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6.10 A Real Business Cycle Aggregate Demand and Supply Model

The model presented above to illustrate the impact of a technology shock is

incomplete because it neglects the impact of supply shocks on the real rate of

interest. In this section we present a more complete ‘real aggregate demand

and supply’ model to illustrate the impact of technology shocks that does

include the influence of changes in the real interest rate on the supply of

labour as specified in the intertemporal labour substitution hypothesis. However,

in this example we will ignore the impact that a technology shock may

have on real aggregate demand via wealth effects.

In a world of rational expectations, perfect price flexibility and full information

relating to the money supply, the neutrality of money is guaranteed. Since

nominal variables do not influence real variables, output and employment are

entirely determined by the real forces which underlie the production function

and supply of factors of production. An IS–LM model which conforms to such

a world is shown in Figure 6.4. The IS curve shows that real aggregate demand

(RAD) is a declining function of the real interest rate. The LM/P curve will

always shift so as to intersect the IS curve at the full employment level of

output, providing prices are perfectly flexible. The position of the real aggregate

supply curve (RAS) is determined by the position of the production function

and the willingness of workers to supply labour (see Figure 6.3). A technology

Figure 6.4 The IS–LM model with flexible prices

Figure 6.5 The real business cycle aggregate demand and supply model

improvement that shifts the production function will cause the RAS curve to

shift to the right and any point on RAS represents a position of equilibrium

(full) employment; that is, the RAS curve is a labour market equilibrium curve.

Because the price level will automatically adjust so that the LM/P curve will

always intersect the RAD curve at the full employment level of output, we need

only consider the RAD and RAS curves. However, in Figure 6.4 no account has

been taken of the impact of the real interest rate on the supply of labour. A real

business cycle aggregate demand and supply model which does incorporate

real interest rate effects on the labour supply is shown in Figure 6.5.

The RAS curve is now shown to have a positive slope because an increase

in the real rate of interest will also increase the current real wage relative to

the expected future real wage, thereby increasing the supply of labour (shifting

the labour supply curve to the right), and hence output. Equation (6.11)

indicates that the current supply of labour will increase if the real interest rate

rises. Several important points are worth noting:

1. This model is entirely real, since the quantity of money and the aggregate

price level have no impact on aggregate output or employment.

2. The distinction between the long-run and short-run aggregate supply

curves which play an important role in monetarist, early new classical

and new Keynesian models is abandoned.

3. The RAS schedule traces out a range of equilibrium positions which are

all consistent with ‘full employment’.

4. The assumption of price flexibility allows the real interest rate to equilibrate

the goods market, so that RAD = RAS.

5. In explaining fluctuations in output, real business cycle theorists have

emphasized shifts of the RAS curve due to technological shocks (see

Kydland and Prescott, 1982; Plosser, 1989).

6. Some equilibrium theorists have shown that real aggregate demand shocks

can also be important during some periods as an explanation of aggregate

fluctuations. For example, Barro has shown how a temporary increase

in government expenditure can cause output to expand (see Barro, 1993,

chap. 12). He concludes that ‘variations in government purchases play a

major role during wartime but not in peacetime business fluctuations’

(see below, Figure 6.7).

In Figure 6.6 we illustrate the impact of a favourable technology shock,

taking into account the impact of such a shock on real output (Y), the real rate

of interest (r), and the real wage (W/P). In Figure 6.6 we re-label the RAD

and RAS curves as Cd and Ys respectively. The initial equilibrium position is

at point a in all four quadrants of Figure 6.6. A favourable technology shock

shifts the Ys curve from Ys1 to Ys2 in quadrant (d) and the production function

up from AF(K,L) to A*F(K,L) in quadrant (b). A favourable technology shock

increases the marginal productivity of labour, thereby shifting the labour

demand curve (DL) to the right in quadrant (a); that is, from DL1 to DL2.

However, the labour supply curve also shifts from SL1 to SL2 in quadrant (a),

this decrease in labour supply being a rational intertemporal response to the

fall in the real interest rate (from r1 to r2). The new equilibrium taking into

account all of these effects is given by point b in all four quadrants of Figure

6.6. Thus a favourable technology shock increases real output (from Y1 to Y2),

lowers the real rate of interest (from r1 to r2), increases labour productivity

and the real wage (from (W/P)1 to (W/P)2). That is, the real wage and labour

productivity are procyclical, as the stylized facts suggest.

Figure 6.7 shows the likely impact of an increase in government purchases.

As before the initial equilibrium position is at point a in all four quadrants of

Figure 6.7. An increase in government purchases shifts the real aggregate

demand curve from Cd1 to Cd2. In this case real output increases (from Y1 to

Y2), the real rate of interest rises (from r1 to r2) and the real wage falls (from

(W/P)1 to (W/P)2) in response to an increase in labour supply, with the labour

supply curve shifting from SL1 to SL2 in quadrant (a). The new equilibrium

taking into account all of these effects is given by point b in all four quadrants

of Figure 6.7. In the old classical model aggregate supply is perfectly

inelastic, as in Figure 6.4, and an increase in government purchases has no

effect on real output. In contrast, in REBCT, an increase in government

purchases leads to an increase in real output because the induced rise in the

real rate of interest encourages an increase in labour supply, thereby increasing

employment and real output.

Finally, we can use the Cd–Ys model to examine the impact of temporary

v. permanent technology shocks. In this case we simply reproduce the Cd–Ys

diagram on its own, but we also allow for possible wealth effects on the Cd

curve.

Figure 6.8 represents the basic market-clearing diagram which is central to

the modern new classical equilibrium approach to macroeconomic analysis.

Following Barro (1993), the market-clearing condition is given by (6.12):

Cd(r,) Ys(r,) (6.12)

Figure 6.6 The impact of a technology shock

(b)

b

a

Y2

Y1

Y Y* = A*F(K,L)

Y = AF(K,L)

L1L2 L

(c)

b

a

Y2

Y1

Y

Y1 Y2 Y

45

(a)

b

a

(W/P)2

L1L2 L

(d)

r2

r1

r

Y1 Y2 Y

a

b

YS1

YS2

Cd

SL2(r2)

SL1(r1)

DL2

DL1

(W/P)1

(W/P)

Figure 6.7 The impact of a government expenditure shock

(b)

b

a

Y2

Y1

Y Y = AF(K,L)

L1 L2 L

(c)

b

a

Y2

Y1

Y

Y1 Y2 Y

45

(a)

b

a

(W/P)2

L1 L2 L

(d)

r2

r1

r

Y1 Y2 Y

a

b

YS

Cd2

SL2(r2)

SL1(r1)

DL

(W/P)1

(W/P)

Cd1

In equation (6.12) variables omitted and indicated by … include the various

wealth and substitution effects which result from shocks to the production

function or government expenditure and so on. The response of Cd and Ys to

changes in the real rate of interest is illustrated by movements along the

aggregate demand and supply curves. The Cd and Ys curves will shift if any

of the other variables which influence Cd and Ys change, as with a shock to

the production function or an increase in government expenditure.

To see how a technology shock will influence aggregate output in this

model, consider Figure 6.8, where, starting from point a, we assume a beneficial

technology change takes place of the type considered in Figure 6.3. Such

a shock will clearly shift the Ys curve to the right from Ys1 to Ys*. If the

technology shock is seen to be temporary, the impact on consumer demand of

the wealth effect is likely to be small and the resultant rightward shift of Cd

Figure 6.8 The impact of temporary and permanent technology shocks in

the real business cycle model

will be less than the shift of Ys: a movement from point a to b. Output rises

from Y1 to Y2 and the real interest rate falls to r2. If the technology shock is

seen to be permanent, then the wealth effect of the shock on consumption is

more powerful. In this case the rightward shifts of Ys and Cd are likely to be

of a similar magnitude, leading to a rise in output from Y1 to Y* but with the

real interest rate remaining at r1: a movement from point a to c. According to

Barro, this model does reasonably well in accounting for the stylized facts of

business fluctuations. For a detailed discussion of these issues, see Barro

(1993), especially pp. 232–41.