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# 2.3 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)

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 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

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 WiLi. The extra revenue generated by an additional

worker is the extra output produced (Qi) multiplied by the price of the

firm’s product (Pi). The additional revenue is therefore PiQi. It pays for a

profit-maximizing firm to hire labour as long as WiLi < PiQi. To maximize

profits requires satisfaction of the following condition:

PiQi WiLi (2.3)

This is equivalent to:

Q

L

W

P

i

i

i

i

(2.4)

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:

MC

W

MPL i

i

i

(2.5)

Combining (2.5) and (2.2) yields equation (2.6):

P

W

MPL

i MC

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 downwardsloping

(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 (Wi / Pi ) (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 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):

DL DL (W / P) (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 SL (W / P) (2.9)

Figure 2.2 Output and employment determination in the classical model

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.