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 produc-tion funcproduc-tion 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) of Figure 2.1.
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 (∆Y/∆L) which declines as employment increases. Successive increases in the amount of labour employed yield less and less additional output. Since ∆Y/∆L meas-ures 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 produc-tion (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 Wi∆Li. The extra revenue generated by an addi-tional worker is the extra output produced (∆Qi) multiplied by the price of the firm’s product (Pi). The additional revenue is therefore Pi∆Qi. It pays for a profit-maximizing firm to hire labour as long as Wi∆Li < Pi∆Qi. To maximize profits requires satisfaction of the following condition:
P Qi∆ i=W Li∆ i (2.3)
Since ∆Qi/∆Li is the marginal product of labour, a firm should hire labour until the marginal product of labour equals the real wage rate. This condition is simply another way of expressing equation (2.2). Since MCi is the cost of the additional worker (Wi) divided by the extra output produced by that worker (MPLi) we can write this relationship as:
42 Modern macroeconomics
MC W
i MPLi
i
= (2.5)
Combining (2.5) and (2.2) yields equation (2.6):
P W
MPL MC
i i
i
= = i (2.6)
Because the MPL is a declining function of the amount of labour employed, owing to the influence of diminishing returns, the MPL curve is downward-sloping (see panel (b) of Figure 2.1). Since we have shown that profits will be maximized when a firm equates the MPLi with Wi/Pi, the marginal product curve is equivalent to the firm’s demand curve for labour (DLi). Equation (2.7) expresses this relationship:
DLi =DLi(W Pi/ i) (2.7) 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 aver-age money waver-age 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):
DL=D W PL( / ) (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 SL.
SL =S W PL( / ) (2.9)
Figure 2.2 Output and employment determination in the classical model
44 Modern macroeconomics
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 prefer-ences 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 posi-tively 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 unemploy-ment 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 equi-librium 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 mini-mum 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 de-mand 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.