Download 2. Keynes and the failure of self-correction

Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected])
2. Keynes and the failure of self-correction
Index:
2. Keynes and the failure of self-correction...................................................................1
2.1
2.2
Introduction........................................................................................2
The Classical view .............................................................................3
2.2.1 Simple model .............................................................................................3
2.2.2 Labour market............................................................................................4
2.2.3 Savings and investment..............................................................................5
2.2.4 Full employment output.............................................................................6
2.2.5 The Say’s Law ...........................................................................................6
2.2.6 The classical dichotomy.............................................................................7
2.3
Keynes and the failure of self correction ...........................................9
2.3.1 Introduction................................................................................................9
2.3.2 The theory of liquidity preference .............................................................9
2.3.3 Sticky wages and aggregate supply .........................................................11
2.3.4 Monetary impotence ................................................................................13
2.3.5 Expectations and unresponsive investment .............................................13
2.3.6 Liquidity trap ...........................................................................................14
2.3.7 Savings and investment again..................................................................15
2.3.8 The multiplier...........................................................................................17
2.3.9 The Paradox of thrift................................................................................17
2.3.10 Fiscal policy ...........................................................................................19
2.4
Conclusions and discussion .............................................................21
Further reading.............................................................................................23
Review questions and exercises...................................................................................24
Review questions .........................................................................................24
Problems ......................................................................................................24
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2.1
Introduction
The term ‘classical economists’ reefers to a group of philosophers in the 18th and 19th
centuries, such as Adam Smith, J. S. Mill, Thomas Malthus and David Ricardo, who
advocated the laisser-faire. Among them, Adam Smith is considered “The father of
Economics”. Adam Smith developed the theory of markets and emphasized the role of prices
in coordinating economic activities 1 . For instance, if demand in a particular industry
increased, then prices and profits should increased, attracting more producers into that
industry. Then, competition would ensure that producers would try to out-price each other
and this would bring prices down again. In the end, profits would return to its normal level,
meaning that consumers would be paying the lowest possible price for the good. The price
system would therefore coordinate the re-allocation of available resources to where they are
needed, all this achieved in a system with selfish agents, and without the need for government
intervention. Classical economists trusted the self-correction mechanism of the market
system (“The invisible hand”).
The classical view was challenged by the advent of the Great Depression. The Great
Depression started in 1929 and defied the understanding that market economies are smoothly
self-regulating. In the context of the Great Depression, John Maynard Keynes proposed a
new theoretical framework, to conclude that an economy would not necessarily be able to
adjust smoothly following an adverse macroeconomic shock 2 . The key argument of the
Keynesian doctrine is that certain key prices in the economy, particularly wages, are not
entirely flexible, so they will not move fast enough to clear markets. In this case, output is
determined by “effective demand”, and the economy may find itself stuck in an
“equilibrium” that does not correspond to “full employment”. Even if output will naturally
return to full employment, the process will be too slow. The economy would be producing
below potential for too long, subjecting citizens to unnecessary pain. Keynes then defended
that governments should implement stabilization policies to prevent or counteract economic
downturns.
The Keynesian attack to the classical thinking is based on some key ingredients: a
new theory implying that the interest rate is determined in the money market instead as in the
1
Smith, A. 1776. The Wealth of Nations, reprinted in Cannan, E. (ed.), 1961, London: Methuen.
2
Keynes, J.M, 1936. The General Theory of Employment, Interest and Money. London: Macmillan.
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market for goods and services; a key role for income in balancing the market for goods and
services; nominal wage stickiness, implying that a fall in prices will drive real wages up,
causing involuntary unemployment. This note briefly reviews the classical doctrine and the
Keynesian attack to classical view.
2.2
The Classical view
The classical view focused on the production side of the economy. The model relies
on two key assumptions, competitive markets and flexible prices, and delivers four main
propositions: 1. The Economy will always be in full employment; 2. Supply creates it’s own
demand (The say’s Law); 3. The classical dichotomy. In the following, we review these three
ideas.
The classical doctrine was not formalized in terms of models. In the following, we do
not present a full model either. Instead, we present some pieces and graphical analysis, to
make the point in a simple way.
2.2.1
Simple model
Consider a closed economy with perfect competition and flexible prices, where
production takes place using two factors of production, labour and capital, according to a
constant returns to scale technology (land could be added, but without any relevant role in
this setup):
Q  zF  N , K  , FN  0 , FNN  0
(2.1)
In this economy, households are the suppliers of labour and capital, and they also the
owners of firms. For simplicity, the labour supply is inelastic:
N S  N*
(2.2)
The capital stock is determined by past investment decisions, but the current level is
pre-determined:
K  K*
(2.3).
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Because households are the suppliers of labour and capital and also the owners of
firms, all production in this economy will return to households, in the form of labour and
capital income3.
Given the income they get, households decide how much to spend in consumption
and how much to save:
QCS
(2.4)
Figure 1 describes the flow income chart of this economy
Figure 1 The flow income chart of a closed economy without government
2.2.2
Labour market
Firms take productivity (z), the output price (P), and the nominal wage rate (W) as
given and choose the employment level so as to maximize profits. This problem delivers the
well know optimality condition stating that the demand for labour is such that the marginal
product of labour is equal to the real wage:
zFN 
W
P
(2.5)
3
Actually, perfect competition together with the fact that the production function
exhibits constant returns to scale implies that labour and capital income will exhaust the
value of output (that is, profits are zero).
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The key assumption in the classical model is that prices are flexible. In the labour
market, the real wage w  W P will adjust to clear demand and supply of labour:
w* : N S  N d
(2.6)
The equilibrium in the labour market is described in Figure 2.
Figure 2: equilibrium in the labour market
2.2.3
Savings and investment
Capital is pre-determined each moment in time, but it shall evolve over time as a
result of two opposing forces, gross investment and depreciation. The level of gross
investment is optimally decided by firms, taking into account the marginal product of capital
and the costs involved in holding capital and in investing. In this section, we abstract from all
these details. Simply, it is assumed that profit maximization by firms leads to a negative
relationship between the optimal investment and the real interest rate, r, as depicted in Figure
3.
By the same token, we abstract from the consumer problem, postulating that savings
are a positive function of the interest rate: if the interest rate increases, people will transfer
more consumption to the future, through savings and asset accumulation.
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Figure 3 – Savings and investment in the classical model
The equilibrium in the market for loanable funds is described in Figure 3. Because the
real interest rate is assumed to be flexible, it will adjust to ensure that savings and investment
are equal:
r* : S  I
(2.7)
The fact that savings are equal to investment implies that demand for goods will be
equal to supply. To see this, just combine the equilibrium condition (2.7) and the accountancy
equation (2.4) to obtain:
CI Q
(2.8)
Equation (2.9) states that the market for final goods is in equilibrium. When (2.7)
holds, (2.9) holds and vice-versa.
2.2.4
Full employment output
Because prices are flexible, there will be full employment of labour and capital.
Hence, output will be the maximum feasible, given the technology and resource constraints:
Q*  zF N * , K * 
(2.9)
Equation (2.9) states that output in this economy is entirely determined on the supply
side. Thus, for instance, if the labour-supply increases or productivity increases, employment
and output will expand.
Also note that a higher savings rate, by causing the interest rate to decline, leads to
more investment and hence to more output in the future. In the classical model, savings are
expansionary.
2.2.5
The Say’s Law
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In the classical model, the output level is entirely determined on the supply side.
Combining (2.9) with (2.8), one obtains
C  I  Q*
(2.8a)
Equation (2.8a) illustrates the Say’s Law: The Say’s law states that “aggregate
production necessarily creates an equal quantity of aggregate demand”. For instance, a
technological improvement or an increase in the size of the work force will give rise to an
output expansion and thereby to a higher income and demand for consumption and
investment4.
2.2.6
The classical dichotomy
In the classical model, because prices are flexible, money is neutral: a monetary
expansion does not impact on output.
To see this, let’s appeal to the classical theory of the money demand, labelled as the
“Quantity theory of money”5. This theory states that the quantity of real money demanded is
proportional to real income:
m d  kQ
(2.10)
The underlying assumption is that people need money for transactions (with the
volume of transactions being measured by real income, Q), and that the quantity of money
needed per transaction is a fixed proportion, k.
The nominal money supply M S is determined by the central bank. The equilibrium in
the money market then implies6:
4
The Say’s Law owes its name to its author, the French economist Jean Batiste Say (in 1803). It is also
known as “The Law of Markets”.
5
The theory was proposed by Newcomb, S. (1893), in "Has the standard gold dollar appreciated?",
Journal of Political Economy 1, 503-512, but popularised by Irwin Fisher, in Irving Fisher (1911), The
Purchasing Power of Money, New York: Macmillan.
6
Note that the quantitative theory of money is not the same as the quantitative equation of money. The
quantitative equation is an accounting identity: it basically defines money velocity as equal to the ratio between
nominal output and the quantity of money, that is, V=PQ/M. The quantitative theory postulates that money
velocity in the quantitative equation is constant over time. A simple rearrangement of the terms in (2.11) reveals
that this is the case in this model, with V  1 k .
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MS
 kQ
P
(2.11)
Thus, whenever the volume of desired transactions increases, the demand for money
will increase in the same proportion.
Given the nominal money supply, the equilibrium in the money market implies a
negative relationship between output and prices. This negative relationship describes the
classical Aggregate Demand curve (AD), depicted in Figure 4. The Aggregate Supply (AS) is
given by full employment output (2.9) and is vertical because it is unaffected by nominal
variables.
Then, given the output level (2.9), equilibrium in the money market (2.11) implies a
proportional relationship between money and prices. Thus, for instance, the supply of money
increases from M S  M 0 to M S  M 1 , causing an expansion in aggregate demand as
depicted in Figure 4 from AD to AD’, prices will increase proportionally from P0 to P1 , from
point 0 to point 1. Why is that? Because agents want to hold a constant ratio, k, between real
money and transactions. This, if the supply of nominal money increases, this means that
people will be holding more money than they desire. In result, agents will try to get rid of
money, buying more goods with the excess money, causing the demand for goods to increase.
Since the supply of goods is fixed (determined on the supply side), then prices have to
increase. In other words, because the availability of money increased, the purchasing power
of money, 1 P , had to decrease.
Note that the increase in the price level causes nominal wages to increase (from
W0  P0 w* to W1  P1w* ), but real wages are unaffected (there is no change in Figure 2). This
illustrates the “classical dichotomy”: In the classical model, the real variables, such as output,
employment and relative prices, are determined in the real side of the economy. Money is
only a veil, which produces nominal effects without any impact on the real side of the
economy.
Figure 4 – Aggregate supply and demand in the classical model
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An important feature of the classical model is the role of prices in correcting any
eventual situation of excess supply or demand: Suppose that in Figure 4 prices were initially
at P1 and money in M 0 (point 2). In that case, the quantity of goods demanded would fall
short aggregate supply. In other angle: there would be an excess demand for money, leading
people to buy fewer goods to accumulate money. The excess supply of goods would translate
into a fall in prices and, as prices fell down to P0 , the economy would return to full
employment (point 0). As we will see next, Keynes argues that this self-correction
mechanism fails, in a World where aggregate demand is vertical and aggregate supply is
positively sloped.
2.3
2.3.1
Keynes and the failure of self correction
Introduction
During the Great Depression, the high unemployment and the failure of selfcorrection challenged the classical doctrine. Keynes asked: if supply creates its own demand,
why are we having a depression?.
Keynes argued that the price mechanism is not fast enough to ensure the selfcorrection of the economy in a reasonable time. Keynes contended that in the short term
prices and wages are “sticky”, which together with some other assumptions, implies that the
economy may be stuck in an equilibrium that is not full employment.
Keynes distinguished “full employment output”, driven by technology and resources
(just like in the classical model), from “equilibrium output”, which is the quantity of goods
firms actually produce each moment in time. The later is driven by the firms perception of
what consumers, investors, government and foreigners are planning to buy. This is a critical
reversal of the classical doctrine: Keynes reversed the Say’s Law, contending that “effective
demand determines output”, not the other way around.
The Keynes argument was mainly descriptive, but his main ideas can be sketched out
in a simple analytical framework.
2.3.2
The theory of liquidity preference
A central piece in the Keynes doctrine is the departure from the Quantitative Theory
of Money. Keynes assumed that the demand for money depends on the interest rate, opening
a channel through which monetary policy affect interest rates and thereby consumption and
investment.
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Keynes maintains the classical idea that the demand for money is driven by
transaction purposes, so it shall increase when the volume of transactions increases, but
contended that the relationship between money and transactions is not linear: it may be
destabilized by confidence factors, or by changes in the opportunity cost of holding money
(the yield of nominal bonds). This view is summarized by equation (2.10a):
  
m d  m i,Q,.. 


(2.10a)
Money shares with bonds the property that it is a nominal asset, but it differs from
bonds in two aspects: it is more liquid (it provides liquidity services) and pays no return.
Hence, when the interest rate on bonds increases, people will reduce the fraction of wealth
they hold in the form of money, switching to bonds. When the interest rate on bonds declines,
people will optimally decide to hold more cash, reducing their transaction costs. Formally,
Keynes allowed the velocity of money to be an increasing function of the nominal interest
rate, introducing a “speculation motive” in the demand for money7:
Of course the departure from a linear relationship between money and transactions
presumes that the same volume of transactions can be achieved with less money (that is,
velocity increases). The rationale is that holding less money people will face higher costs of
transacting. But people may be able to accept these higher costs (dealing with a given volume
of transactions with less money) when the opportunity cost of holding money increases.
When the money demand takes the form (2.10a), the equilibrium in the money market
is as follows:
MS
 mi, Q 
P
(2.11a)
The fact that money demand depends on the interest rate does not challenge by itself
the macroeconomic adjustment: if the interest rate was determined in the market for savings
and investment (like in Figure 3), then it would be exogenous to the money market, leaving
to prices the function of clearing the money market8. So, one needs an additional ingredient.
7
Keynes also argued that the demand for money increases in periods of high uncertainty, because
money is a safer asset than bonds. But in the model we ignore this extra term.
8
The fact that the demand for money depends on the nominal interest rate while savings and
investment depend on the real interest rate poses an analytical problem to this model. The nominal interest rate
relates to the real interest rate as follows: i  r   , where  is the inflation rate. In the following, let’s
assume that the inflation rate is constant, implying that the difference between nominal and real interest rates is
irrelevant.
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The key point in the Keynesian argument is that prices are sticky, and hence they will not
adjust to clear the money market. Then, if prices fail to clear the money market, it will be
interest rate the one adjusting to clear the money market. This is illustrated in Figure 5: in the
figure, the expansion of nominal money supply implies a decline in the nominal interest rate
from 0 to 1.
The underlying mechanism is as follows: when the money supply increases, at the
given output and interest rate, there will be an excess supply of money. People holding
money in excess will try to buy bonds. Since the economy is closed and the supply of bonds
is given, the excess demand for bonds will drive its prices up, and the implied yield (i) down.
This is basically the adjustment underlying the move from 0 to 19.
Figure 5 – Adjustment in the money market following a monetary expansion
2.3.3
Sticky wages and aggregate supply
A second line of attack of Keynes to the classical thinking is that wages are sticky and
stickier than prices. Thus, whenever prices decline, real wages will increase, giving rise to
involuntary unemployment.
9
Often, a monetary expansion comes thorugh an open market operation, whereby the central bank buys
bonds from the public in exchange for newly created money. Such move would cause the price of bonds to
increase and hence the implied yield to decrease, just as described in Figure 5. In that case, it is the central bank
attempt to swap bonds for money that causes the interest rate to decline, inducing individuals to hold more
money.
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This is illustrated in Figure 6, which replicates the labour market described in Figure
2, with the difference that now nominal wages are fixed. Thus, if by chance prices are such
that real wages are at the market clearing level, full employment will be me (point 0). But if
wages fail to decline in the same proportion as prices, then real wages will increase and the
economy will meet a situation of involuntary unemployment: at the prevailing real wages,
workers will desire to work more than what firms are willing to hire.
Figure 6 – Nominal wage stickiness in the Keynesian world
A corollary of this is that the aggregate supply will now become a positive function
of the price level: holding constant the use of capital, the negative relationship between prices
and employment in Figure 6 translates into a positive relationship between prices and output
in Figure 7. Thus, when prices fall (say from point 0 to point 1), output this will fall, because
real wages are increasing and firms hire fewer workers.
Figure 7 – Aggregate supply and demand in the Keynesian world
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A very important textbook case arises when the production function takes the form
Q  zN (that is FNN  0 ). In this case, profit maximization together with sticky wages (at
) imply an aggegate supply that is flat at the level P  W z . In this case, firms will be able
to supply any amount of output until Q* at the given price. This case is known as of
Keynesian unemployment and the corresponding horizontal AS is labelled the Keynesian
supply curve.
W
2.3.4
Monetary impotence
The fact that the interest rate is determined in the money market could be good news.
To see this, consider a world where the interest rate is determined in the money market, and
the price level is determined so as to equal aggregate demand and supply in the market for
goods.
In that world (which constitute the general case in the IS-LM analysis), in face of an
insufficient demand for output, prices would eventually end up decreasing. All else equal, the
real money supply would increase, driving the interest rate down and – by then –
consumption and investment up. Hence, the aggregate demand in Figure 7 should be
negatively sloped (though, for different reasons than in the classical model), rather than
vertical. In that world, monetary authorities have a powerful tool to influence output: by
expanding money and lowering the interest rate, the central would be able to induce higher
levels of consumption and investment, shifting the (downward sloping) aggregate demand to
the right. Since the AS curve is positively sloped (or even horizontal, in the extreme case in
which FNN  0 ), output would expand.
This link between changes in the money market and their impact on a downward
sloping Aggregate Demand, via interest rate is known as the “Keynes effect”. Ironically,
however, Keynes contended that the Keynes effect was absent in the Great Depression. For
two reasons: (a) consumption and investment were not responding to the interest rate; (b)
even if they did, the interest rate would not decline, because the money market was caught in
a liquidity trap. This argument is reviewed in the following two sections.
2.3.5
Expectations and unresponsive investment
According to Keynes, one reason why monetary policy would fail to expand
aggregate demand is that the interest rate plays a little role in influencing consumption and
investment: Economic agents are human beings, and hence driven by “animal spirits”
(changes in the collective mood that have little to do with rationality). Thus, whenever the
collective mood is of anxiety regarding the future, people will refrain from consuming and
investing. When, in contrast, people become more optimistic, tilted by some “irrational
exuberance” then consumption and investment will increase, irrespectively as to what
happens to the interest rate.
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Keynes contended that savings are primarily a function of income and not very
responsive to the interest rate (“People don’t change their standard of living simply because
the interest rate changes a few points”). By the same token, investment is much more
influenced by the sate of business expectations than by the interest rate.
If investment and consumption do not respond to a fall in interest rate, then a
monetary policy that successfully expands the money supply and lowers the interest rate will
not be capable of shifting the aggregate demand to the right.
In plus, any fall in the price level, even if causing real money balances to increase and
the interest rate to decline, would not have any impact on consumption and investment. This
is one reason why in the pure Keynesian doctrine the AD curve is vertical.
2.3.6
Liquidity trap
A second reason for the aggregate demand to be vertical (and for monetary policy to
be impotent) was a phenomenon specific to the Great Depression, labelled as the “liquidity
trap”10.
Keynes argued that, in the specific context of the Great Depression, the link between
the money demand and the interest rate became dysfunctional: at the time, the interest rate
was already so low (meaning: the prices of bonds were so high) that any further expansion in
the money supply by the central bank would not induce people to buy more bonds: people
would be afraid of suffering future capital losses (when interest rates started increasing the
prices of bonds should fall), so any further increase in the money supply would be hoarded by
people. People would save in the form of cash and henceforth printing more money would
not deliver a lower interest rate.
The adjustment in the money market in this case is described in Figure 8:
Figure 8 – Adjustment in the money market in a Liquidity Trap
10
This case became known as the “liquidity trap”. In our days, the corresponding phenomenon is more
commonly labour as the “the zero lower bound”, owing the name to the fact that the nominal interest rate will
hardly fall below zero.
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The liquidity trap implies that the central bank is impotent to expand aggregate demand. It
also implies that a decline in the price level leading to an increase in real money balance
would not be capable of inducing a decline in the interest rate and an expansion of
consumption and investment. Hence, the aggregate demand would be vertical11.
2.3.7
Savings and investment again
The main implication of the liquidity services theory, together with the assumption
that prices are sticky is that the interest rate is determined in the money market. But if the
interest rate is determined in the money market, how will the goods market equilibrium (as
implied by the equality between savings and investment) hold?
In order to achieve the equilibrium between savings and investment, Keynes
emphasized the role of income as determinant of savings. In microeconomics, relative price
effects matter, he argued. But in macroeconomics, income effects dominate, making income
more important in determining aggregate economic behaviour.
Keynes contended that savings depend on income:
11
Actually, Keynes goes even further, sugesting that the aggregate demand can be positively sloped.
There are two reasons for this: first, when prices decline, people may expect further decreases in the price level,
and will respond postponing consumption (the “expectations effect”); second, a fall in the price level will cause
the real value of bonds to increase, leading to a “redistributive effect” from debtors to creditors. Since debtors
spend more on extran income than creditors, the “redistributive effect” will also transalte into a positive
relationship between the price level and aggregate spending. The evidence for the Great Recession is that,
betweem 1929 and 1933, the cummulative fall in prices was about 24%.
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S  sQ  ar  , with ar  0
(2.12)
In (2.12), the marginal propensity to save, s, measures the impact on savings of a unit
increase in income.
The equilibrium between savings and investment in the Keynesian model is described
in Figure 9. Suppose that the interest rate, as determined in the money market, caught in the
liquidity trap, is too high to make planned savings and investment equal (point 0).
In that situation, we will have:
sQ*  ar   I
(2.7a)
Implying (from 2.4):
C  I  ar   1  s Q*  I  Q*
(2.9b)
Thus, the (vertical) aggregate demand will fall short full employment output. This
situation is described by point 1 in Figure 9.
Figure 9 – Savings and investment in the Keynesian model
Keynes contented that in such a situation, firms would reduce production: if the
supply of goods exceeds the demand for goods, then firms will start accumulating
inventories. Since firms do not profit with unsold production, they will reduce output until
the goods market equilibrium is met:
C  I  a r   1  s Q  I  Q
(2.13)
All in all, output will contract, adjusting to the level determined by aggregate demand.
This is illustrated by point 1 in Figure 9 and in Figure 7.
In the Keynes model, the Say’s Law holds in reverse.
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2.3.8
The multiplier
An essential claim in the Keynesian doctrine is that the failure of the monetary
transmission mechanism implies that shocks to the economy are amplified, through a
“multiplier” effect. The multiplier is obtained solving (2.13) for Q:
Q
1
ar   I 
s
(2.13a)
For instance, with a saving rate equal to 20%, the multiplier will be equal to 5. Thus,
if investment increases by one unit of output, output will expand by five units.
2.3.9
The Paradox of thrift
An important feature of equation (2.13) – or (2.13a) – is that output adjusts so that the
level of planned savings equals investment. That is, investment is exogenous while aggregate
savings are endogenous. Thus, whatever will be the desire for savings by individuals in the
society considered in isolation, it will be impossible to change the level of aggregate savings.
To see this, suppose that in this economy people decided to save more, for each level
of the interest rate. One possible reason could be excess leveraging: household, being too
indebted, decided to save a larger proportion on their income, in order to start repaying their
debts.
The implications of an increase in the marginal propensity to save in the Keynesian
model are illustrated in Figure 10. In this figure, we display savings as functions of income12.
Investment is assumed exogenous and driven by “animal spirits”.
12
A change in the interest rate would shift the savings curve, but since we are in the liquidity rap such
possibility is ruled out.
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Figure 10 – The Paradox of Thrift
The initial equilibrium corresponds to point 0, with the marginal propensity to save
equal to s. As implied by equation (2.13), the level of output is such that aggregate savings
are equal to the exogenous investment level.
The equilibrium after the increase in the marginal propensity to save is described by
point 1: given the investment level and the initial level of output, the change in the slope of
the savings curve creates a situation of excess savings over investment – or which is the
same, of excess supply of goods relative to demand – so firms start reducing production. In
the new equilibrium, the level of output is lower and exactly the needed to make aggregate
savings equal to exogenous investment.
In the end, the attempt of households to save more resulted in a situation where
aggregate savings did not increase. The only implication was a decrease in expenditure,
deepening the recession. Note how different this result is from what we saw in the classical
model, where savings are a good thing, because they bring more investment and by then
higher output in the future. Now, a higher saving rate depresses demand and output resulting
in a lower income.
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To make the case even darker, assume that investment was driven by expected
changes in demand conditions. This is the theory of the accelerator, put forward by early
economicts like J. M. Clark13:

I t  I  v Qte1  Qt

In that case, the observed contraction in aggregate demand could weel raise fears
among investors (“animal spirits”), causing aggregate investment to decline. A further fall in
income would then, in a vicious cycle. The accelerator theory is well at the hearth of the
keynesian business cycle theory 14.
The Paradox of Thrift first appeared in the Fable of the Bees, by Mandaville, but it
was popularized by Keynes 15 . The Paradox of Thrift is an example of the Fallacy of
Composition: the fallacy of composition arises when one infers that what is true for
individual agents is true for the aggregate economy. Thus, while individual thrift may be a
good thing from the individual point of view, collective thrift may be bad for the economy.
The fallacy of composition implies that using representative agents to characterize the all
economy does not always lead to accurate conclusions.
2.3.10 Fiscal policy
The main normative implication of the Keynesian doctrine is that, if the private sector
is not prepared to spend, then the government should do it instead.
13
This is the theory of the accelerator, first put forward by J. M. Clark [Clark, 1917, Business
acceleration and the law of demand: a technical factor in economic cycles, Journal of Political Economy,
March. In terms of our model, suppose that the production function (2.1) is a Cob-Douglas, Q  zK  N 1  , and
that capital depreciates at the rate  each year. In this case, profit maximization implies the following demand
for capital  Q K     r , where r is the real interest rate. Assuming that the right hand side is constant, the
change in capital stock each year (net investment) will be equal to K     r Q , implying a gross
investment equal to I     r Q  K .
14
The interaction between the investment multiplier and the accelerator was explored by John Hicks
[Hicks, J,. 1939, “Interactions between the multiplier analysis and the principle of acceleration, Review of
Economics and Statistics, May]. More recently, Olivier Blanchard said that the accelerator principle is still
alive as an important explanation of the business cycle [Blanchard, O., 1981, What is left of the multiplier
accelerator?, American Economic Review, May].
15
Bernard Mandeville (1714), The Fable of the Bees, Private Vices, Publick Benefits, Oxford.
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The model above can be easily extended to include a government that purchases
goods from firms and taxes the households to finance the policy.
The difference between revenues (T) and expenditures (S) are government savings:
Sg  T  G
(2.14)
The flow income chart of the closed economy with a government is as follows:
Figure 11- The flow income chart in a closed economy with a government
In this case, the household disposable income will be equal to Q-T, and the (private)
saving function will be:
S P  ar   sQ  T 
(2.12a)
In this extended version of the model, equilibrium is met when total savings (private
and official) equal investment, that is
S P  SG  ar   sQ  T   T  G  I
Solving for output, this implies:
Q
1
ar   T 1  s   I  G 
s
(2.13b)
The multiplier of government spending is the same as that of investment:
Q 1

G s
If the increase in government spending is fully financed with an increase in taxes,
then the multiplier of the incrementally balanced expansion will be:
Q
G
1
dG dT
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Thus, in the Keynesian framework (remember, we are in the liquidity trap), the
government will be able to drive the economy to full employment, even with a balanced
budget policy. Note however that in this later case, the extra output being produced
corresponds to government expenditure: the household sector will not be consuming more.
Still, the level of employment in the economy will be higher.
The stabilizing role of the government is illustrated in Figure 12.
Figure 12- A fiscal expansion in the Keynesian model
2.4
Conclusions and discussion
In this note, we confronted two opposing views regarding the functioning of a market
economy. The classical economists believed in the self-correcting role of the price
mechanism. In the classical economy, output is determined on the supply side of the
economy and is always at full employment, so there is no role for government in stabilizing
the economy. In the classical framework, real variables are determined independently of the
price level. Only relative prices matter. Money only produces nominal effects.
The Keynesian attack to the classical doctrine was launched in two fronts: first,
problems in aggregate supply: wages are slower to adjust than prices, implying that during a
depression the fall in prices will translate into higher real wages and unemployment. Second,
problems in aggregate demand, resulting from the failure of the transmission mechanism:
either because of the liquidity trap, or because consumption and investment fail to respond to
the interest rate, Keynes contended that the equilibrium in the goods markets is achieved by
changes in income, rather than by adjustments in the interest rate. Whenever savings are too
high, aggregate demand will fall short aggregate supply, implying that firms will produce
less. In the Keynesian model, effective demand determines supply, not the other way around.
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The contributions of Keynes changed the course of macroeconomics. Many of his
basic ideas, such and the aggregate demand and supply and the distinction between
equilibrium output and full employment output are still and the centre of modern
macroeconomics. But even if his thinking was path-breaking, there were many missing
issues. First, the post-war economic conditions, with full employment and rising inflation,
urged economists to adapt the Keynesian ideas to contexts other than the Great Depression.
Second, a follow up work was needed to formalize the theory and make it consistent with the
other pieces of economic thinking. The attempt to merge the Keynesian ideas with those of
the earlier economist, and the refinements that this effort allowed gave rise to a new
consensus that was labelled the “neo-classical synthesis”.
Among the main contributions, John Hicks (1937) and later Alvin Hansen launched
the IS-LM model 16 : the Keynesian model relies on the liquidity trap, which basically
segments the money market and the goods market. In normal times, however, monetary
expansions drive the drive the interest rate down, inducing expansions in aggregate demand
and in income that then feed-back to the money market, via transactions demand for money.
This interaction could only be solved in a simultaneous equation system that became known
as the IS-LM model. In light of this model, the Keynesian equilibrium is a special case.
Other important contributions include the theories of consumption, independently
developed by Franco Modigliani and Milton Friedman, drawing on a previous work by Irwin
Fisher, James Tobin and his theories of money and investment, and many others17. In 1958,
the neo-Zealand economist William Phillips, discovered an empirical regularity in the UK,
consisting in a negative relationship between changes in nominal wages and unemployment.
Two years later, Paul Samuelson and Robert Solow popularized the negative inflationunemployment relationship, and coined it as “Phillips curve”18. Based on these findings, there
16
Hicks, J. R. (1937). "Mr. Keynes and the ‘Classics’: A Suggested Interpretation". Econometrica 5
(2): 147–159. Hansen, A. H. (1953). A Guide to Keynes. New York: McGraw Hill
17
Fisher, I., (1930), “The Theory of Interest”, McMillan. Modigliani, Franco, 'The Life Cycle
Hypothesis of Saving, the Demand for Wealth and the Supply of Capital, Social Research, (1966: summer).
Extracted from PCI Full Text, published by ProQuest Information and Learning Company. Friedman, M.
(1956). "A Theory of the Consumption Function" (PDF). Princeton, NJ: Princeton University Press. Tobin,
James (1956). "The Interest-Elasticity of Transactions Demand for Cash," Review of Economics and Statistics,
38(3). Tobin, James (1969). "A General Equilibrium Approach to Monetary Theory". Journal of Money, Credit,
and Banking 1.1 (1): 15–29
18
Phillips, A. W. (1958). "The Relationship between Unemployment and the Rate of Change of Money
Wages in the United Kingdom 1861-1957". Economica 25 (100): 283–299. Samuelson, Paul A., and Robert M.
Solow. 1960. “Analytical Aspects of Anti ‐ Inflation Policy,” American Economic Review Papers and
Proceedings 50: May, no. 2, 177‐94.
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was a period in which policymakers believed they could exploit the trade-off between
inflation and unemployment to reduce unemployment at a small cost of additional inflation.
The Phillips curve was well in line with the Keynesian tradition, and was integrated in the
large macroeconomic simulation and forecasting models, such as those developed by
Lawrence Klein for the US, in the early 1960s.
For three decades, the Keynes’ policy recommendations became mainstream across
the world. During the 1950s and the 1960s, economists and policymakers believed that
stabilization policies (specially the fiscal policy) were a powerful tool to mitigate business
cycles. But in the 1970s, after two oil shocks, the world met a new phenomenon coined as
“stagflation”, that is, a combination of inflation and unemployment. This particular
combination of symptoms was not accounted for in the Keynesian doctrine, nor by the
Phillips curve. Moreover the mainstream prescription of expanding fiscal and monetary
policies did not succeed in overcoming the crisis: on the contrary, it gave rise to more
inflation. The established believe that government intervention could be used to influence
employment and output and reduce the amplitude of the business cycle without creating
inflation became seriously into question.
Further reading
Robert Gordon, Macroeconomics, 9th edition: Chapter 7.8-7.10.
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Review questions and exercises
Review questions
1. Keynes attacked the classical view of self-correction in two fronts: failure of the
“transmission mechanism” and nominal wage rigidity. Explain the arguments.
2. In a depressed and leveraged economy, price deflation is stabilizing or destabilizing?
Why?
3. Referring to the article from Paul Krugman (“How did economists...”), explain how
the Great Capitol Hill Baby-sitting Co-op entered into crises. How does this example
relate to monetary theory? Is this a general case?
Problems
4. (The Classical model) Consider a closed Classical) economy with no government,
where the representative production function takes the following form Q  zN .
Further assume that the labour supply is constant at N S  100 , and that prices and
wages are fully flexible. Workers are the only consumers in this economy.
a) Assuming that firms maximize profits, find out the labour demand in this economy.
Display the equilibrium in the labour market in a graph, assuming that z  10 . What
will be the equilibrium output in this case?
b) Now assume that the demand for real money was given by m d  Q , and the supply of
nominal money was M S  1000 . (b1) Describe the equilibrium in the money market;
(b2) Which theory underlies this specification?
c) Represent in a graph the aggregate demand and the aggregate supply in this economy,
and find out the equilibrium prices and nominal wages. Explain what will happen to
prices and wages if the supply of money increased to M S  2000 . Which proposition
is being illustrated here?
d) Finally, assume that productivity increased to z  20 . What would be the impact on
production, income and consumption? Which Law is being illustrated here?
5. (Money Market) Point 0 in the following figure describes the initial situation in a
money market. Assuming that the nominal money supply increases from M0 to M1,
how will the new equilibrium look like, in light of the:
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a) The classical model
b) The Keynesian model with liquidity trap
c) The conventional IS-LM model
Explain the adjustment process in each case.
6. (The Paradox of Thrift). Consider a (Keynesian) economy without government,
where Investment is basically exogenous and the consumption function is given by
C  a  1  s Y .
a) Using the equality S=I, find out the expression for the equilibrium level of income in
this economy. What is the expression for the multiplier?
b) Suppose that all agents in this economy were largely indebted, so they decided to
increase their propensity to save. Would this deliver more total savings in the
aggregate? Explain, with the help of a graph.
c) Now suppose that investors, driven by “animal spirits” responded to the fall in output
reducing current investment. How would the economy adjust?
7. (Transmission mechanism) Consider a closed economy with no government, where
the representative production function takes the following form Q  10 N . Further
assume that the labour supply is constant at N S  10 . The output price is flexible, but
the wage rate is constant at W=10. Further assume that the money demand is given by
m d  Q 10i , the consumption function is C  20 10r   0.75Q , and planned
investment responds to the interest rate according to I  5 10r  . In this economy,
there is no inflation, so the nominal and real interest rates are the same.
a) Assuming that firms maximize profits, find out the aggregate supply function in this
economy.
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b) Using the equilibrium in the money market and the equality between savings and
investment, find out the expression of aggregate demand in this economy. Explain its
slope in the (P,Q) locus.
c) Suppose that the money supply was equal to M=81. Would the economy be in full
employment in that case? How much would be investment and consumption?
d) Could monetary policy be used to drive the economy to full employment? What
would happen to consumption and investment?
e) Could monetary policy be used to expand the economy above full employment?
8. (Keynesian model) Consider a Keynesian economy in a liquidity trap and where
nominal wages are stuck in W=1. Prices are however flexible. Investment is
exogenous and the consumption function is given by C  1  s Q  T , with s=0.2.
Initially, there are no taxes nor government spending.
a) Assume that, due to a confidence shock, investment is initially I  20 and then falls
to I  15 . Compute the equilibrium output before and after the shock. Explain how
the aggregate demand shifts, in the (Q,P) locus.
b) Now assumes that the supply side of the economy is described by a labour force equal
to N S  100 and perfect competition in the output market, being the production
function of the representative curve given by: Q  10N . Find out the labour
demand and the output supply curve in this market.
0 .5
c) Describe what happens in the labour market and in the output market following the
confidence crises. In particular, explain the change in prices, real wages, employment
and output. Use graphical analysis.
d) Finally, consider the possibility of the government intervening in this economy, with
a balanced budget, that is, with T=G>0. Would the policy bring the economy to full
employment?
9. Consider a closed economy in a liquidity trap, where P=1 and natural output is
Q *  100 . In this economy, the consumption function is given by C  1  s Q  T  ,
and the government budget is always balanced, that is T  G . Initially, G=0.
a) Assume that Investment is equal to I  20 . Explain how this economy will adjust to
an increase in the saving rate from s=0.2 to s=0.25. In particular, find out: (a1) The
level of output before and after the shock; (a2) aggregate savings before and after the
shock. (a3) Represent in a graph. (a4) Explain what could have drive the increase in
the saving rate. (a4) Explain what is this exercise trying to capture.
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b) Assume now that investment, instead of exogenous, was determined according to
I  20  0.125Q  Q *  . (b1) Explain this theory. In that case, how would the
economy adjust to the increase in the saving rate from s=0.2 to s=0.25? In particular,
find out: (b1) the level of output before and after the shock; (b2) aggregate savings
before and after the shock. (b3) Explain what is this exercise trying to capture.
c) Finally, assume that the government in this economy wanted the economy to operate
in full employment permanently. Departing from (b), what would be the optimal
policy rule, for G as a function of s? Exemplify when s=0.2 and s=0.25.
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