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 in¬‚uences 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)

Keynes v. the ˜old™ classical model 41

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 ¬rst consider how much labour a pro¬t-maximizing ¬rm

will employ. The well-known condition for pro¬t maximization is that a ¬rm

should set its marginal revenue (MRi) equal to the marginal cost of produc-

tion (MCi). For a perfectly competitive ¬rm, MRi = Pi, the output price of

¬rm i. We can therefore write the pro¬t-maximizing rule as equation (2.2):

Pi = MCi (2.2)

If a ¬rm 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

¬rm™s product (Pi). The additional revenue is therefore Pi∆Qi. It pays for a

pro¬t-maximizing ¬rm to hire labour as long as Wi∆Li < Pi∆Qi. To maximize

pro¬ts requires satisfaction of the following condition:

Pi ∆Qi = Wi ∆Li (2.3)

This is equivalent to:

∆Qi Wi

= (2.4)

∆Li Pi

Since ∆Qi/∆Li is the marginal product of labour, a ¬rm 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

Wi

MCi = (2.5)

MPLi

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

Wi

Pi = = MCi (2.6)

MPLi

Because the MPL is a declining function of the amount of labour employed,

owing to the in¬‚uence of diminishing returns, the MPL curve is downward-

sloping (see panel (b) of Figure 2.1). Since we have shown that pro¬ts will be

maximized when a ¬rm equates the MPLi with Wi/Pi, the marginal product

curve is equivalent to the ¬rm™s demand curve for labour (DLi). Equation (2.7)

expresses this relationship:

DLi = DLi (Wi / Pi ) (2.7)

This relationship tells us that a ¬rm™s demand for labour will be an inverse

function of the real wage: the lower the real wage the more labour will be

pro¬tably employed.

In the above analysis we considered the behaviour of an individual ¬rm.

The same reasoning can be applied to the economy as a whole. Since the

individual ¬rm™s demand for labour is an inverse function of the real wage,

by aggregating such functions over all the ¬rms 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 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)

Keynes v. the ˜old™ classical model 43

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