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 6.5 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.
The real business cycle school 317
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
318 Modern macroeconomics
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)
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
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.
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 6.5 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.
The real business cycle school 317
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
318 Modern macroeconomics
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)
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
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.
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