Employment and Output Determination
The classical neutrality proposition implies that the level of real output will
be independent of the quantity of money in the economy. We now consider
what determines real output. A key component of the classical model is the
short-run production function. In general terms at the micro level a production
function expresses the maximum amount of output that a firm can produce
from any given amounts of factor inputs. The more inputs of labour (L) and
capital (K) that a firm uses, the greater will be the output produced (providing
the inputs are used effectively). However, in the short run, it is assumed that
the only variable input is labour. The amount of capital input and the state of
technology are taken as constant. When we consider the economy as a whole
the quantity of aggregate output (GDP = Y) will also depend on the amount of
inputs used and how efficiently they are used. This relationship, known as the
short-run aggregate production function, can be written in the following
form:
Y = AF(K, L) (2.1)
where (1) Y = real output per period,
(2) K = the quantity of capital inputs used per period,
(3) L = the quantity of labour inputs used per period,
(4) A = an index of total factor productivity, and
(5) F = a function which relates real output to the inputs of K and L.
The symbol A represents an autonomous growth factor which captures the
impact of improvements in technology and any other influences which raise
the overall effectiveness of an economy’s use of its factors of production.
Equation (2.1) simply tells us that aggregate output will depend on the
amount of labour employed, given the existing capital stock, technology and
organization of inputs. This relationship is expressed graphically in panel (a).
The short-run aggregate production function displays certain properties.
Three points are worth noting. First, for given values of A and K there is a
positive relationship between employment (L) and output (Y), shown as a
movement along the production function from, for example, point a to b.
Second, the production function exhibits diminishing returns to the variable
input, labour. This is indicated by the slope of the production function (ΔY/ΔL)
which declines as employment increases. Successive increases in the amount
of labour employed yield less and less additional output. Since ΔY/ΔL measures
the marginal product of labour (MPL), we can see by the slope of the
production function that an increase in employment is associated with a
declining marginal product of labour. This is illustrated in panel (b) of Figure
2.1, where DL shows the MPL to be both positive and diminishing (MPL
declines as employment expands from L0 to L1; that is, MPLa > MPLb). Third,
the production function will shift upwards if the capital input is increased
and/or there is an increase in the productivity of the inputs represented by an
increase in the value of A (for example, a technological improvement). Such
40 Modern macroeconomics
Figure 2.1 The aggregate production function (a) and the marginal product
of labour (b)
a change is shown in panel (a) of Figure 2.1 by a shift in the production
function from Y to Y* caused by A increasing to A*. In panel (b) the impact of
the upward shift of the production function causes the MPL schedule to shift
up from DL to DL
*. Note that following such a change the productivity of
labour increases (L0 amount of labour employed can now produce Y1 rather
than Y0 amount of output). We will see in Chapter 6 that such production
function shifts play a crucial role in the most recent new classical real
business cycle theories (see Plosser, 1989).
Although equation (2.1) and Figure 2.1 tell us a great deal about the
relationship between an economy’s output and the inputs used, they tell us
nothing about how much labour will actually be employed in any particular
time period. To see how the aggregate level of employment is determined in
the classical model, we must examine the classical economists’ model of the
labour market. We first consider how much labour a profit-maximizing firm
will employ. The well-known condition for profit maximization is that a firm
should set its marginal revenue (MRi) equal to the marginal cost of production
(MCi). For a perfectly competitive firm, MRi = Pi, the output price of
firm i. We can therefore write the profit-maximizing rule as equation (2.2):
Pi = MCi (2.2)
If a firm hires labour within a competitive labour market, a money wage
equal to Wi must be paid to each extra worker. The additional cost of hiring an
extra unit of labour will be WiΔLi. The extra revenue generated by an additional
worker is the extra output produced (ΔQi) multiplied by the price of the
firm’s product (Pi). The additional revenue is therefore PiΔQi. It pays for a
profit-maximizing firm to hire labour as long as WiΔLi < PiΔQi. To maximize
profits requires satisfaction of the following condition:
PiΔQi = WiΔLi (2.3)
This relationship tells us that a firm’s demand for labour will be an inverse
function of the real wage: the lower the real wage the more labour will be
profitably employed.
In the above analysis we considered the behaviour of an individual firm.
The same reasoning can be applied to the economy as a whole. Since the
individual firm’s demand for labour is an inverse function of the real wage,
by aggregating such functions over all the firms in an economy we arrive at
the classical postulate that the aggregate demand for labour is also an inverse
function of the real wage. In this case W represents the economy-wide average
money wage and P represents the general price level. In panel (b) of
Figure 2.1 this relationship is shown as DL. When the real wage is reduced
from (W/P)a to (W/P)b, employment expands from L0 to L1. The aggregate
labour demand function is expressed in equation (2.8):
So far we have been considering the factors which determine the demand
for labour. We now need to consider the supply side of the labour market. It is
assumed in the classical model that households aim to maximize their utility.
The market supply of labour is therefore a positive function of the real wage
rate and is given by equation (2.9); this is shown in panel (b) of Figure 2.2 as
How much labour is supplied for a given population depends on household
preferences for consumption and leisure, both of which yield positive utility.
But in order to consume, income must be earned by replacing leisure time
with working time. Work is viewed as yielding disutility. Hence the preferences
of workers and the real wage will determine the equilibrium amount of
labour supplied. A rise in the real wage makes leisure more expensive in
terms of forgone income and will tend to increase the supply of labour. This
is known as the substitution effect. However, a rise in the real wage also
makes workers better off, so they can afford to choose more leisure. This is
known as the income effect. The classical model assumes that the substitution
effect dominates the income effect so that the labour supply responds positively
to an increase in the real wage. For a more detailed discussion of these
issues, see, for example, Begg et al. (2003, chap. 10).
Now that we have explained the derivation of the demand and supply
curves for labour, we are in a position to examine the determination of the
competitive equilibrium output and employment in the classical model. The
classical labour market is illustrated in panel (b) of Figure 2.2, where the
forces of demand and supply establish an equilibrium market-clearing real
wage (W/P)e and an equilibrium level of employment (Le). If the real wage
were lower than (W/P)e, such as (W/P)2, then there would be excess demand
for labour of ZX and money wages would rise in response to the competitive
bidding of firms, restoring the real wage to its equilibrium value. If the real
wage were above equilibrium, such as (W/P)1, there would be an excess
supply of labour equal to HG. In this case money wages would fall until the
real wage returned to (W/P)e. This result is guaranteed in the classical model
because the classical economists assumed perfectly competitive markets,
flexible prices and full information. The level of employment in equilibrium
(Le) represents ‘full employment’, in that all those members of the labour
force who desire to work at the equilibrium real wage can do so. Whereas the
schedule SL shows how many people are prepared to accept job offers at each
real wage and the schedule LT indicates the total number of people who wish
to be in the labour force at each real wage rate. LT has a positive slope,
indicating that at higher real wages more people wish to enter the labour
force. In the classical model labour market equilibrium is associated with
unemployment equal to the distance EN in panel (b) of Figure 2.2. Classical
full employment equilibrium is perfectly compatible with the existence of
frictional and voluntary unemployment, but does not admit the possibility of
involuntary unemployment. Friedman (1968a) later introduced the concept of
the natural rate of unemployment when discussing equilibrium unemployment
in the labour market (see Chapter 4, section 4.3). Once the equilibrium
level of employment is determined in the labour market, the level of output is
determined by the position of the aggregate production function. By referring
to panel (a) of Figure 2.2, we can see that Le amount of employment will
produce Ye level of output.
So far the simple stylized model we have reproduced here has enabled us
to see how the classical economists explained the determination of the equilibrium
level of real output, employment and real wages as well as the
equilibrium level of unemployment. Changes in the equilibrium values of the
above variables can obviously come about if the labour demand curve shifts
and/or the labour supply curve shifts. For example, an upward shift of the
production function due to technological change would move the labour
demand curve to the right. Providing the labour supply curve has a positive
slope, this will lead to an increase in employment, output and the real wage.
Population growth, by shifting the labour supply curve to the right, would
increase employment and output but lower the real wage. Readers should
verify this for themselves.
We have seen in the analysis above that competition in the labour market
ensures full employment in the classical model. At the equilibrium real wage
no person who wishes to work at that real wage is without employment. In
this sense ‘the classical postulates do not admit the possibility of involuntary
unemployment’ (Keynes, 1936, p. 6). However, the classical economists were
perfectly aware that persistent unemployment in excess of the equilibrium
level was possible if artificial restrictions were placed on the equilibrating
function of real wages. If real wages are held above equilibrium (such as
(W/P)1, in panel (b) of Figure 2.2) by trade union monopoly power or minimum
wage legislation, then obviously everyone who wishes to work at the
‘distorted’ real wage will not be able to do so. For classical economists the
solution to such ‘classical unemployment’ was simple and obvious. Real
wages should be reduced by cutting the money wage.
Keynes regarded the equilibrium outcome depicted in Figure 2.2 as a
‘special case’ which was not typical of the ‘economic society in which we
actually live’ (Keynes, 1936, p. 3). The full employment equilibrium of the
classical model was a special case because it corresponded to a situation
where aggregate demand was just sufficient to absorb the level of output
produced. Keynes objected that there was no guarantee that aggregate demand
would be at such a level. The classical economists denied the possibility
of a deficiency of aggregate demand by appealing to ‘Say’s Law’ which is
‘equivalent to the proposition that there is no obstacle to full employment’
(Keynes, 1936, p. 26). It is to this proposition that we now turn.
The classical neutrality proposition implies that the level of real output will
be independent of the quantity of money in the economy. We now consider
what determines real output. A key component of the classical model is the
short-run production function. In general terms at the micro level a production
function expresses the maximum amount of output that a firm can produce
from any given amounts of factor inputs. The more inputs of labour (L) and
capital (K) that a firm uses, the greater will be the output produced (providing
the inputs are used effectively). However, in the short run, it is assumed that
the only variable input is labour. The amount of capital input and the state of
technology are taken as constant. When we consider the economy as a whole
the quantity of aggregate output (GDP = Y) will also depend on the amount of
inputs used and how efficiently they are used. This relationship, known as the
short-run aggregate production function, can be written in the following
form:
Y = AF(K, L) (2.1)
where (1) Y = real output per period,
(2) K = the quantity of capital inputs used per period,
(3) L = the quantity of labour inputs used per period,
(4) A = an index of total factor productivity, and
(5) F = a function which relates real output to the inputs of K and L.
The symbol A represents an autonomous growth factor which captures the
impact of improvements in technology and any other influences which raise
the overall effectiveness of an economy’s use of its factors of production.
Equation (2.1) simply tells us that aggregate output will depend on the
amount of labour employed, given the existing capital stock, technology and
organization of inputs. This relationship is expressed graphically in panel (a).
The short-run aggregate production function displays certain properties.
Three points are worth noting. First, for given values of A and K there is a
positive relationship between employment (L) and output (Y), shown as a
movement along the production function from, for example, point a to b.
Second, the production function exhibits diminishing returns to the variable
input, labour. This is indicated by the slope of the production function (ΔY/ΔL)
which declines as employment increases. Successive increases in the amount
of labour employed yield less and less additional output. Since ΔY/ΔL measures
the marginal product of labour (MPL), we can see by the slope of the
production function that an increase in employment is associated with a
declining marginal product of labour. This is illustrated in panel (b) of Figure
2.1, where DL shows the MPL to be both positive and diminishing (MPL
declines as employment expands from L0 to L1; that is, MPLa > MPLb). Third,
the production function will shift upwards if the capital input is increased
and/or there is an increase in the productivity of the inputs represented by an
increase in the value of A (for example, a technological improvement). Such
40 Modern macroeconomics
Figure 2.1 The aggregate production function (a) and the marginal product
of labour (b)
a change is shown in panel (a) of Figure 2.1 by a shift in the production
function from Y to Y* caused by A increasing to A*. In panel (b) the impact of
the upward shift of the production function causes the MPL schedule to shift
up from DL to DL
*. Note that following such a change the productivity of
labour increases (L0 amount of labour employed can now produce Y1 rather
than Y0 amount of output). We will see in Chapter 6 that such production
function shifts play a crucial role in the most recent new classical real
business cycle theories (see Plosser, 1989).
Although equation (2.1) and Figure 2.1 tell us a great deal about the
relationship between an economy’s output and the inputs used, they tell us
nothing about how much labour will actually be employed in any particular
time period. To see how the aggregate level of employment is determined in
the classical model, we must examine the classical economists’ model of the
labour market. We first consider how much labour a profit-maximizing firm
will employ. The well-known condition for profit maximization is that a firm
should set its marginal revenue (MRi) equal to the marginal cost of production
(MCi). For a perfectly competitive firm, MRi = Pi, the output price of
firm i. We can therefore write the profit-maximizing rule as equation (2.2):
Pi = MCi (2.2)
If a firm hires labour within a competitive labour market, a money wage
equal to Wi must be paid to each extra worker. The additional cost of hiring an
extra unit of labour will be WiΔLi. The extra revenue generated by an additional
worker is the extra output produced (ΔQi) multiplied by the price of the
firm’s product (Pi). The additional revenue is therefore PiΔQi. It pays for a
profit-maximizing firm to hire labour as long as WiΔLi < PiΔQi. To maximize
profits requires satisfaction of the following condition:
PiΔQi = WiΔLi (2.3)
This relationship tells us that a firm’s demand for labour will be an inverse
function of the real wage: the lower the real wage the more labour will be
profitably employed.
In the above analysis we considered the behaviour of an individual firm.
The same reasoning can be applied to the economy as a whole. Since the
individual firm’s demand for labour is an inverse function of the real wage,
by aggregating such functions over all the firms in an economy we arrive at
the classical postulate that the aggregate demand for labour is also an inverse
function of the real wage. In this case W represents the economy-wide average
money wage and P represents the general price level. In panel (b) of
Figure 2.1 this relationship is shown as DL. When the real wage is reduced
from (W/P)a to (W/P)b, employment expands from L0 to L1. The aggregate
labour demand function is expressed in equation (2.8):
So far we have been considering the factors which determine the demand
for labour. We now need to consider the supply side of the labour market. It is
assumed in the classical model that households aim to maximize their utility.
The market supply of labour is therefore a positive function of the real wage
rate and is given by equation (2.9); this is shown in panel (b) of Figure 2.2 as
How much labour is supplied for a given population depends on household
preferences for consumption and leisure, both of which yield positive utility.
But in order to consume, income must be earned by replacing leisure time
with working time. Work is viewed as yielding disutility. Hence the preferences
of workers and the real wage will determine the equilibrium amount of
labour supplied. A rise in the real wage makes leisure more expensive in
terms of forgone income and will tend to increase the supply of labour. This
is known as the substitution effect. However, a rise in the real wage also
makes workers better off, so they can afford to choose more leisure. This is
known as the income effect. The classical model assumes that the substitution
effect dominates the income effect so that the labour supply responds positively
to an increase in the real wage. For a more detailed discussion of these
issues, see, for example, Begg et al. (2003, chap. 10).
Now that we have explained the derivation of the demand and supply
curves for labour, we are in a position to examine the determination of the
competitive equilibrium output and employment in the classical model. The
classical labour market is illustrated in panel (b) of Figure 2.2, where the
forces of demand and supply establish an equilibrium market-clearing real
wage (W/P)e and an equilibrium level of employment (Le). If the real wage
were lower than (W/P)e, such as (W/P)2, then there would be excess demand
for labour of ZX and money wages would rise in response to the competitive
bidding of firms, restoring the real wage to its equilibrium value. If the real
wage were above equilibrium, such as (W/P)1, there would be an excess
supply of labour equal to HG. In this case money wages would fall until the
real wage returned to (W/P)e. This result is guaranteed in the classical model
because the classical economists assumed perfectly competitive markets,
flexible prices and full information. The level of employment in equilibrium
(Le) represents ‘full employment’, in that all those members of the labour
force who desire to work at the equilibrium real wage can do so. Whereas the
schedule SL shows how many people are prepared to accept job offers at each
real wage and the schedule LT indicates the total number of people who wish
to be in the labour force at each real wage rate. LT has a positive slope,
indicating that at higher real wages more people wish to enter the labour
force. In the classical model labour market equilibrium is associated with
unemployment equal to the distance EN in panel (b) of Figure 2.2. Classical
full employment equilibrium is perfectly compatible with the existence of
frictional and voluntary unemployment, but does not admit the possibility of
involuntary unemployment. Friedman (1968a) later introduced the concept of
the natural rate of unemployment when discussing equilibrium unemployment
in the labour market (see Chapter 4, section 4.3). Once the equilibrium
level of employment is determined in the labour market, the level of output is
determined by the position of the aggregate production function. By referring
to panel (a) of Figure 2.2, we can see that Le amount of employment will
produce Ye level of output.
So far the simple stylized model we have reproduced here has enabled us
to see how the classical economists explained the determination of the equilibrium
level of real output, employment and real wages as well as the
equilibrium level of unemployment. Changes in the equilibrium values of the
above variables can obviously come about if the labour demand curve shifts
and/or the labour supply curve shifts. For example, an upward shift of the
production function due to technological change would move the labour
demand curve to the right. Providing the labour supply curve has a positive
slope, this will lead to an increase in employment, output and the real wage.
Population growth, by shifting the labour supply curve to the right, would
increase employment and output but lower the real wage. Readers should
verify this for themselves.
We have seen in the analysis above that competition in the labour market
ensures full employment in the classical model. At the equilibrium real wage
no person who wishes to work at that real wage is without employment. In
this sense ‘the classical postulates do not admit the possibility of involuntary
unemployment’ (Keynes, 1936, p. 6). However, the classical economists were
perfectly aware that persistent unemployment in excess of the equilibrium
level was possible if artificial restrictions were placed on the equilibrating
function of real wages. If real wages are held above equilibrium (such as
(W/P)1, in panel (b) of Figure 2.2) by trade union monopoly power or minimum
wage legislation, then obviously everyone who wishes to work at the
‘distorted’ real wage will not be able to do so. For classical economists the
solution to such ‘classical unemployment’ was simple and obvious. Real
wages should be reduced by cutting the money wage.
Keynes regarded the equilibrium outcome depicted in Figure 2.2 as a
‘special case’ which was not typical of the ‘economic society in which we
actually live’ (Keynes, 1936, p. 3). The full employment equilibrium of the
classical model was a special case because it corresponded to a situation
where aggregate demand was just sufficient to absorb the level of output
produced. Keynes objected that there was no guarantee that aggregate demand
would be at such a level. The classical economists denied the possibility
of a deficiency of aggregate demand by appealing to ‘Say’s Law’ which is
‘equivalent to the proposition that there is no obstacle to full employment’
(Keynes, 1936, p. 26). It is to this proposition that we now turn.
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