#### Transcript VII Keynesian revolution - CERGE-EI

```X. Keynesian model of a closed
economy
John Maynard Keynes
• 1883-1946
• Cambridge, UK
• Thinker – economics,
logic, probability
• Practitioner –
Treasury during WWI,
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
C  CYD
• Marginal propensity to consume, MPC, is positive
and less than one: MPC = CYD , 0  CYD  1
• Savings function
S  YD C  YD CYD  S = SYD
• Marginal 
propensity to save, MPS
MPS = SYD , 0  S YD  1

and

CYD  SYD  1
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
(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:
dY
1
dY  CY dY  dI , and

dI 1  CY
• The term 1 1 CY   1 SY  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



1
dY  dI  CY dI  C dI  ...  dI 1  CY  C  ... 
dI
1  CY
2
Y
2
Y
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 money
1. 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:
MD
 L Y, r 
P
r
L(Y1 , r) L(Y2 , r)
Y1  Y2
L Y  0, L r  0
M/P
X.2 Equilibrium in the Keynesian
system
X.2.1 Goods market and effective
demand
Effective demand and supply
determination
– 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:
(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)
Short-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 exogenous
then
• Price is not a decisive factor in determining supply and demand
• In equilibrating processes, producers generate output according
– 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
Y  CY  T  Ir   G or SY  T  Ir   BD
! Remember basic macroeconomic identities !
• Solution  equilibrium output
• Quantitative adjustment – during the
equilibrating processes, quantities, not prices,
– AD>AS  real investment higher than planned
 decrease of production
• Graphical illustration – Paul Samuelson
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
unintended
investment > 0
unintended
investment < 0
E
45
Y1
Y0
Y2
S T
Y
S,I
E
Y1
Y0

Y2
I  BD
Y
Output multiplier
• For a moment, assume interest r fixed
• Equilibrium on the goods market:
Y  C Y  TY  Ir   G
• Differentiating equilibrium condition and after
arrangement (with dr = 0)
dY 
1
1  CY  T 1  TY 
dG   dG
• Multiplier of a change in exogenous variable (G)
 =1 1-CY-T 1-TY 
AD  CY  T  Ir   G1
E1
AD  CY  T  Ir   G0
E0
45 o
Y0
Y1
S,I
E1
E0
Y0
SY  T   T
Y
Ir   G1
Ir   G 0
Y1
Y
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: MS P
• Equilibrium and interest determination:
MS
 L Y, r 
P
– 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
r
MS
P
r1
r0
E
L Y,r
r2
M0
P

M
P
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:
Y  C Y  TY  Ir   G
• 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
dr 1  CY-T 1  TY  1


0
dY
Ir
I r
S,I
S+T
E1
Ir1   G
E0
Y0
Ir0   G
Y1
Y
r
r0
E0
E1
r1
Y0
Y1
IS
Y
IS curve (1)
• Differentiation of equilibrium condition =
movement along IS
• Slope of IS given by
– Multiplier 
– Interest elasticity of investment
• Low interest elasticity I r  0 means almost
vertical IS dr dY  
• Keynes – low interest elasticity of investment,
hence small change of investment, AD and
product due to changes in r
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
MS
 LY, r 
P
• 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
dr
LY

0
dY
Lr
r
r
S
M
P
r1
E1
r0
E0
LM
E1
r1
LY1, r 
r0
E0
LY0 , r 
M
 
 P 0
M
P
Y0
Y1 Y
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
Lr   , then LM curve almost
horizontal dr dY  0
•  liquidity trap
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
Y  C Y  TY  Ir   G
S
M
 LY, r 
P
r
LM
ESG
ESM
ESG
EDM
EDG
ESM
EDG
EDM
IS
Y
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
– 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: G>0  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
LM
r
r2
r1
E2
E1
A
IS2
IS1
Y1
Y2
YA
Y
Multiplier of governmental
expenditures
• Differentiation of both equations:
dY = CY-T 1 - TY  dY + Ir dr + dG


0 = L YdY + L r dr , hence dr = - L Y Lr dY
• Substituting in the first equation for dr from second
equation and after arrangement we have
dY =
• By assumptions
1
LY
1-C Y-T 1-TY +Ir
Lr
dG = .dG
LY
0 < CY-T 1 - TY <1 and Ir
>0
Lr
and
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
LY
• Formally: impact of the term Ir .
Lr
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 Ir  0 and/or L r  •
• Classical model (long term): vertical LM
 increase of governmental expenditures
fully crowds out private investment
Lr  0
Tax policies
• Simplification: TY = tY, 0 < t < 1
• Tax multiplier (derived equally as above)
dY =
-C Y-T Y
L
1-C Y-T 1-t  + Ir Y
Lr
dt = -  C Y-T Ydt
• 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
.
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 dG = d  TY ?
• We have
dY = CY-TdY - CY-TdG + dG
and after arrangement
dY dG = 1
• Balanced budget multiplier is equal one.
X.5.2 Monetary policy in ISLM
• Original equilibrium in E2
S
• Increase of money supply M > 0
• 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
LM1
r
LM 2
r1
r2
rA
E1
E2
A
Y1
IS
Y2
Y
Multiplier of monetary policy
• Again, differentiation of both equilibrium
S
conditions, hence dG= 0 , but dM P ° 0
• After arrangements
Ir
Lr
S
S
dM
Ir dM
dY =

= 
>0
LY
P
Lr P
1 - C Y-T 1-TY  + Ir
Lr
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 L r  • (flat LM) , than multiplier of monetary
policy is equal to zero and monetary policy is entirely
ineffective  liquidity trap
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
P
AS
P1
Y1
Y2
Yf
Y
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