when expansionary fiscal policy is contractionary: a neoklassikal scenario

8
When Expansionary Fiscal Policy is Contractionary: A Neoklassikal Scenario* WILLIAM COLEMAN The Research School of Economics, The Australian National University, Canberra, Australia The paper presents a simple theoretical account of how an increase in government purchases may reduce total employment. It is shown that in a ‘neoklassikal’ model – in which utility maxi- mising consumption choices are combined with a fixed-coefficient technology – an increase in government purchases will reduce the demand for labour at the given wage rate. The reasoning turns on the link between optimising consumption behaviour and employ- ment in the investment sector. An increase in G will (as a matter of arithmetic) make current consumption scarcer relative to future consumption; and thereby reduce the valuation of future consump- tion in terms of current consumption. As labour is valued accord- ing to its contribution to future consumption (through its contribution to capital formation), it follows that an increase in G will reduce the wage at any given volume of employment. I Introduction The Keynesian doctrine of a positive govern- ment spending multiplier has been subject to a manifold critique, both empirically and theoreti- cally. While much of this criticism is under- pinned by a confidence in the ‘self-correcting’ properties of the economy, criticisms of the effectiveness of government spending in stimu- lating employment have long been pursued within a framework of involuntary unemployment. Some of these critiques invoke the implications of monetary equilibrium; (interest rate crowding out; or, in the open economy, exchange rate crowding out, Fleming (1962) and Mundell (1963)); others invoke capital market equilibrium (see, for example, Makin (2009) and the account of Peden (1984) of the ‘Treasury View’ of the 1930s); while another influential path of criticism has invoked the ‘rational consumer’ (the perma- nent income hypothesis (Friedman, 1957) and Ricardian equivalence (Barro, 1974)). 1 This paper articulates another avenue of criti- cism of the government spending multiplier. This path of criticism reaches further than that reached by earlier critiques. For the present paper’s cri- tique, contends that government spending will actually be counter productive; it will reduce employment. * The author wishes to record the paper’s signifi- cant debt to the reports of two anonymous referees. The usual disavowals apply. Titles are not subject to copyright, which is all the more reason to acknowl- edge my evident obligation to Makin (1998). JEL classifications: E24, E12 Correspondence: William Coleman, The Research School of Economics, The Australian National University, Canberra, ACT 0200, Australia. Email: [email protected] 1 The critique by way of the rational consumer is not restricted to the efficacy of tax cuts. The perma- nent income hypothesis suggests a high-marginal pro- pensity to save, and so a low government spending multiplier. Ricardian equivalence treats every increase in G as if accompanied by an equal increase in T, leaving the impact of G only a matter of the (small) balanced budget multiplier. THE ECONOMIC RECORD, VOL. 86, SPECIAL ISSUE, SEPTEMBER, 2010, 61–68 61 Ó 2010 The Economic Society of Australia doi: 10.1111/j.1475-4932.2010.00678.x

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* The author wishes to record the paper’s signifi-cant debt to the reports of two anonymous referees.The usual disavowals apply. Titles are not subject tocopyright, which is all the more reason to acknowl-edge my evident obligation to Makin (1998).

JEL classifications: E24, E12Correspondence: William Coleman, The Research

School of Economics, The Australian NationalUniversity, Canberra, ACT 0200, Australia. Email:

1 The critique by way of the rational consumer isnot restricted to the efficacy of tax cuts. The perma-nent income hypothesis suggests a high-marginal pro-pensity to save, and so a low government spendingmultiplier. Ricardian equivalence treats every increasein G as if accompanied by an equal increase in T,leaving the impact of G only a matter of the (small)balanced budget multiplier.

THE ECONOMIC RECORD, VOL. 86, SPECIAL ISSUE, SEPTEMBER, 2010, 61–68

[email protected]

When Expansionary Fiscal Policy is Contractionary:A Neoklassikal Scenario*

WILLIAM COLEMAN

The Research School of Economics, The Australian National University, Canberra, Australia

� 2010 The Economdoi: 10.1111/j.1475

The paper presents a simple theoretical account of how anincrease in government purchases may reduce total employment.It is shown that in a ‘neoklassikal’ model – in which utility maxi-mising consumption choices are combined with a fixed-coefficienttechnology – an increase in government purchases will reduce thedemand for labour at the given wage rate. The reasoning turns onthe link between optimising consumption behaviour and employ-ment in the investment sector. An increase in G will (as a matterof arithmetic) make current consumption scarcer relative to futureconsumption; and thereby reduce the valuation of future consump-tion in terms of current consumption. As labour is valued accord-ing to its contribution to future consumption (through itscontribution to capital formation), it follows that an increase in Gwill reduce the wage at any given volume of employment.

I IntroductionThe Keynesian doctrine of a positive govern-

ment spending multiplier has been subject to amanifold critique, both empirically and theoreti-cally. While much of this criticism is under-pinned by a confidence in the ‘self-correcting’properties of the economy, criticisms of theeffectiveness of government spending in stimu-lating employment have long been pursued withina framework of involuntary unemployment. Someof these critiques invoke the implications ofmonetary equilibrium; (interest rate crowdingout; or, in the open economy, exchange rate

61

ic Society of Australia-4932.2010.00678.x

crowding out, Fleming (1962) and Mundell(1963)); others invoke capital market equilibrium(see, for example, Makin (2009) and the accountof Peden (1984) of the ‘Treasury View’ of the1930s); while another influential path of criticismhas invoked the ‘rational consumer’ (the perma-nent income hypothesis (Friedman, 1957) andRicardian equivalence (Barro, 1974)).1

This paper articulates another avenue of criti-cism of the government spending multiplier. Thispath of criticism reaches further than that reachedby earlier critiques. For the present paper’s cri-tique, contends that government spending will actuallybe counter productive; it will reduce employment.

62 ECONOMIC RECORD SEPTEMBER

The paper’s critique of the government spend-ing multiplier is fashioned in large part out ofstandard neoclassical materials: perfect fore-sight, utility maximisation, perfect competitionamong firms and the absence of any money illu-sion or rigidities. But it is all done in the con-text of unemployment, and will allow, as weshall see, for employment to respond positivelyin some measure to ‘demand’.

To the extent that the paper has a novel ingredi-ent that accounts for its results, it is a refusal of astandard neoclassical assumption. For it will besupposed that the demand for labour is not a man-ifestation of the diminishing marginal productiv-ity of an aggregate production function. Insteadof the ‘neoclassical’ twice differentiable aggre-gate production function, the model assumes a‘klassikal’ fixed coefficient technology operatingin two sectors: consumption goods and capitalgoods. In consequence of this technology, thewage is driven by the valuation, measured interms of current consumption, of its contributionto future consumption by means of its contribu-tion to capital formation. It is demonstrated thatgovernment expenditure reduces that valuation,so that the demand for labour falls.2

II The Elements of the ModelThis section presents the paper’s ‘neoklassi-

kal’ model; a model that makes all the standardneoclassical assumptions (utility maximisation,perfect foresight, price-taking firms) save one:instead of the neoclassical twice differentiableaggregate production function, the model assu-mes a ‘klassikal’ fixed coefficient technologyoperating in two sectors; consumption goodsand capital goods.3

2 The neologism ‘neoklassikal’ is modelled on TWHutchison’s coinage ‘Klassikal economics’ to denotethe conception of Keynes and his followers of classicaleconomics, as distinguished from classical economicsitself. (See Hutchison, 1978, p. 123). As ‘Klassikal eco-nomics’ both resembles and (at points) diverges fromclassical economics, so ‘neoklassikal’ indicates anapproach that both resembles and, in some respects,diverges from the standard neoclassical approach.

3 It is well understood that ‘neoclassical’ models candeal with fixed coefficients (see for example Phelps,1963). It is well known that Leon Walras used fixedcoefficients in the first three editions of the Elements ofPure Economics (e.g. Walras, 1874). Nevertheless, ‘neo-classical aggregate production function’ is synonymouswith putty capital and flexible capital ⁄ labour ratios.

The economy has two outputs; consumptionand capital. The production of a units of con-sumption requires 1 unit of capital and b unitsof labour. There is no possibility of substitutinglabour for capital in the production of consump-tion: the isoquants are L shaped, and there is no‘marginal product of labour’. Hence, as long ascapital is not a free good, the supply of con-sumption is determined by the supply of capital

Ct ¼ aKt: ð1ÞThe production of one unit of capital requires

one unit of labour, and no other input; we mightimagine a labourer fashioning with their hands‘a machine’. A unit of capital ‘evaporates’ atrate d.4 Thus the quantity of capital in the nextperiod equals 1 ) d of capital in the current per-iod plus the production of capital this period.And because the production of capital this per-iod equals total employment minus employmentin the consumption sector, bK, we have,

Ktþ1 ¼ Kt½1� d� þ Lt � bKt: ð2Þ

Consumption is determined by the maximisa-tion of identical homothetic utility functions ofthe form,

U ¼ Cct þ

Cctþ1

1þ dþ

Cctþ2

½1þ d�2þ � � �; c < 1 ð3Þ

by a given cohort of infinitely lived personsyielding,5

Ctþ1

Ct

¼ 1þ qt

1þ d

� �r

r � 11� c

ð4Þ

where qt = rate of profit on investment made inperiod t.

4 Instead being the ‘rate of evaporation’, d could beequally interpreted as the amount of labour that needsto be spent to ‘repair’ a machine, without which themachine would have zero productivity. Hence, both band d can be interpreted as operating coefficients.This explains why b appears summed with d through-out the model. It also explains why b + d < 1: ifb + d > 1 then building a machine is irrational, as theamount of labour that builds a machine exceeds thatamount required to operate it. Its construction, there-fore, will necessitate the abandonment of othermachines to free up sufficient labour to operate it.

5 ‘Perfect capital markets’ are assumed to exist.

� 2010 The Economic Society of Australia

2010 WHEN FISCAL EXPANSION IS CONTRACTIONARY 63

While (4) can be ‘read’ as a consumptionfunction, it might be more useful here to read itas the basic neoclassical account of the valua-tion of future consumption in terms of currentconsumption, 1 ⁄ [1 + q]. For (4) implies thepresent value of future consumption, 1 ⁄ [1 + q],falls as future consumption becomes plentifulrelative to current consumption; that is, as cur-rent consumption becomes scarcer relative tofuture consumption. This proposition – the scar-cer current consumption, the less valuable futureconsumption – is critical to the conclusion ofthe paper.

The present value of future consumption mustalso conform to a technological condition: itmust equal the ratio of the present consumptioncost of producing a machine, w, to the futureconsumption payoff from producing a machine.

11þ qt

¼ wt

a� bwtþ1 þ ½1� d�Pk;tþ1; ð5Þ

where Pk,t = price of a unit of capital in termsof consumption in t.

Or, to cast (5) in terms of an expression forthe profit rate,

1þ qt ¼a� bwtþ1 þ ½1� d�Pk;tþ1

wt: ð6Þ

But as long as some capital is produced thenthe price of capital must match its cost ofproduction,

Pk;tþ1 ¼ wtþ1; ð7Þ

thus (6) becomes

1þ qt ¼aþ ½1� b� d�wtþ1

wt: ð8Þ

The model is completed by invoking a wage set-ting process.

III A Full-employment ModelSuppose, to begin, that the wage rate instantly

adjusts to secure full-employment. Then we maywrite,

Lt ¼ R; ð9Þ

where R is the supply of labour. Equations (9)and (2) imply,

Ktþ1 ¼ Rþ ð1� b� dÞKt: ð10Þ

� 2010 The Economic Society of Australia

Equation (10) constitutes the ‘equation ofmotion’ in the capital stock. It is a first-orderdifference equation with the solution,

Kt ¼ Kð0Þ � Rbþ d

� �½1� b� d�t þ R

bþ d: ð11Þ

Equation (11) states that the profile of capitalover time is entirely determined by K(0), R, band d, and is completely independent of prefer-ence parameters, d and r. It also implies that, aslong as K=R < 1=ðbþ dÞ, K will grow over timeuntil a steady state quantity of capital isreached.

KSS ¼R

bþ d: ð12Þ

Unlike the Ramsey–Solow model, the steadystate here is not a matter of an equality betweenthe rate of time preference and the marginalproduct of capital; there is no marginal productof capital. Rather, the steady state occursbecause so much capital has been produced thatthe entire workforce is absorbed in either oper-ating the existing capital, or in buildingmachines to replace those that wear out. Sothere is no labour left over to add to the capitalstock.

As Ct = aKt the path of consumption exactlytracks the quantity of capital,

Ctþ1

Ct

¼Ktþ1

Kt

: ð13Þ

But the growth rate in consumption governs therate of profit through the equimarginal conditionof utility maximisation. So by (13), (10) and(4), we can infer,

1þ qt

1þ d¼ R

Ktþ 1� b� d

� �1=r

: ð14Þ

Evidently (14) determines the rate of profit inany period, by reference to the supply of labourper unit of capital in t and parameters. Equation(14) also implies that as R ⁄ K falls over time,the profit rate will fall over time, until thesteady state quantity of capital is reached yield-ing a steady state rate of profit,

qss ¼ d: ð15Þ

With the profit rate in hand, the expression forthe rate of profit rate, (8), can be rewritten todetermine the wage rate:

wt

Lt

αβ

bKt dKt

FIGURE 1The Demand for Labour in t is a Negative Function

of the Wage Rate in t

64 ECONOMIC RECORD SEPTEMBER

wt ¼a

1þ qtþ ½1� b� d�wtþ1

1þ qt: ð16Þ

Repeated leading and substitution yields,

wt ¼a

1þ qtþ ½1� b� d�a½1þ qt�½1þ qtþ1�

þ ½1� b� d�2a½1þ qt�½1þ qtþ1�½1þ qtþ2�

þ � � � : ð17Þ

The wage rate equals a sort of ‘discounted prod-uct’ of capital. Given (11) and the expressionfor the rate of profit in any period t + i,

1þ qtþi ¼R

Ktþiþ 1� b� d

� �1=r

½1þ d�;

the wage in t can be boiled down to an expres-sion composed solely of parameters and thequantity of capital in t. And given the mono-tonic fall in the rate of profit over time as capi-tal rises over time, the wage must rise overtime. It ultimately assumes its own steady statevalue,

wSS ¼a

dþ bþ d: ð18Þ

In summary terms, the competitive equilib-rium of this neoklassikal model mimics the stan-dard neoclassical model: a falling profit rateprofile, a rising wage rate profile and a risingcapital per head profile; all ultimately flatteningout at steady state values.

IV An Unemployment ModelSuppose now that the wage is not set so as to

secure full employment, but is arbitrarily given.Employment is now an endogenous variable,dependent on the given wage rate. What is thecharacter of that dependency?

The demand for labour is the sum of ‘con-sumption sector labour’,

LC;t ¼ bKt; ð19Þ

and ‘investment sector labour’,

LI;t ¼ Ktþ1 � ½1� d�Kt: ð20ÞConsumption sector labour is completely

inelastic to the wage rate (at least until the wageis so high that profit on producing consumergoods has shrunk to zero). But investment sectorlabour is negatively related to the wage rate, asa higher wage means a lower profit rate, and so

a lower growth rate in consumption, and so alower growth rate in capital, and so less invest-ment, and so less investment labour.

Aggregate labour can be derived using anadaption of (8),

1þ qt

1þ d¼ aþ ½1� b� d�wtþ1

½1þ d�wtð21Þ

and invoking in turn

1þ qt

1þ d

� �r

¼ Ctþ1

Ctð22Þ

and

Ctþ1

Ct¼ Ktþ1

Ktð23Þ

and

Ktþ1

Kt¼ Lt

Ktþ 1� b� d ð24Þ

yielding:

Lt ¼ Ktaþ ½1� b� d�wtþ1

wt½1þ d�

� �r

�1þ bþ d

� �: ð25Þ

Equation (25) constitutes a labour demand sche-dule, and is illustrated in Figure 1.

Before turning to analyse the impact of gov-ernment spending it is worth noting that thisemployment equation shares with ‘Keynesian’models the property that employment increasesin response to a rise in the ‘marginal efficiencyof investment’. Suppose there is an increase in

� 2010 The Economic Society of Australia

7 ‘If the Treasury were to fill old bottles with bank-notes, bury them at suitable depths in disused coal-mines which are then filled up to the surface withtown rubbish, and leave it to private enterprise onwell-tried principles of laissez faire to dig the notesup again […] there need be no more unemploymentand, with the help of the repercussions, the realincome of the community […] would probablybecome a good deal greater than it actually is. It

2010 WHEN FISCAL EXPANSION IS CONTRACTIONARY 65

the profitability of machinery on account ofmachinery in the future requiring less operatinglabour, and so bt+1 < bt.

Lt ¼ Ktaþ ½1� btþ1 � d�wtþ1

wt½1þ d�

� �r

�1þ bt þ d

� �:

ð26Þ

Equation (26) implies that for bt+1 to fall belowbt is to increase employment at a given wage,reflecting the increase in investment employmenton account of the higher ex ante profit rate.

V The Impact of Government ConsumptionPurchases

We are now prepared to approach the analysisof the magnitude of the government spendingmultiplier.

(i) A Fiscal FrameworkA sound analysis of the government spending

multiplier calls for a characterisation of thegovernment’s spending. We might suppose thegovernment purchases consumption goods, andgives them to the population. This, however,should have no effect on anything: governmenthas simply become the purchasing agent ofhouseholds, as government purchases have sim-ply substituted for household purchases. Theaction would be as effectless as simultaneouslyimposing a tax on households to fund an equalsized tax refund to households.

The characterisation of G that this paperchooses turns on the presumption that thegovernment purchase of consumption goods isintended to increase total demand for consump-tion goods, and not simply to implement the pur-chasing plans of households. In consequence ofthis presumption, we suppose that householdswill not receive utility from the governmentpurchases of consumption goods. This supposi-tion is in harmony with the classic Keynesiancontention that the existence of a (non-zero) gov-ernment spending multiplier does not require thatthe government spending itself directly providesany utility. The classic Keynesian contention,recall, is that in times of unemployment it wouldincrease social income for the government to paypeople to shift sand (to use Giblin’s suggestion of19326), or to pay people to fill old holes and then

6 See Giblin’s letter to JA Lyons of 19 April 1932,quoted in Coleman et al. (2006, p. 97)

� 2010 The Economic Society of Australia

dig them up again (to use Keynes’ suggestionof 19367). To pay someone to do such uselesstasks is no different from paying someone tomake a consumer good, and then not use it. Thissection therefore proceeds on the assumption thatthis is what government purchase amounts to,until a relaxation is introduced in the final sub-section. Section V turns to the multiplier when Gconsists of purchasing capital goods.

A reliable analysis of the government spendingmultiplier also requires a characterisation of thefinancing of G. It is simplest to assume that a flattax finances G. But the analysis would be unal-tered if we supposed G was financed by a con-sumption tax, at such a rate as to yield revenuesof G. And, if households have foresight of theirfuture tax liabilities, then the analysis would bealso unaltered if we supposed G was financed bygovernment borrowing, as long as the future taxburden is financed by a consumption tax.

(ii) A Temporary Shock to GSuppose now the government decides to spend

G, in real terms, in the current period, but notother periods. Under the fiscal frameworkassumed in the preceding subsection, the con-sumption growth rate equation is now altered to,

Ctþ1

Ct¼ aKtþ1

aKt � G: ð27Þ

Thus the employment equation becomes,

Lt ¼ Ktaþ ½1� b� d�wtþ1

wt½1þ d�

� �r

�½1� b� d�� �

� G

aaþ ½1� b� d�wtþ1

wt½1þ d�

� �: ð28Þ

The first term in (28) is identical to the right-handside of (25), and is the level of employment with

would, indeed, be more sensible to build houses andthe like; but if there are political and practical diffi-culties in the way of this, the above would be betterthan nothing. (Keynes, 1936, p. 129).

66 ECONOMIC RECORD SEPTEMBER

a fixed wage and no fiscal policy. Evidently, then,employment for a given wage is reduced by G.Why? The answer turns on the fall in employmentin the investment sector, as employment in theconsumption goods sector remains exactly thesame as long as profits are positive.

One way of understanding why investmentemployment falls is to register that a personalways faces a choice between consuming them-selves or instead paying consumption as wagesto someone else to build a machine. To paysomeone to build a machine amounts to this per-son sacrificing their current consumption for thesake of increasing their future consumption.8

How much this person is willing to pay someoneto build a machine will therefore be dictated byhow much the person values future consump-tion, in terms of current consumption. But anincrease in G will cause the value of futureconsumption, in terms of current consumption,to fall on account of the reduction in currentconsumption (relative to future consumption)necessitated by the increase in G. Hence, for agiven volume of investment the wage rate mustfall. Equivalently, for a given wage rate, invest-ment must fall.

A second way of understanding the fall ininvestment employment is to conceive of theeconomy as articulated into households (thatconsume) and firms (that invest). An increasein G must reduce the current consumptionof households. The Euler condition of utilitymaximisation, (22), implies that as a conse-quence households will reduce their plannedconsumption in the following period. Thatimplies a reduction in the required capital stockin the next period, and firms reduce investmentaccordingly.

(iii) A Future Shock to GSuppose now the government decides to spend

G, in real terms, in period t + 1, but not thecurrent period. Under the fiscal framework

8 This trade-off is a private one. Under the assumedtechnology, a social intertemporal trade-off existsonly under a circumstance we are not treating; the cir-cumstance where capital is idle and profits are zero.As long as profits are positive and all capital isemployed, society as a whole does not have theopportunity to increase future consumption by reduc-ing current consumption. But decisions are made atthe level of the private agent, where the private trade-off is perfectly real.

assumed in the preceding subsection, theconsumption growth rate equation is now alteredto,

Ctþ1

Ct¼ Ktþ1 � G=a

Kt: ð29Þ

Thus the employment equation becomes,

Lt¼Ktaþ ½1� b� d�wtþ1

wt½1þ d�

� �r

�½1� b� d�� �

þ G

a:

ð30Þ

Comparing (30) with (25), it is evident thatemployment for a given wage is increased by G.Equivalently, the wage rate for a given level ofemployment is increased by future G. Why?Anyone who pays labour to build a machine iseffectively sacrificing current consumption forfuture consumption. How much one is willing topay that person is dictated by the value of futureconsumption, in terms of current consumption.The value of future consumption, in terms ofcurrent consumption, has been increased onaccount of the reduction in future consumption.Hence the amount one is willing to pay someoneto build a machine has increased.

(iv) A Permanent Shock to GSuppose now the government decides to

spend G, in real terms, in all periods. Theconsumption growth rate equation is now alteredto,

Ctþ1

Ct¼ Ktþ1 � G=a

Kt � G=að31Þ

and so

Lt ¼ Ktaþ ½1� b� d�wtþ1

wt½1þ d�

� �r

��

1� b� d

�� �

þ G

a1� aþ ½1� b� d�wtþ1

wt½1þ d�

� �r� �:

ð32Þ

Evidently, the net effect of current and future Gon labour demand is negative as long as invest-ment is positive. Employment for a given wageis reduced by G. This is because a given abso-lute reduction in C in both the present and inthe future increases the ratio of next period C tocurrent C, and so reduces the valuation of nextperiod consumption.

� 2010 The Economic Society of Australia

2010 WHEN FISCAL EXPANSION IS CONTRACTIONARY 67

(v) When Government Purchases Provide SomeUtility

The conclusion that government spendingreduces employment does not require theassumption that government purchases providezero utility. Suppose that the government pur-chase of consumption good provides householdsthe utility provided by a fraction, c, of a house-hold purchase of consumption good. So whereasc has thus been assumed zero, we now allowc > 0. In the case of a temporary G, (27)becomes

Ctþ1

Ct¼ aKtþ1

aKt � ½1� c�G : ð33Þ

By the previous train of substitutions we obtain,

Lt ¼ Ktaþ ½1� b� d�wtþ1

wt½1þ d�

� �r

�½1� b� d�� �

� ½1� c�Ga

aþ ½1� b� d�wtþ1

wt½1þ d�

� �: ð34Þ

The impact of G on L remains negative, barringthe polar case c = 1 when the impact is zero.9

V The Impact of Government InvestmentPurchases

We now turn to analyse the case where taxrevenues are used by the government topurchase the capital good. Again, we are inter-ested in assessing an attempt of government toincrease aggregate demand by its purchases,rather than anything else. So to prevent thispolicy amounting also to an extension of gov-ernment ownership of the capital stock, we sup-pose the income stream of these machines isused to reduce tax liabilities of households. Wecan model this as the government giving awaythe machines to households.

What will be the impact on total employ-ment of this initiative? To the extent that thistype of G shock increases total employmentin period t, Ktþ1=Kt must rise. But, critically,the implication of this new characterisationof G has restored the equality of the growthin consumption to the growth in the capitalstock, as G no longer wastes capital’s outputof consumer goods. So it is once more truethat:

9 The analysis of this subsection is owed to areferee.

� 2010 The Economic Society of Australia

Ctþ1

Ct¼ Ktþ1

Kt:

Thus to the extent that this type of G shockincreases total employment in period t itincreases Ctþ1=Ct, and that will reduce the valua-tion placed on future consumption. And that willreduce the wage, by the logic explained before.But the wage cannot be reduced, by virtue of ourfixed wage assumption. The conclusion is thatthis type of G shock does not increase totalemployment at all. Government investmentemployment exactly displaces an equal amountof private ‘investment employment’. In effect,households – seeing the government tax them(say) $1 million to build machines that they willgive back to them – simply let the governmentdo their investment for them to the extent of $1million, and scale back their own investment by$1 million. The employment multiplier in thiscase is not negative, it is zero.

VI ConclusionThe paper has added another strand to the

variegated theoretical critique of the Keynesiandoctrine of a positive government spending mul-tiplier. The paper has advanced a model of themacroeconomy that is simple, has intelligiblemicrofoundations, allows for unemployment,and predicts a positive response in output to anincreased profitability of investment; but inwhich a permanent increase in government con-sumption purchases will reduce employment.

The intuition is that an increase in G will (asa matter of arithmetic) make current consump-tion scarcer relative to future consumption. Thatwill reduce the valuation of future consumptionin terms of current consumption. And, as labourin the model is valued according to its contribu-tion to future consumption (through its additionto capital formation), it follows that an increasein G will reduce the wage at any given volumeof labour.

The conclusion is constructed out a number of(inevitably) disputable assumptions, of whichthe assumption of a fixed coefficient technologyis the most critical, and the most salient. Butalthough the technology assumed by the paper isspecial, it is not in any way ‘ill behaved’. Onthe contrary, Section III has shown that in anequilibrium setting the assumed technologymimics the behaviour of the Ramsey–Solowmodel with a ‘well-behaved’ twice differentia-ble production function.

68 ECONOMIC RECORD SEPTEMBER

The upshot of the paper is to draw attentionto the sensitivity of the sign of the governmentspending multiplier to assumptions about tech-nology. The paper therefore suggests that anycase for government spending as a remedy forinvoluntary unemployment needs to be securedwith some ‘right’ (or facilitating) assumptionabout technology, in addition to previouslyrecognised need of certain requisite assumptionsregarding consumer behaviour and the marketsfor labour, money and capital.

REFERENCES

Barro, R.J. (1974), ‘Are Government Bonds NetWealth?’, The Journal of Political Economy, 82,1095–117.

Coleman, W., Cornish, S. and Hagger, A. (2006),Giblin’s Platoon: The Trials and Triumph of theEconomist in Australian Public Life, ANU E Press,Canberra.

Fleming, J. M. (1962), ‘Domestic Financial PoliciesUnder Fixed and Under Floating Exchange Rates’,International Monetary Fund Staff Papers, 10,369–80.

Friedman, M. (1957), A Theory of the ConsumptionFunction, Princeton University Press, New York.

Hutchison, T.W. (1978), On Revolutions and Progressin Economic Knowledge, Cambridge UniversityPress, Cambridge.

Keynes, J.M. (1936), The General Theory of Employ-ment Interest and Money, Macmillan, London.

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