation– Review: Appendix to this Lecture

Y

P AS

Yf

P1

Y1

AD1 AD2

Y2

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

                                           

Linearization of the modelTaking total differentials of all equations

dKFdNFdY 2 KN

P

dP-

W

dW

F

FdN 3

NN

N

drLdYLP

M.

P

dP-

P

dM 4 rY

dGdIdCdY 1

dYT-1CdC (5) YT-Y

drIdI (6) r

IS curveSubstitute (5) and (6) above into (1) to get

where

(7) is combination of all Y and r that satisfy equilibrium on the goods market – IS curve (investment = savings); in a (Y,r)-plane IS is decreasing (has negative slope):

If in (7) we assume dY=0 and allow G vary, than

i.e. with increased G, IS shifts “up and right”; and vice versa

dGdrIdY (7) r YT-Y T-1C-1

1

0I

1|

dY

dr

rIS

0I

1-

dG

dr

r

LM curve (2)

i.e. with increasing M, LM shifts to the right, and vice versa, decreasing M shifts LM to the left; respectively

i.e. with increasing nominal wage W, LM shifts to the left, and vice versa, decreasing W shifts LM to the right

0P

1.

L

1

dM

dr

r

0P.W

1.

L

1-

dW

dr

r

LM curve (1)

From (3) single out dP/P and substitute into (4) to get

(8) is combination of all Y and r that satisfy equilibrium on money market – LM curve (liquidity/money); in a (Y,r)-plane LM is increasing (has positive slope):

If in (8) we put dY=0 and allow M to vary (keeping dW=0), respectively allow W vary (keeping dM=0), we get (see next slide):

dYL-

P

M.

F

F

W

dW.

P

M-

P

dM

L

1dr (8) Y2

N

NN

r

0L-P

M.

F

F

L

1|

dY

drY2

N

NN

rLM

Equilibrium as ISLM• (7) and (8) are 2 equations in 2 unknowns, Y and r

• Solution: values of output and interest (and by substitution of other 4 endogenous variables) that

– Ensure the equilibrium on goods and money markets

– On the labor market allow for equilibrium (as state of the rest), where demand of labor does not have to be equal to labor supply

r

Y

ISLM

Y0

r0

VII.3.3 Graphical interpretation of the full model

• Full model: we distinguish between i and r again (πe≠0)

• Equilibrium output determined by effective demand (ISLM)

• This level of output determines the employment (on demand for labor schedule)

• Demand for labor determines real wage and when nominal wage is given, then this determines price P, consistent with equilibrium on money market (with LM curve)

• Equilibrium (state of rest) with involuntary unemployment

Y

i

IS

LM

Y

Y

45°

Y

N

F

N

W/P NS

ND

Y0

i0

Y0

Y0Y0

N0

N0

(W/P)0

VII.4 Underemployment equilibrium?

VII.4.1 “Keynes effect”• The model above

– In the instantaneous moment of time, model allows for underemployment equilibrium – see above

– Crucial assumption: exogenously given nominal wage– In reality, when we allow wage to change in time, even

Keynesian model does not stay in underemployment equilibrium

• Adjustment mechanism described by Keynes himself before General Theory in Treatise on Money (1930) – so-called “Keynes effect”

• Excess supply of labor → W↓ → production costs ↓ → P ↓ → real money (M/P)↑ → excess supply of money, people bid bonds, i↓ and LM shifts to the right (see next slide), at the same time I↑ → AD↑ → Y↑ → N↑

• Higher AD moderates decrease of price level, so nominal wage falls faster than price (unbalanced deflation) → real wage falls

• The model converges towards full employment equilibrium, underemployment equilibrium does not exists (see next slide)

Y

i

IS

LM0

Y

Y

45°

Y

N

F

N

W/P NS

ND

Y0

i0

Y0

Y0Y0

N0

N0

W0/P0

N1

N1

Y1Y1

Y1

Y1

i1

LM1

W1/P1

VII.4.2 Underemployment equilibrium

• Given the reality of Great Depression, Keynes was seeking for an explanation of long-lasting underemployment equilibrium

• In the longer-run, nominal wage could not have been considered as fixed

• When – with flexible wages - his model converges to full employment equilibrium, he needed additional assumptions to allow for a theoretical possibility of stable underemployment equilibrium

• He, indeed, claims that two cases arise when underemployment equilibrium exists:– Liquidity trap– Interest-inelastic investment function

VII.4.2.1 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, today?)

Keynes effect locked• When interest very low, only increase expected,

i.e. only fall of bond prices expected as well →• Even when amount of real money increases,

people do not bid for bond, but keep additional idle balance as cash →

• Fall of nominal wages and prices (both decrease proportionally - balanced deflation) does not lead to fall of interest, increase of investment, AD, output and employment

• Economy remains at state of rest with involuntary unemployment

• Graphical illustration – next slide

Y

i

IS

LM0

Y

Y

45°

Y

N

F

N

W/PNS

ND

Y0

i0

Y0

Y0

Y0

N0

N0

(W/P)0

LM1

VII.4.2.2 Interest-inelastic investment function

• When investment reacts very slowly to 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

Y

i IS LM0

Y

Y

45°

Y

N

F

N

W/P NS

ND

Y0

i0

Y0

Y0 Y0

N0

N0

(W/P)0

N1

N1

Y1

Y1

Y1

Y1i1

LM1

(W/P)1

(W/P)F

NF

NF

YF

YF

YF

YF

VII.5 No “General” Theory

Underemployment equilibrium

• Given the explanation so far, under realistic assumptions, i.e. flexible prices and nominal wages (perhaps sluggish), the existence of underemployment equilibrium in Keynesian model is possible if only and only either the assumption of liquidity trap and/or of extremely interest inelastic investment function applies

• However, even this conclusion turned out to be wrong

Pigou’s vengeance• Arthur Cecil Pigou (see LIV), in 1943,

published an article where he proved that if we make the consumption function slightly more complex, introducing the wealth, the strict Keynesian underemployment equilibrium can not exist

• Pigou effect: falling prices increase real wealth and consumption and aggregate demand

• Increase of AD → shift of IS curve to the right → the economy converges to full employment equilibrium even at either liquidity trap or with very interest inelastic investment function

Criticism of Pigou effect

• If dynamic expectation introduced• If we search for the time-length of the effect• If we discuss how to define exactly the net wealth that

determines the consumption behavior of an individualthen Pigou effect does not have an practical impactHowever: if we take the Keynesian theory, as presented in

General Theory, it is an unequivocal truth that underemployment equilibrium can exist only with fixed nominal wages. This was the end of the title „General Theory“

… but it was not the end of Keynes

VII.5 Conclusions

Incomplete theory• Greatest contribution: Keynes

opened entirely new avenues in theoretical thinking

• Fallacy:– his theory is not a general theory –

equilibrium with excess labor supply depends on assumption of rigid nominal wage

– his conclusions are fit for economies in deep depressions (depend on the assumption of liquidity trap and low interest elasticity of investment)

Keynesian revolution

• Departure from existing economic thinking (classical model)

• Pioneering:– Equilibrium with unemployment

• equilibrium when DS

– New explanation of long-term unemployment– New sort of economic policies – see next

Lecture– New discipline - macroeconomics– Closer to real data – System of national

accounts

Literature to Ch. VII• Snowdon, B., Vane, H.: Modern

Macroeconomics, Edvard Elgar, 2005, Ch.1-3 (and the literature given here – General Theory, Hicks, Pigou, etc.)

• Sargent, T., Macroeconomic Theory, Academic Press 1987 (2nd ed.), Ch. 2

• Heijdra, B.J., van der Ploeg, F.: Foundations of Modern Macroeconomics, Oxford University Press, 2000, Ch. 1

• ISLM model – any intermediate textbook on macroeconomics

Appendix: ISLM model

• “Historical” simplification (unfortunate)• Simultaneous equilibrium on two markets, of

goods and money, prices fixed• John Hicks: Mr. Keynes and the “Classics”

(1937)• ISLM model is presented here only for the sake

of completeness • However, it is assumed that students will

understand ISLM very well from standard course of macroeconomics

The widespread interpretation• Involuntary unemployment production with

less than full utilization of resources• Simplification: fixed prices (including nominal

wages)– Interpretation: with high unemployment the firms

can increase production (higher workers) without increasing wages (i.e. costs and prices)

• „right-angled“ aggregate supply (see main text of this Lecture)

• Keynes never fully confirmed this approach

A.1 Goods market and IS curve

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

45

0E

0Y

0Y

1GrITYCAD

1E

1GrI

TTYS 1Y

1Y

0E

1E

Y

0GrITYCAD

0GrI

Construction of 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

A.2 Money market and 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

A.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