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V Keynesian revolution
Notice
• This is the only more technical Lecture
in the whole course
• Slides with blue background are for
mathematically more inclined students
with higher interest in macroeconomics
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
• 1936: The General
Theory of
Employment, Interest
and Money
Foreword
Macroeconomics before JMK
• Classical model – just a name, following
JMK‘s label given to his intellectual
predecessors in General Theory
• Reflects general socio-economic
framework before WWI
• As a compact macroeconomic model
formulated ex-post
• Useful simplification of reality
Full employment product and
aggregate supply
• Equilibrium on labor market: full employment N0
– everybody who wants to work at given real wage, can
find and gets the job
• Capital fixed in the short run: K
• Production function: Y0 = F(K,N0)
• Output (product) Y0 determined by full
employment N0 → full employment product
(output, income, etc.), equals aggregate supply
AS = Y0
• Changes in Y0 only if:
– shift in labor demand/supply schedules
– shifts in production function
W
 
 P 
W
 
 P 0
Y
NS
E
ND
N0
N
FN, K 
Y0
N0
N
Aggregate demand
• Consumption function:
C  CYD, r  , CYD  0 , Cr  0
• Investment function:
I  Ir  , Ir  0
• Government expenditure exogenous: G
• Aggregate demand:
AD  CY - TY, r  Ir   G
Goods market equilibrium - condition
Aggregate supply AS
• Labor market in equilibrium, ND=NS →
employment N0
• Production function ≡ aggregate supply
Y0 = F(K, N0)
Aggregate demand
AD  CY - TY, r  Ir   G
Equilibrium: AD=AS, hence
Y  CY - TY  Ir   G
Equilibrium - mechanism
• “Classical” question: what ensures that
– if supply is determined by full
employment from labor market – AD
exactly matches AS?
• Say‘s law: supply creates its own
demand
• Mathematically: if output Y determined
by labor market, the equilibrium
condition Y=AD determines real
interest r
Quantitative theory of money
• Nominal money M supply exogenous
• Output Y determined as above
• Velocity of money V constant (at least in
the short-term)
• Quantity equation of money: M.V = P.Y
– Ex-post, as identity, always valid
– Ex- ante, equilibrium condition
– Implicitly, price equation:
P
P = (M.V/Y), hyperbola:
Shifts with
different
money supply M
(V constant)
Y
Dichotomy of the classical model
• Real sector: labor market, flexible nominal
wage, production function, Say’s law
– Full employment equilibrium product
– Supply side determines the product at given
price and amount of money
– Price then given by quantity equation
• Involuntary unemployment could not exist
– Everybody, who wanted to work, could get a
job, at given wage
Classical dichotomy, money neutral
P
AS
P0
M0V
W0
W0/P0
W/P
Y0
Y
ND
N0
NS
N
F(K,N)
P
AS
M1<M0
W1<W0
P0
M0V
W0
P1
W1
W0/P1
W/P
M1V
Y1 Y 0
W0/P0
Y
N1
ND
Y1<Y0
N0
NS
N
W1/P1=W0/P0
F(K,N)
V.1 General Theory – fundamental
contributions
A. Consumption
Three basic conjectures about consumption and
savings
1. Consumption function of disposable income YD only
2. Marginal propensity to consume, MPC, is positive and
less than one, as is marginal propensity to save,
MPS, and MPC + MPS = 1
3. Average propensity to consume APC = C/YD:
• Keynes assumed that APC falls with increasing
income
• If this is true: danger of secular stagnation of
capitalist economy (see later)
Linear consumption function C  C  cYD satisfies all
three postulates
B. Marginal efficiency of investment
• Investment as a decreasing function of real interest
• 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)
– Animal spirits, stronger risk aversion of the investors in the
times of the crisis
C. Keynes and interest
• Before Keynes, real interest r in the center of
attention, both in consumption and investment
functions
• Pre-Keynesian macroeconomic thinking did not
build on nominal interest
– On financial markets crucial parameter, of course
– Demand for money based on a quantitative theory of money,
(QTM), where neither real or nominal interest played any role
• 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
D. 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)?
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  C Y dY  dI , and

dI 1  C Y
• 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
• Alternatively: sum of expenditures’ increments after
initial increase of AD


1
dY  dI  C Y dI  C dI  ...  dI 1  C Y  C  ... 
dI
1  CY
2
Y
2
Y
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)
E. 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
W/P
NS
ND
Y
F
Y1
Y2
W1/P2
W1/P1
N2
N1
N3
N
Fall of price → increase of real
wage → if nominal wage rigid
→ unemployment N3 – N2
N2
N1
N
If equilibrium employment N2
→ equilibrium output Y2, lower
than full employment output Y1
F. Liquidity preference and interest
(Keynesian demand for money)
• 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)
–
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:
D
M
 L(Y, i)
P
L(Y1 , i)
i
L(Y2 , i)
Y1  Y2
LY  0 , Li  0
M/P
V.2 Keynesian equilibrium
V.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)
• Equilibrium:
Y = AD
Y = C(Y-T) + I(i-πe) + G
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 exogenous
then
• 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)
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,AD
unintended
investment > 0
unintended
investment < 0
AD
E
45 o
Y1
Y0
Y2
S T
Y
S,I
E
Y1 Y0
I+BD
Y2
Y
V.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, i)
P
– 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
i
i1
i0
MS
P
E
i2
L(Y, i)
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
V.2.3 ISLM
S,I
S+T
E1
Ir1   G
E0
Ir0   G
Y0
Y
Y1
r
r0
E0
E1
r1
IS
Y0
Y1
Y
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
r
ESG
ESM
LM
ESG
EDM
EDG
ESM
EDG
EDM
IS
Y
V.2.4 Graphical interpretation of
Keynesian equilibrium
• 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
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
LM
i
NS
W/P
(W/P)0
i0
IS
Y0
ND
N0
Y
N
Y
Y
F
Y0
Y0
45°
Y0
Y
N0
N
V.3 Underemployment
equilibrium?
“Keynes effect”
• The model above
– In the instantaneous moment of time, model allows for
underemployment equilibrium – see above
– Crucial, „Great Depression“ 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, money cheaper,
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)
LM0
i
NS
W/P
LM1
W0/P0
i0
W1/P1
IS
i1
Y0
Y1
ND
N0
Y
N1
N
Y
Y
F
Y1
Y1
Y0
Y0
45°
Y0
Y1
Y
N0
N1
N
Why - then - lasting high
unemployment?
• Given the reality of Great Depression, Keynes was seeking
for an explanation of long-lasting underemployment
equilibrium
• In the longer-run, nominal wage assumption not realistic
• BUT: 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
V.3.1 Liquidity trap
• When interest so low, that demand for money
becomes infinitely interest elastic (horizontal
– see V.1 F above), then
– Absolute liquidity preference (everybody keeps
money now)
– Interest does not react to changes in supply of
nominal money  liquidity trap
• LM curve becomes for some low value of
interest also horizontal
• Historically, 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
LM0
i
NS
W/P
LM1
(W/P)0
i0
IS
Y0
ND
N0
Y
N
Y
Y
F
Y0
Y0
45°
Y0
Y
N0
N
V.3.2 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
i
LM0
IS
LM1
(W/P)0
(W/P)1
i0
i1
NS
W/P
(W/P)F
ND
Y1
Y0
YF
N0
Y
N1
NF
N
Y
Y
F
Y1
YF
Y1
Y0
YF
Y0
45°
Y0 Y1 YF
Y
N0 N1 NF
N
No „General Theory“
• 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
• Even this conclusion theoretically rebutted, but
there are situations when economies are close
to underemployment equilibrium
– 2008-2009?
• Here is the Keynesian magic for economic
policies
V.4 Keynesian revolution –
economic policies
Legacy for economic policy
• Keynesian theory suffered significant setbacks, BUT
• Two Keynesian conclusions survived till today:
1. Capitalist economy, if left to market forces, can operate
for a long time with substantial involuntary
unemployment
For practical purpose, it is not important whether the economy
might converge towards full employment equilibrium, if this
happens with long delay
2. Insufficient demand is the principal culprit of depression
situation, hence fiscal and/monetary demand stimulation
are the principle tools of short term economic policies
It is the role of the Government to perform this demand
stimulating policies
V.4.1 Fiscal and monetary
stimulation of aggregate demand
Keynes’ policy prescriptions
• His principal focus – the depression situation aggregate demand requires stimulation
• Subsequent simplifications: fiscal and monetary
multipliers in the framework of ISLM model
– Easy illustration of the basic idea, bellow we will do
the same
• Keynes himself – much wider considerations:
– Concern about autonomous components of
consumption and – especially – investments (famous
quote on “socialization of investment”)
– Understanding the role of expectations
– Concern about the political forces and the role of
trade unions
Policy innovations (1)
• Fiscal and monetary policies
• Preference of fiscal policies
– Monetary policy less efficient due to almost
flat LM curve and interest-inelastic investment
in Depression times
• Sharp departure from pre-1930 policy
taboos:
– Accepts budget deficits
– Refuses the crowding-out effect (see above
and bellow), here his views were shared by
many economists, but widely opposed by
British Treasury (Finance Ministry) – the
“Treasury view” problem
Policy innovations (2)
• Refused wage cuts as a remedy for depression
– Both on political and economic grounds
– Political power of trade unions and social tension during the
depression
– In the US, real wages were falling during most of 1930’s,
without any practical impact
– Similar situation observed in many other countries (except
Britain, due to overvalued currency)
• Fiscal multiplier and its effect on growth and
employment
• The policy role of the governments: the theory provides
the tools to increase the product (and employment) by
stimulating aggregate demand
– Government is the only “agent” on the market,
capable to perform this role
V.4.2 ISLM illustration
A. Fiscal policy in ISLM
• Changes of governmental
expenditures
• Changes in tax rates
• Transfers to population (not included in
the simple model here)
• Time aspect
Increase of governmental
expenditures
• Initial equilibrium in E1
• Increase of government expenditure: ΔG  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 E 2
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 L r dY
• Substituting in the first equation for dr from second
equation and after arrangement we have
dY =
1
L
1-C Y-T 1-TY +Ir Y
Lr
• By assumptions
and
dG   dG
LY
0 < C Y-T 1 - TY <1 a Ir
>0
Lr
1 β  α
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
LY
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 Lr  
• Classical model (long term): vertical LM ↔ increase of
governmental expenditures fully crowds out private
investment L r  0 
Tax policies
• Simplification:
TY = tY, 0 <t<1
• Tax multiplier (derived equally as above)
dY =
-C Y-T Y
1-CY-T 1-t  + Ir
LY
Lr
dt = - CY-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.
dG = d  TY
• after arrangement dY = CY-TdY - CY-TdG + dG
• Balanced budget multiplier is equal one.
dY dG = 1
B. Monetary policy in ISLM
• Original equilibrium in E1
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
LM 1
r
LM 2
r1
r2
rA
E1
E2
A
Y1
IS
Y2
Y
Multiplier of monetary policy
• Again, differentiation of both equilibrium
conditions, hence
dG  0 but dM P  0
S
• After arrangements
Ir
Lr
S
S
dM
Ir dM
dY =

= 
>0
LY
P
L
P
r
1 - CY-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
V.4.3 Some crucial differences with
Classical model
• Equilibrium at less than full employment
– and demand does not have to equal supply on
some markets
• Quantitative adjustment, wages and prices
adjust slowly
• Money in not neutral
– It is not a veil
• Demand stimulation is not completely
crowded out
ISLM simplification: AS x AD
• ISLM: price exogenous, in textbook
version consider fixed
• This might have been close to reality
during Great Depression
• Consequent simplification for aggregate
supply (AS) curve
– Horizontal at given price up to full
employment output, then vertical
• Actual output then given by position of
aad curve (by effective demand)
– See next slide
P
AD1
AS
AD 2
P1
Y1
Y2
Yf
Y
V.5 Conclusions
Basics
• Capitalist economy must be steered towards
full employment output by policies, performed
by the governments, stimulating aggregate
demand
• Monetary policies less efficient → crucial role
of fiscal policies
– Multiplier effect
• When output at less than full employment
level, then wages and prices adjust slowly
– Downward wage rigidity as general concept
• At full employment out put level – classical
model applies again
• But …
Keynes’ wrong predictions
(1)
• Estimate if numerical value of fiscal multiplier
– Expectations up to value of 3, in reality just above 1
• Inherent stagnation of the capitalist economy,
APC falls with growing income
– Not proved by the data (Kuznets)
• High interest elasticity of money demand
(reason for liquidity trap) or low interest
elasticity of investment
– Not validated by the data
Keynes’ wrong predictions
(2)
• Expectation about the return of recession
after the end of WWII
– Lack of aggregate demand, either because of lack
of consumer demand (low income and/or falling
APC) or investment demand (after the war economy
stops to generate government military demand)
• Completely refuted by the post-WWII
economic development
– Till today discussion of this was result of the
application of Keynesian recommendations of not
– See next Lectures, but: after WWII, it was mainly
the effect of private investment that filled the gap
between AD and AS
Lasting impact on economic policy
• After Keynes: for more than 3 decades, a
prevailing view was that the governments must
intervene to steer capitalist economy towards
production at full employment
– This remained accepted by many (not only economists),
even by those who criticize Keynes or understand his
fallacies
• After 1970 – a reversal in prevailing views (see
chapters later)
• Today:
– his model is considered as one stage in the
development of macroeconomics
– new Keynesian economics (see later)
Literature to Lecture V
Basic for this Lecture:
• Snowdon, B., Vane, H.: Modern Macroeconomics,
Edvard Elgar, 2005, Ch.1-3 (and the literature
given here)
• Blaugh, M.: Economic Theory in Retrospect, CUP
1997 (5th edition), Chapter 16, namely parts 16.116.5 and 16.19-16.23
Models:
• ISLM model – any intermediate textbook on
macroeconomics
• 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
Appendix
Complete Keynesian model
A.1 Keynesian Model
• Market with goods and services
Y  C I G
Y  FK, N
demand and equilibrium,
assuming AD=AS
supply
• Labor market
N  N D W P 
demand
• Financial markets (money market)
M P  L(Y, i)
demand and equilibrium,
assuming MD=MS
• Components of aggregate demand
C  CY - TY
I  I(i - π e )
consumption function
investment function
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
A.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
P
AD1
AS
AD 2
P1
Y1
Y2
Yf
Y
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 model
Taking total differentials of all equations
1
dY  dC  dI  dG
2
dY  FN dN  FK dK
3
dN 
4
dM dP M
- .  L Y dY  L r dr
P P P
(5)
(6)
FN  dW dP 
- 

FNN  W P 
dC  CY-T 1 - TY dY
dI  Ir dr
IS curve
Substitute (5) and (6) above into (1) to get
1
where


(7) dY   Ir dr  dG


1 - C Y -T 1 - TY 
(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):
dr
1
|IS 
0
dY
I r
If in (7) we assume dY=0 and allow G vary, than
dr
1
- 0
dG
Ir
i.e. with increased G, IS shifts “up and right”; and vice versa
LM curve (2)
dr
1 1
 . 0
dM L r P
i.e. with increasing M, LM shifts to the right, and vice
versa, decreasing M shifts LM to the left;
respectively
dr
1 1
- .
0
dW
L r P.W
i.e. with increasing nominal wage W, LM shifts to the
left, and vice versa, decreasing W shifts LM to the
right
LM curve (1)
From (3) single out dP/P and substitute into (4) to get
 
1  dM M dW  FNN M
(8) dr 
- .
  2 . - L Y dY 

L r  P P W  FN P
 
(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):
dr
1
|LM 
dY
Lr
 FNN M

 2 . - L Y   0
 FN P

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):
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
LM
IS
r0
Y0
Y