Keynes

Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected])

Keynes and the failure of self-correction !"#$%&

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 ............................................ .................................................................. ............................................. ......................... .. 7

2.2.6

The classical dichotomy......................................... ................................................................ .................................... .............7

2.3

Keynes and a nd the failure of self correction .......................... ............................................ ..................10

2.3.1

Introduction .......................................... ................................................................ ............................................ .............................. ........10

2.3.2

The theory of liquidity preference ........................................................... ...........................................................10

2.3.3

Sticky wages and aggregate supply ..................................................... ......................................................... ....13

2.3.4

Monetary impotence ........................................... ................................................................. ..................................... ...............15

2.3.5

Unresponsive investment ........................................... ................................................................. .............................. ........ 15

2.3.6

Liquidity trap ........................................... ................................................................. ............................................ .......................... .... 16

2.3.7

Savings and investment again ............................. ................................................... ..................................... ...............17

2.3.8

The multiplier.................................................. ........................................................................ ......................................... ...................19

2.3.9

The Paradox of thrift ....................................... ............................................................. ......................................... ...................19

2.3.10

Fiscal policy ........................................... ................................................................. ............................................ .......................... .... 21

2.4 Conclusions and discussion .......................................... ................................................................ ......................23 Further reading..................................................... ........................................................................... ........................................ ..................25 Review questions and exercises ................................... ......................................................... ............................................ .......................... ....27 Review questions .......................................... ................................................................ ............................................ ......................... ... 27 Problems ............................................ .................................................................. ............................................ .................................... ..............27 1 15/09/2015


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 1 in coordinating economic activities . 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 confidence shock. The key argument of Keynes is that certain key prices in the economy, particularly wages, are not flexible, so they will not move fast enough to clear markets. Hence, the economy may find itself stuck in an equilibrium that does not correspond to full employment. The economy would be producing below potential for a considerable length of time, 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, Nations , reprinted in Cannan, E. (ed.), 1961, London: Methuen.

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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 the point as simple as possible. 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 ) =

(2.1)

,

In this economy, households are the suppliers of labour and capital, and they also the owners of firms. For simplicity, let’s assume that the labour supply is given: N

S =

*

N

(2.2)

The capital stock is determined by past investments, but the current level is predetermined: 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 2 capital income . 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

2

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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well know optimality condition stating that the demand for labour is such that the marginal product of labour is equal to the real wage: zF N

W =

P

(2.5)

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: =

*

S

w : N

d

=

N

(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, assuming that profit maximization by firms leads to a negative relationship between the optimal investment and the real interest rate, r, as depicted in Figure 2.

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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. 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 make sure 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

(2.9)

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 *

(2.8)

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Equation (2.8) 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

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

(2.9a)

Equation (2.9a) 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 investment3. 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.

3

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”.

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To see this, let’s appeal to the classical theory of the money demand, labelled as the “Quantity theory of money” 4. This theory states that the quantity of real money demanded is proportional to real income:

md

=

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 implies5:

M S P

=

kQ

(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, depicted in Figure 4.

4

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. 5

Note that the quantitative theory of money is not the same as the quantitative equation of money. The quantitative equation is an identity: it basically defines money velocity as 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. A simple rearrangement of the terms in (2.11) reveals that this is the case in our model, with V (1 k ). =

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Then, given the output level (2.8), 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 in Figure 4, prices will increase proportionally from =

. P 0 to P 1

=

Why is that? Because agents want to hold a certain ratio between real money and

transactions, k. If the nominal money increases, this means that people will be holding more money than they want. In result, agents will try to by more goods with the excess money, causing the aggregate 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, its purchasing power, 1 P , has to decrease. W 0

=

Note that the increase in the price level causes nominal wages to increase (from * * P 0 w to W 1 P w ), but real wages are unaffected. This result illustrates the “classical 1 =

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, that produces nominal effects without any impact on the real side of the economy. Figure 4 – Aggregate supply and demand in the classical model

Another view of Figure 4 is the role of prices in correcting any eventual situation of excess supply: if prices were initially at P 1 and money in M 0 , then aggregate demand would fall short aggregate supply (in other angle: there would be an excess demand for money, leading people to buy less goods to accumulate money). The excess supply of goods would translate into a fall in prices and, as prices fell down to P 0 , the economy would return to full employment. 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. 9 15/09/2015


2.3

Keynes and the failure of self correction

2.3.1 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? 6. Keynes argued that prices do not adjust fast enough to ensure the self-correction 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 will produce, because this is the quantity they believe consumers, investors, government and foreigners will plan to buy. By assuming that prices are sticky, Keynes reversed the Say’s Law, contending that “effective demand determines output”, not the other way around. The Keynes argument was mainly descriptive, but in the following we use a simple model to describe his ideas. 2.3.2

The theory of liquidity preference

A central piece in the Keynes theory is the departure from the Quantitative Theory of Money. Keynes maintains the classical idea that the demand for money is driven by

6

Keynes, J.M, 1936. The General Theory of Employment, Interest and Money. London: Macmillan.

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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). 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 intere st rate on bonds declines, people will optimally decide to hold more cash, speculating that the interest rate in the future will increase, driving down the value of bonds. 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 money 7:

& ' # m = m$ i Q ! % " +

d

,

(2.10a)

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: S

M

=

P

m(i Q ) ,

(2.11a)

The fact that money demand depends on the interest rate does not constitutes per se a problem to 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

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.

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8

market, leaving to prices the function of clearing the money market . But Keynes argued that it is the interest rate, not the price level, which adjusts 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. 9 This is basically the adjustment underlying the move from 0 to 1 .

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. 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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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 the 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. 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

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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. This is illustrated in Figure 7, where a price decline from 0 to 1 causes production to decline. 10 The underlying mechanism is the increase in real wages that reduces the demand for labour .

10

A very important case arises when the production function takes the form

Q zN . =

In this case,

profit maximization together with sticky wages (at W ) 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 full capacity at the given price,

so output will be determined by demand only, even if aggregate demand is not vertical.

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Figure 7 – Aggregate supply and demand in the Keynesian world

2.3.4 Monetary impotence

The fact that the interest rate is determined in the money market could be good news: If, due to insufficient demand, prices decreased, all else equal, the real money supply would increase, driving the interest rate down and – by then – consumption and investment up. That is, the aggregate demand should be negatively sloped in Figure 6 (though for different reasons than in the classical model). Also for monetary authorities, the possibility of commanding the interest rate would constitute a powerful mechanism to expand aggregate demand. By expanding money and lowering the interest rate, the central would be able to induce higher levels of consumption and investment, shifting the aggregate demand to the right. The link between changes in the money market and their impact, via interest rate, in the goods market 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 is caught in a liquidity trap. 2.3.5

Unresponsive investment

One reason why the 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 15 15/09/2015


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 to what happens to the interest rate. 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 monetary policy 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. In other words, the aggregate demand curve in Figure 7 would be 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”11. 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), so any further increase in the money supply would be hoarded by people. People would save in the form of cash so printing more money would not deliver a lower interest rate. The adjustment in the money market in this case is described in Figure 6:

11

This case became known as the “liquidity trap”. In our days, the corresponding phenomenon is the fact that the nominal interest rate will hardly fall below zero (“the zero lower bound”).

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Figure 8 – Adjustment in the money market in a Liquidity Trap

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 12 consumption and investment. Hence, the aggregate demand would be vertical . 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

12

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 tend to have a larger propensity to consume 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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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. But in macroeconomics, income effects dominate, making income more important in determining aggregate economic behaviour. Keynes contended that savings depend on income:

S sQ ! a(r ) , with =

a

r

<

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 2.3):

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 7. Figure 9 – Savings and investment in the Keynesian model

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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. 2.3.8

The multiplier

An essential claim in the Keynesian doctrine is that the failure of the monetary transmission mechanism implies that shocks in the economy are amplified, through a “multiplier” effect. The multiplier is obtained solving (2.13) for Q: Q

=

1

s

[a(r ) I ] +

(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, 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 the 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. The underlying reason could be an 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 figures, we display savings as functions of income, 19 15/09/2015


13

rather than as functions of the interest rate . Investment is assumed exogenous and driven by “animal spirits”. 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 decided to reduce their 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 expenditures, deepening the recession14. Note how different this result from what happens in the classical

13

A change in the interest rate would shift the savings curve, but since we are in the liquidity rap such possibility is ruled out. 14

Of course, if entrepeneurs responded to this contractiin in demand with a contraction of investment, the fall in output would be even lower, in a vicious cycle.

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model, where higher savings are a good thing, because they bring more investment and by then higher output in the future. The Paradox of Thrift first appeared in the Fable of the Bees, by Mandaville, but it 15 was popularized by Keynes . 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 the right 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. 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:

S g

=

T ! G

(2.14)

The flow income chart of the closed economy with a government is as follows:

15

Bernard Mandeville (1714), The Fable of the Bees, Private Vices, Publick Benefits, Oxford.

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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 + S G

=

!a (r ) + s Q ! T

+

T ! G

=

I

Solving for output, this implies: Q

=

1

s

[a(r ) ! T (1 ! s)

+

]

I + G

(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 incremental budget balance will be: !Q !G dG dT

=

1

=

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. 22 15/09/2015


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 self-correction mechanism of prices and the role of government in stabilizing the economy. The classical economists believed in the self-correcting role of the market economy. 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: ether 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. 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. 23 15/09/2015


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 and full employment 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. Other important contributions include the theories of consumption, independently developed by Franco Modigliani and Milton Friedman, drawing on a previous work by Irwin Fisher, whereby expectations of future income were formally accounted for as 17 determinants of current consumption , James Tobin and his theories of money and investment, and many others 18 . 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

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 18

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

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Solow popularized the negative inflation-unemployment relationship, and coined it as “Phillips curve”19. Even if these authors questioned the stability of such relationship, there was a period in which policymakers believed they could exploit the trade-off to reduce unemployment at a small cost of additional inflation, well in line with the Keynesian tradition. The Phillips curve became part of the neo-classical synthesis and incorporated in the large macroeconomic simulation and forecasting models, such as those constructed 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, and moreover the Keynesian 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.

19

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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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? =

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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:

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 28

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the wage rate is constant at W=10. Further assume that the money demand is given by md 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. 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 demand and the output supply curve in this market.

0.5 =

10 N

.

Find out the labour

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?

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Keynes

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