Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

pital is constant. In a more o the economy as a whole. et. We study the cases with y. The latter case allows for ployment, investment, and

e effects of a policy shock or not. A policy shock is n coincides (postdates) the affects either the marginal -diate effect on investment re marginal capital produc- e-point stable, i.e. there is ng a shock. At impact the but Tobin's q can jump to

lications. For example, an subsidy leads to an invest- r investment orders to get 'vestment subsidy causes a '-sidy does. Intuitively this investment plans in order ►e predictions accord with

it is easily incorporated in sed against that model, ubstantially weakened. By re of interest rates into the y of intertemporal effects. consumption it is possible This is because the downaggregate demand which consumption has not yet

,1 its initial level.

The analyses of Abel (1982) iodel can be generalized by vestment literature stresses c-Ists. Key articles are: Abel

Chapter 4: Anticipation Effects and Economic Policy

and Eberly (1994), Abel et al. (1996), Dixit and Pindyck (1994), and Caballero and Leahy

(1996). A good survey is Caballero (1999).

Sargent (1987b) and Nickell (1986) develop a dynamic theory of labour demand based on adjustment costs on the stock of labour. Hamermesh and Pfann (1996) present a recent survey of this literature. In Chapter 11 we show how saddle-point equilibria naturally arise in the open economy context. Key papers are Dornbusch (1976) and Buiter and Miller (1981, 1982), and a good survey is Scarth (1988, ch. 9).

105

The Macroeconomics of

Quantity Rationing

The purpose of this chapter is to discuss the following issues:

1.To introduce the first attempt by (neo-) Keynesians to provide microeconomic foundations of Keynesian macroeconomics,

2.To analyse the effects of fiscal and monetary policy in the different disequilibrium configurations,

3.To ascertain the lasting contributions made by the quantity rationing approach.

5.1 (Neo-) Keynesians go Micro

Without any doubt, the Keynesian camp was in great disarray during the middle and late 1970s. First of all, the neoclassical synthesis was under great stress from the attacks by the monetarists at first and the new classicals later on. Furthermore, the Lucas critique had caused serious doubts as to the validity of macroeconomic models that are not based on a firm microeconomic underpinning (which describes a great many Keynesian models of those days).

Not surprisingly, a new research programme was launched by predominantly Keynesian macroeconomists such as Robert Barro (!) and Herschel Grossman (1971, 1976), and Edmond Malinvaud (1977), building on earlier work by Robert Clower (1965) and Don Patinkin (1965), that was specifically aimed at providing Keynesian macroeconomics with firm micro-foundations. (Note, however, that Barro "jumped ship" in the late 1970s and became one of the leaders of the new classical school. See Barro (1979b) for his reasons.) In this chapter we wish to provide a selective survey of what these neo-Keynesian theories amount to.

Lie basic ideas wirprisingly, in view Ui

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the different disequilibrium

tantity rationing approach.

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I

died by predominantly Herschel Grossman (1971, r work by Robert Glower led at providing Keynesian -ever, that Barro "jumped ,f the new classical school. sh to provide a selective

Chapter 5: The Macroeconomics of Quantity Rationing

5.1.1 The basic ideas

Not surprisingly, in view of Modigliani's interpretation of the Keynesian innovation, the crucial assumption that the neo-Keynesians use is the notion of comprehensive price and wage fixity (in the short run). As we have already seen in the previous chapters, the non-functioning of a price signal implies the automatic emergence of a quantity signal. For example, a large part of the Amsterdam market for rental accommodation is price regulated. As a result the price signal is not allowed to do its job (of clearing the market) and large waiting periods of up to ten years or more are the consequence (that is the quantity signal). Similarly, the long queues one used to routinely observe in the Eastern Bloc countries are a tell-tale sign of quantity signals taking over where price signals are not allowed to work.

Hence, given the assumption that prices and wages are fixed, it should come as no surprise that macroeconomic quantities such as output and employment will be influenced. More precisely: we should expect rationing to emerge in one or more markets. For example, if the real wage W /P is "too high", one would expect the demand for labour to be "too low" vis-a-vis labour supply and unemployment to exist. (As it turns out, however, this basic intuition in some cases provides an incorrect causal link between the level of real wages and unemployment.) But if agents are unemployed, they are likely to change their consumption plans also. In other words, the problem that exists in one market (e.g. an excessive real wage) also has an effect in the other market (e.g. lower demand for goods because the unemployed consume less). This is an example of so-called spillover effects that may exist between markets.

It is clear that we have to be very specific about the kind of restrictions that agents face when making their decisions. Glower (1965) formulated the dual decision hypothesis for this purpose. Loosely speaking, the dual decision hypothesis suggests that agents, when formulating their optimal plans in one market, take into account the possible quantity restrictions that they may face in one or more different markets. The plans that are made according to the dual decision hypothesis are called effective plans. Plans that are based only on the usual budget restriction are called notional plans.

A final element in the theories to be discussed is the minimum transaction rule, according to which the short side of the market determines the quantity that is actually traded. The idea can be illustrated with the aid of Figure 5.1, which depicts a market for some particular good in isolation. The demand and supply schedules are QD and Qs, respectively, and the fixed price is equal to Po. This price is too low for the market to clear, and there exists an excess demand for the good, i.e. QD (Po) > Qs (Po )• If we postulate that exchange in this market is voluntary, nobody is forced to trade more than he/she wishes, and the actual amount traded is the minimum of demand and supply:

Q = min [Qs (Po), QD (Po)] , (5.1)

107

The Foundation of Modern Macroeconomics	I
P

Po

Aimee plan

Q = Qs(Po)	QD(p0)	Q

Figure 5.1. The minimum transaction rule

which equals Qs(P0) in the case depicted. Equation (5.1) is a formal representation of the minimum transaction rule. By trying several different price levels, the minimum transaction rule is obtained graphically as the thick line in Figure 5.1.

5.1.2 Notional behaviour of households

We assume that there is a representative household that consumes goods (C), leisure (1— N), and real money balances (m M/P, where M is the nominal money supply and P is the price level). There are no interest-bearing assets so the household can only save by holding money. The household's utility function is given by:

	Lagra
	e I
iits. Re 6.	I

.1111t sb use Lai,: ac '10

- =L .

- =

UH = U (C, 1 — N, m),		(5.2)
where Uc > 0,	> 0, and Urn > 0. Real money balances appear in the util-
ity function as a proxy for future consumption possibilities (see Muellbauer and
Portes (1978) for an explicit two-period approach). The budget restriction of the
representative household is:
m — mo =	wN — C,	(5.3)

a

-14116 dia

AWL. Adholhari....NACti 4 ,

where n-0	I10 /11 is real profit income received at the beginning of the period,
mo MOP] is initial real money balances, and w W /P] is the real wage rate.
Equation (5.3) says that the excess of income over consumption spending is to be		-
saved in the form of additional money balances. The budget restriction can also be		At
108

Q

a formal representation of - ice levels, the minimum n Figure 5.1.

sumes goods (C), leisure le nominal money supply ts so the household can

)n is given by:

(5.2)

ances appear in the utilties (see Muellbauer and budget restriction of the

(5.3)

ginning of the period, )J is the real wage rate. ration spending is to be restriction can also be

Chapter 5: The Macroeconomics of Quantity Rationing

written in a more intuitive form:

Cd-w(1-N)+m=m0+7ro+w,

(5.4)

where the right-hand side of (5.4) is the definition of full income, i.e. the maximum amount of income the household can generate by working the maximum amount of hours at its disposal (and not consuming any leisure). The left-hand side of (5.4) says that this full income can be spent on three spending categories: consumption of goods, consumption of leisure, and real money balances.

The notional plans for the household are obtained by maximizing (5.2) subject to (5.4). The first-order conditions characterizing the notional plans are easily derived by using the Lagrange multiplier method (see Chapter 2 and the Mathematical Appendix). The Lagrangean is:

U(C , 1 - N , m) X [mo + + w - C - w(1 - N) - m] ,

(5.5)

where X is the Lagrange multiplier associated with the budget restriction (5.4). The first-order conditions for C, 1 - N, and m are:

	a.c_		(5.6)
	aC	uc =
	aL		(5.7)
	au —N) = Ul-N - A.W =
	a.c	= urn — = o,	(5.8)
	am

where, of course, the final first-order condition, min. = 0, implies the household budget restriction (5.4). By substituting the Lagrange multiplier X, equations (5.6)- (5.8) can be summarized by two first-order conditions: Uc = Urn and Ui_N/Uc = w. In words, the first condition states that the marginal rate of substitution between consumption and money should equal unity, and the second condition states that the marginal rate of substitution between consumption and leisure should equal the opportunity cost of leisure (i.e. the real wage rate). Of course, the second condition has already been discussed extensively in Chapter 1. In order to get the simplest possible expressions, we use a Cobb-Douglas utility function to represent the household's preferences:

U = ( 1 - N)i6 m ,

(5.9)

with 0 < a, p,y < 1 and a + p + y 1. The advantage of using this specific form is that the solutions for C, N, and m that satisfy the first-order conditions plus the

109

The Foundation of Modern Macroeconomics

household budget restriction are very straightforward: 1

CD = CD(w,P,Mo + no)= a [CI° p+ 11° ) + Iv] ,

Ns = Ns(w,P,M0 + no) = 1 - ( 12) KM° n° ) + ,

mD =	Mop+ no
	v Mo + no) = Y

where CD is the notional demand for goods, Ns is the notional supply of labour, and mD is the notional demand for real money balances. Equations (5.10)-(5.12) imply that consumption, leisure, and real money balances are all normal goods: as full income increases more of each is purchased. The following partial derivatives will be useful below.

aCD	= a > 0,			- aCD		= a(MC 4- TIC)			0,
aw				- a	P		P2
CD — 8CD	-	0 Nws = aNs = 13(M° + n°) > 0,
amo P >				aw			Pw2
Ns - aNs	= 13	(Mo +	no)	> 0,	aNs				< 0.
						=	amo	=
P aP		wP2						wP

These effects are intuitive. Note that, due to the Cobb-Douglas assumption, the notional labour supply equation is guaranteed to be upward sloping in the wage rate, i.e. the income effect is dominated by the substitution effect. Note finally, that the effects of the absolute price level operate via a wealth effect: a rise in the price erodes the real value of the initial profit income and money balances (since no rio/P and mo Mo/P)•

5.1.3 Notional behaviour of firms

We model firms in the simplest possible way. Unlike Muellbauer and Portes (1978), we do not allow for the possibility of simultaneous rationing of firms in both the goods market and the labour market. 2 Firms are assumed to be unable to hold

1 Notation is a perennial problem in rationing models. After some soul-searching we settled on the following conventions. Superscripts "D" and "S" stand for notional demands and supplies, respectively. Superscripts "DE" and "SE" stand for effective demands and supplies, respectively. Quantity variables

with a bar refer to actually traded quantities (and perceived quantity constraints). For example, ND is the notional demand for labour, WE is the effective supply of labour, and N is the actual amount of

labour traded.

2 If the firms can also make a non-trivial inventory decision, it is possible for them to be simultane-

ously rationed in both the labour market and the goods market. The resulting underconsumption regime is rarely observed in practice, and including it does not seem worth the effort.

nor

y vr/C =

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110

le notional supply of labour, aces. Equations (5.10)-(5.12) ces are all normal goods: as following partial derivatives

	( 5.13)
0,	(5.14)

I

<0. (5.15)

bb-Douglas assumption, the upward sloping in the wage tution effect. Note finally, a wealth effect: a rise in the and money balances (since

fuellbauer and Portes (1978), ming of firms in both the umed to be unable to hold

me soul-searching we settled on the iemands and supplies, respectively. es, respectively. Quantity variables iy constraints). For example, ND is Jur, and N is the actual amount of

possible for them to be simultanesuiting underconsumption regime

effort.

Chapter 5: The Macroeconomics of Quantity Rationing

inventories, nor to be able to invest. As a consequence, the firm maximizes its profit:

= Y -wN=F (N ) - wN,

(5.16)

where TC is current period real profit (to be handed over to households in the future), I = F(N) is production in the current period (there is no physical capital). Below we will occasionally make use of the following Cobb-Douglas specification to get simple expressions:

Y = F(N) NE, 0 < E < 1. (5.17)

In the absence of rationing, the firm chooses its production level Y and its demand for labour N such that (5.16) is maximized. The first-order condition is obtained in the usual fashion:

do	(5.18)
dN =0: FN(N) = w.

Equation (5.18) says that the marginal product of labour should be equated to the real wage rate. Obviously (5.18) and the production function imply two implicit functions relating the notional demand for labour (ND) and the notional supply of goods (Ys) to the real wage rate.

ND = ND (w),	= 1/FNN <0,		(5.19)
Ys = F (ND (w)) = Ys (w),		= FN/FNN < 0.	(5.20)

5.1.4 Walrasian equilibrium

The government levies no taxes and pays no transfers, but it does consume goods (denoted by G), and pays for these goods by issuing new money. The government budget restriction can be written as: 3

(m - mo) + - 70) = G,

(5.21)

which says that the net acquisition of financial assets by the private sector (households plus firms) equals government consumption.

Before we discuss disequilibrium in product and labour markets, it is useful first to consider the Walrasian equilibrium (WE) in which prices and wages are flexible and all markets clear. Since households and firms face no constraints due to quantity

3 The national income identity is Y = C + G. By substituting this identity, as well as the profit definition (5.16), into the household budget constraint (5.3) we obtain (5.21).

111

The Foundation of Modern Macroeconomics

Ew

Ew

No* N1*

Figure 5.2. The Walrasian equilibrium and the effects of fiscal policy

rationing, the model is closed by the following two equilibrium conditions:

yS (w) =	± no) ± G,	(GME)
ND (w) = (w, P, Mo + no),		(LME)

where GME and LME stand for, respectively, the goods market equilibrium and labour market equilibrium.

The Walrasian equilibrium can be illustrated with the aid of Figure 5.2. By differentiating the GME we obtain:

= CwD dw + dP + Cfs dMo + dG

dw =	-CD dP - dMo - dG	(5.22)
	Cp„ - Yi54,

From this we conclude that GME is upward sloping in (w, P) space, and shifts down and to the right if government spending or the money supply are increased:

	0,	( OW)	1	(5.23)
			yS < 0
\al') GME	CD _ ysw	" G GME	D w
	w		W
( w	w			(5.24)
	D
=
	yS < U.
amo GME

In words, if w rises, the demand for goods is increased but the supply of goods is reduced. As a result, there is an excess demand for goods that can only be eliminated if the price of these goods rises. Similarly, an increase in government consumption (or the money supply) creates an excess demand for goods (for a given real wage rate), which can only be eliminated if the price level rises and household demand for goods is sufficiently cut back.

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=

112

(CDE

I No*

s of fiscal policy

uilibrium conditions:

(GME)

(LME)

ids market equilibrium and

e aid of Figure 5.2. By differ-

(5.22)

P) space, and shifts down supply are increased:

FyS <0,	(5.23)
	(5.24)

1 but the supply of goods is that can only be eliminated government consumption pods (for a given real wage and household demand

Chapter 5: The Macroeconomics of Quantity Rationing

By differentiating the LME, we obtain the following:

—N,s, dP — dMo	(5.25)
dw + dP + dmo = dw dw = Ns _ ND •

Hence, the LME is downward sloping in (w, P) space, and shifts up and to the right if the money supply is increased:

aw)	NS	aw	NMS	>0 .	(5.26)
	< 0

aP LME 8/40)LmE

In words, for a given level of the real wage rate w, an increase in the price level increases labour supply and induces an excess supply of labour that only disappears if the real wage rate falls. Similarly, for a given price level, an increase in the money supply reduces labour supply (as households are wealthier) and creates an excess demand for labour that vanishes if the real wage rate rises.

The effects of fiscal policy have been illustrated in Figure 5.2. The initial Walrasian equilibrium is at E. An increase in G shifts GME down and to the right. This leads to a fall in the real wage rate and a rise in the price level. Employment rises: households work harder despite the fall in real wages because of the negative effect on wealth of the higher price level.

Monetary policy, consisting of a helicopter drop of money balances at the beginning of the period (i.e. dMo > 0) has an ambiguous effect on employment and the real wage rate. This is because both GME and LME curves shift to the right: the wealth effect causes households to consume more and work less.

5.1.5 Effective demands and supplies of households

The household can face quantity restrictions in the labour market, the goods market, or both. Starting with the first case, suppose that the household faces a binding restriction on the number of hours of work equal to N (< Ns ). In the face of this restriction, the household formulates effective demands for goods and real money balances and MDE , respectively). These are obtained by maximizing (5.5) by choice of C and m, with the restriction N = N substituted in. The first-order conditions consist of (5.6) and (5.8) and the budget restriction:

C + m		= +			7	-		(5.27)
						ro + wXT.
For the Cobb—Douglas preferences given in (5.9), the solutions are:
CDE	= (wk" p mo ± no = a ) [(Mo + no						+ wNi,	(5.28)
						P
	= m		DE i	c		MO ± no		(5.29)
			v	N Mo + no) = a+y)[( p
								113

The Foundation of Modern Macroeconomics

Obviously, since N < Ns (the constraint is binding) equation (5.28) implies that CDE < CD . Due to the rationing in the labour market, households cut back consumption. For the Cobb-Douglas case we can use (5.10) and (5.28) to obtain an alternative expression for CDE which clearly shows the spillover effect from the labour market to the goods market:

cDE = cD (	a+ y	) w [NS	(5.30)

If the employment ration (N) happens to coincide with the notional supply of labour (Ns) then effective and notional demands for goods will coincide, i.e. CDE = CD (students should verify that MDE = MD also in that case). From equation (5.28) we obtain the following partial derivatives which will prove useful below:

CDE	OE asi			n	aw
	=	> 0,		DE "		> 0,
				CN = _ =
	Ow	y		aN a y
CDE a cDE = a(Mo			no)	< o, CDE	a OE
	—

amoaP ± Y)P2 + > 0.

(5.31)

(5.32)

Now suppose that the household is restricted in the amount of consumption goods it can purchase at the given price level, i.e. C < C. The effective supply of labour and demand for money are in this case obtained by maximizing (5.5) with respect to N and m, subject to the restriction C = C, and the budget restriction:

w(1-N)+m=mo+no +w- C.

(5.33)

The solutions are, for the Cobb-Douglas case:

NsE = NsE(w,	no	) = 1		+ w -C ,
	mo ±				(5.34)
			GO+)1 )W) [(A"P.
mDE = niDE (w p,c,m			Mo + no	W —	(5.35)
	o + no) = (0		y ) [(

Obviously, since C < CD (the constraint is binding) equation (5.28) implies that NsE < IVi■Ts Due to the rationing in the goods market, households cut back their

labour supply. This is intuitive: if you cannot buy goods with your labour earnings,

then why bother working so hard? By using (5.11) and (5.34) we obtain an alter- .*CA 4111.111107 native expression for effective labour supply which shows the spillover from the

goods market to the labour market:

NsE = Ns ( 0 ±/3 y ( viv	)coL	(5.36)

If the consumption ration (C) happens to coincide with the notional demand for goods (0) then the effective and notional labour supplies coincide, i.e. NsE Ns (and thus also mDE = mD ).

114