Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

(5.30)

e notional supply of labour will coincide, i.e. CDE = CD :P ►. From equation (5.28) we

useful below:

amount of consumption < C. The effective supply of ed by maximizing (5.5) with id the budget restriction:

equation (5.28) implies that

. households cut back their s with your labour earnings, [d (5.34) we obtain an alter-

'ws the spillover from the

I

(5.36)

th the notional demand for plies coincide, i.e. NsE = Ns

Hence, the effective labour supply is less elastic than notional labour supply. Finally, if households are simultaneously rationed in both markets, i.e. C < CD

and N < Ns, their choice problem is trivial: they simply accumulate money balances as implied by the budget restriction:

The money balances yield utility to the household in the form of future consumption possibilities.

5.1.6 Effective demands and supplies of firms

When firms cannot get all the labour they wish to purchase according to their notional plans, N < ND , and the effective supply of goods is obtained by substituting N into the production function:

ySE = F(N) ySE = ySE (N), ykE = FN > 0. (5.42)

Obviously, since N < ND the effective supply is less than the notional supply of goods, i.e. YsE < Ys. For the Cobb-Douglas production function we can use (5.20) and (5.42) to obtain an alternative expression for the effective supply of goods:

If the firm is restricted in the amount of goods it can sell at the given price level, Y = Y and the firm expresses an effective demand for labour. This is equal to the amount of labour needed to produce

For the Cobb-Douglas case we can combine (5.19) and (5.44) to obtain:

Obviously, the firm cannot be rationed in both markets simultaneously. Either the labour constraint is binding, or the output constraint is. This is because the firm has no real choice left if either output or employment is determined.

The Foundation of Modern Macroeconomics

5.1.7 The full model

Depending on the particular combination of the real wage rate w and the price level P, there are three possible regimes that the economy can find itself in. These regimes are summarized in Table 5.1. The different regimes can be depicted graphically by means of Figure 5.3. The dashed lines are the notional GME and LME schedules discussed in section 1.4 above. In order to determine the effective goodsand labour market clearing loci, we must be very precise about the different regimes.

Table 5.1. Effective regime classification

Labour market

'411111111111

410, vow- ,r

Amer

,n2Aite. 111;

IA

S

Ige rate w and the price level nd itself in. These regimes I be depicted graphically by

al GME and LME schedules e",?ctive goodsand labour different regimes.

I

(Effective) Excess

Demand (EDL)

Impossible

Repressed

Inflation

cr) G ySE =

ND NSE A1

Si)

• GME

Ns > NDE

CDE+ G < yS

LME

e three regimes

Chapter 5: The Macroeconomics of Quantity Rationing

Consider first the goods market equilibrium locus if there is excess supply of labour. This locus is labelled GME(ESL) and is defined by:

GME(ESL) is upward sloping and lies to the left of GME. For a given real wage, wo,

the left-hand sides of GME and GME(ESL) are the same and thus C D (wo, Po, Mo + no) = CDE (wok , P1, Mo + no). We know, however, that when evaluated at the same wage-price combination the effective demand falls short of the notional demand

because unemployed workers spend less on consumption, i.e. CDE (wo.k, Po, Mo + no) < cD(wo, Po, Mo + no). It follows that P1 must be lower than Po, i.e. GME(ESL) lies to the left of GME in Figure 5.3. (Obviously, at the Walrasian equilibrium point GME and GME(ESL) coincide because there CDE = CD .)

Goods market equilibrium when there is excess demand for labour is denoted by GME(EDL) and is defined by:

Since firms are rationed in their demand for labour, they supply fewer goods ( ySE < Ys) and, for a given real wage rate, the price level has to rise (thus eroding wealth) in order to reduce consumption demand and increase the supply of labour. Alternatively, for a given price level, the real wage rate has to fall in order to restore goods market equilibrium. It follows that GME(EDL) must be steeper than the relevant section of the GME schedule.

Labour market equilibrium with an excess demand for goods is denoted by LME(EDG) and is defined by:

LME(EDG) is downward sloping and lies to the right of LME. For a given real wage rate, wo, the left-hand sides of LME and LME(EDG) are the same so that

NsE (wo, Pi, Ys (wo) — G, Mo + no) = Ns (wo, Po, Mo + no). For the wage-price combination (wo, Po) households cannot buy as many goods as they wish and effective

labour supply falls short of the notional supply, i.e. NsE(wo, Po, I's (w0)—G, mo + no) < Mo + no). It follows that Pi is higher than Po, i.e. LME(EDG) lies to the

right of the LME schedule.

Finally, labour market equilibrium with an excess supply of goods is denoted by LME(ESG) and is defined by:

It is straightforward to show that LME(ESG) coincides with GME(EDL).

117

The Foundation of Modern Macroeconomics

5.1.8 The effectiveness of fiscal and monetary policy

In the regime of Classical Unemployment (CU), households are rationed in both markets, so that the rationing equilibrium is described by:

These expressions contain neither G nor Mo, so it is obvious that both fiscal and monetary policy are ineffective. All that happens if the government increases its consumption is that private consumption is crowded out one-for-one.

In the regime of Keynesian Unemployment (KU) there is excess supply in both markets, and rationing equilibrium is described by:

The comparative static effects of changes in G and Mo are obtained in the usual fashion:

where the numerator is guaranteed to be positive.

These effects can be illustrated with the aid of Figure 5.4. An increase in G (or MO boosts effective demand for goods and shifts the GME(KU) schedule up and to the

LM E(KU)

GM E(KU) i

GM E(KU)0

N

Figure 5.4. The Keynesian unemployment equilibrium and fiscal policy

;at e7er.

• - due

P, )

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)

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e )_ al labota

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bta Ied:

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( .0 4f1 lista

( pol icy

seholds are rationed in both d by:

(LME(CU))

(GME(CU))

Iobvious that both fiscal and the government increases its

tit one-for-one.

ere is excess supply in both

(LME(KU))

(GME(KU))

are obtained in the usual

+ dG

(5.46)

5.4. An increase in G (or MO KU) schedule up and to the

"EIKU)

GME(KU)1

GME(KU)0

N

iuilibrium and

Chapter 5: The Macroeconomics of Quantity Rationing

left. For a given level of employment (at point A), firms experience a greater demand for their products and a relaxation of their sales constraint. As a result, output rises as does the effective demand for labour and hence employment. This gives rise to a multiplier effect due to the additional labour income received by households. The new equilibrium is at 4, with higher employment and output.

In the regime of Repressed Inflation (RI), there is generalized excess demand, so that the rationing equilibrium is given by:

where we have substituted the consuthption ration, i.e. C = Y — G, in the effective supply of labour equation (LME(EDG)) to obtain LME(RI). Fiscal and monetary policy are now counterproductive. Fiscal policy worsens the rationing that households face in the goods markets (cl . < 0) and reduces the effective labour supply and hence employment even further. In terms of Figure 5.5, LME(RI) shifts up and to the left. Firms experience a worsening of the labour constraint and are forced to cut back production even further. This causes a "supply multiplier" effect due to the additional reduction of the effective supply of labour. Eventually, the economy ends up at point ER , with lower output and employment. The output supply multiplier is easily obtained:

N C

N

Figure 5.5. The repressed inflation equilibrium and fiscal policy

119

0111P' igNi r`

a •.1.1a

- e -

ONAllk"

hanges in government

I

Money supply

is also to reduce output due

m summarized in Table 5.2. n this table is that the choice which particular regime the gime, then clearly Keynesian d, the economy is in the CU either impotent (CU regime) opropriate policy measure in Table 5.3, which contains

age and the price level.

Ind RI regimes there is ample level of real wages and/or 1 wage moderation is a very output. This is intuitive: real that lowers them is good for - er, the appropriate policy is demand for labour) and/or a

for goods). All this presumes, interfere directly with real

-

Chapter 5: The Macroeconomics of Quantity Rationing

Table 5.3. Effects on output and employment of changes in the real wage rate and the price level

5.1.9 Wage and price dynamics

So far, we have assumed that wages and prices are fixed altogether. What would happen if prices and wages respond over time to disequilibrium situations? One possibility is to assume that real wages react to the (effective) excess demand for labour and the price level reacts to the (effective) excess demand for goods:

where the notation indicates that effective and notional quantities appear in an alternating fashion, i.e. in the KU regime the relevant labour market disequilibrium measure is (NDE NS ) but in the CU and RI regimes it is (ND — NSE). The dynamic adjustment over time has been indicated with arrows in Figure 5.6. Suppose that the economy starts in a Keynesian unemployment equilibrium at point E. There is an effective excess supply of labour, so that the real wage rate falls over time, and effective excess supply of goods, which leads to price reductions. Eventually the economy moves into the regime of Repressed Inflation, where the real wage and price dynamics are sharply reversed (point A). The cyclical adjustment is stable and eventually restores the Walrasian equilibrium Ew.

121

The Foundation of Modern Macroeconomics

LME(ESG)

GME(EDL)

P

Figure 5.6. Wage and price dynamics and stability

5.2 Rationing in Small Open Economies

For policy purposes it is important to consider the implications of rationing for a small open economy. Dixit (1978) discusses the effects of rationing in a one-sector model of a small open economy with no inventories, immobile labour, tradeable goods, prices determined on the world market (so that purchasing power parity (PPP) holds, P = EP*, where P* is the world price level and E is the nominal exchange rate), and fixed exchange rates. In fact, rationing in such an open economy is much simpler than in a closed economy. Any effective excess demand for (supply of) goods is met by importing (exporting) goods from (to) the rest of the world. Hence, there can never be any spillover effects from the goods market onto the labour market, and thus whether unemployment or overemployment prevails depends entirely on whether the real wage is too high or too low.

The balance of trade (net exports, X) follows from the absorption approach, that is, the excess of production over absorption. When there is excess supply of labour, it is given by:

where we have substituted the constraint on the labour market (N = ND(w)) and PPP (P = EP*). When there is excess demand for labour and firms are rationed in the labour market, the expression for the trade balance is:

where we have again substituted the labour market constraint (N = Ns (.)) and PPP. We assume that there is real wage rigidity, so that w is fixed in the short run,

•t;_44.:.-„,,,r

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FISL)

KU

I P

Id stability

S

iplications of rationing for a of rationing in a one-sector

,immobile labour, tradeable ►urchasing power parity (PPP) 1 E is the nominal exchange an open economy is much

4 'mand for (supply of) goods st of the world. Hence, there

.ket onto the labour market, revails depends entirely on

re absorption approach, that Te is excess supply of labour,

ur market (N = ND (w)) and 1. and firms are rationed in

is:

w is fixed in the short run,

Chapter 5: The Macroeconomics of Quantity Rationing

GME (EDL) i

P= P*E

Figure 5.7. Rationing in a simple model of the small open economy

irrespective of whether exchange rates are fixed or floating. Figure 5.7 presents the four possible outcomes and has some similarity with the familiar Mundell-Swan diagram.

We first consider the case of fixed exchange rates. In the short run, the economy may experience a trade surplus (deficit), but in the long run this leads (in the absence of sterilization) to an increase (decrease) in foreign reserves, the money supply, and wealth, and hence to a downward shift of the effective GME locus and an upward (downward) shift of the LME locus. A trade surplus leads to more wealth, which in the presence of unemployment increases the household's effective demand for goods and thus chokes off some of the trade surplus. When firms are rationed, the increase in wealth reduces the supply of labour and thus the supply of goods, increases the demand for goods, and thus chokes off the trade surplus in two ways. However, in the latter case the initial excess demand for labour is worsened. These adjustment processes are of course related to David Hume's specie-flow mechanism and the monetary approach to the balance of payments.

The adjustment process under floating exchange rates is quite different. When there is an incipient trade surplus, the nominal exchange rate appreciates (i.e. E falls), the home price level falls, and thus real wealth is boosted. This chokes off the excess supply of goods, so that the economy never diverges from the effective GME locus and balanced trade.

A fiscal expansion in an economy with fixed exchange rates shifts the Walrasian equilibrium from Eci'r to Er', so that on impact the trade deficit rises by exactly the same amount as the increase in government spending. As the budget deficit must be financed by money creation, next period's stock of real money balances

123

The Foundation of Modern Macroeconomics

increases by the change in government spending. However, this is exactly offset by the decrease due to the ensuing trade deficit and thus there is no change in the short-run equilibrium over time. Effectively, the government uses its foreign reserves to purchase commodities from abroad, as can be seen from the identity:

(m — mo) +(n — 70) = G + X, (5.52)

i.e. the net acquisition of financial assets by the private sector must equal the sum of the government deficit and the trade surplus.'

With floating exchange rates and real wage rigidity the new equilibrium lies to the north-east of Eli'', say q, so that the fiscal expansion leads to classical unemployment. The reason for this counterintuitive result is that the depreciation of the exchange rate, required to choke off the incipient trade deficit, increases the home price level, erodes real wealth, and increases the supply of labour (whilst the real wage rate and thus labour demand are unaffected).

Note that a devaluation in a situation of unemployment erodes the real value of wealth and therefore reduces the effective demand for goods and causes a trade surplus. (If there were nominal rather than real wage rigidity, labour demand and output increase.) A devaluation in a situation of excess demand for labour increases labour supply and output, decreases demand, and improves the trade balance.

5.3 Intertemporal Spillovers

As a final example of the macroeconomic quantity rationing literature we now discuss a simplified version of the closed-economy model developed by Neary and Stiglitz (1983). They extend the static disequilibrium analysis of Barro and Grossman (1971) and Malinvaud (1977) by allowing for intertemporal considerations. In doing so they are able to demonstrate the critical role of constraint expectations and intertemporal spillovers. Indeed, it is possible to show that when agents expect unemployment tomorrow, it will be more likely that there is unemployment today. Hence there exists a so-called "bootstrap" effect in the sense that pessimistic expectations can lead to bad outcomes today (see also Persson and Svensson, 1983).

We start with a brief description of the model. Households have an inelastic supply of labour (normalized to equal unity) and decide on their lifetime consumption plans on the basis of subjective point expectations about future wages, prices, and constraint levels. To keep things as simple as possible, only the first two periods are studied ("today" and "tomorrow") and the rest of the future is summarized by the inclusion of money balances in the utility function. The representative household

4 The national income identity for the open economy is Y C + G + X. By using this identity plus the profit definition (5.3) in (5.16) we obtain (5.52).

*if

ii yri+ill

=Pat.

W and

piodu

=