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2 . 9 A M A R K E T A T W O R K : T H E L A B O U R M A R K E T

The labour market can be analysed using the supply and demand framework but in many respects it is a unique market and a number of different elements require analysis in considering how it functions. As labour is one of the factors of production, the labour market is also described as a factor market. Since labour is an input into production, labour demand is a derived demand since it depends on the demand for goods and services.

Firms demand labour taking into account, among other factors, the cost of the labour, which in turn depends on the wage rate that must be paid. At higher wage rates we expect firms to hire fewer workers than at lower rates. Labour supply refers to people’s willingness to make some of their time available for paid work and also depends on the wage rate. We expect more people to wish to supply their labour if wage rates are high rather than relatively low. When we discuss price in relation to the labour market we refer to the price of labour, which is the wage rate. The wage rate in a labour market is determined similarly to any equilibrium price, i.e. via supply and demand for labour, which are discussed in more detail below.

2.9.1LABOUR DEMAND

Labour demand is graphed like other demand curves with quantity (of labour) on the horizontal axis and the price (wages) on the vertical axis, as in the example in Figure 2.9. Firms in the industry shown wish to employ 60 000 workers if wages are £10 per hour; at higher wage rates, firms would demand fewer workers because costs rise as wages rise.

Price
£/hour		Labour
20
		Demand
15
10
5
0		Quantity (000, workers)
0	30	60

F I G U R E 2 . 9 I N D U S T R Y L A B O U R D E M A N D C U R V E

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The wage rate enters into the labour demand decision of firms but the firm must also take into account the output that the workers they employ can produce for the firm, and the revenue the firm can earn from that output. The firm must try to work out how many workers it can profitably employ. This process involves consideration of the output of each worker.

The following example is considered to figure out the number of workers demanded by Safelock, a hypothetical company manufacturing steering locks (anti-theft devices for steering wheels).

Given the available machinery and equipment in the steering lock factory, the firm considers that output could be produced as shown in Table 2.3. In the second column Table 2.3 shows the output that could be produced if the firm employed between one and 10 workers. One worker could produce 25 locks per day, rising to 55 if two workers were employed and so on. In the third column the marginal physical product of Labour is computed.

The marginal physical product of labour is the change in the quantity of output ( Q) produced by each additional worker ( L).

T A B L E 2 . 3 L A B O U R O U T P U T

No. of workers	Output (per day)	MPPL
1	25	25
2	55	30
3	82	27
4	102	20
5	116	14
6	124	8
7	130	6
8	132	2
9	130	−2
10	125	−5

A working day is assumed to consist of 8 hours.

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A B

			Daily output							30				MPPL
140
										25
120										20
100										15
80										10
60										5
40										0
20										–5
0										–10	2	3	4	5	6	7	8	9	10 11
1	2	3	4	5	6	7	8	9	10 11	1
				Workers										Workers

F I G U R E 2 . 1 0 P R O D U C T O F

T O T A L O U T P U T A N D M A R G I N A L P H Y S I C A L L A B O U R

For example, the change in output generated by hiring the first worker is 25 ( Q/L = 25/1) since when no workers are hired output is zero. In hiring the second worker output increases from 25 to 55, a change of 30. The second worker adds 30 steering locks extra to total output, the third adds 27 locks and so on.

When a second worker is hired the two can cooperate to divide up the work between them and there are advantages of this division of labour that allows them to produce more than double the output of the first worker (55 compared to 25). Hiring the third worker changes the division of labour too but in this case the additional output is 27 locks extra. This happens because of how the materials and equipment are shared and used among the workers. The total output increases with each worker up until worker 8 but when the next worker is hired, they do not add any additional output. In fact output falls by half a unit – this is because given the available equipment, there is nothing for this worker to do. Hiring the ninth worker leads to a fall in output (from 132 to 130 locks) because the worker actually gets in the way of others trying to do their job. The total output of the factory and the marginal physical product of labour are shown in Figure 2.10.

Once any more than two workers are employed, the additions to total output decline (from 30 to 27 to 20 to 14, etc.) by diminishing amounts. This is reflected in the flattening slope of the total output curve in panel A of Figure 2.10 and in the downward (negative) slope of the MPPL in panel B. This reveals the law of diminishing marginal returns.

The law of diminishing marginal returns states that when a firm adds workers to a given amount of capital – machinery, equipment, etc. – it eventually leads to a

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less efficient match between labour and capital to the extent that if all capital is used by workers, hiring an additional worker will only lead to workers getting in each other’s way and the marginal product of labour declines.

The law of diminishing returns helps us to understand why when capital input is fixed supply curves slope up and the marginal costs of production rise. This is relevant over short periods of time when firms use their available capital rather than changing it by building new factories, buying new machinery, etc.

Safelock uses the above information in considering how many workers it should profitably hire. It also takes into account the price it can earn for its output. There are a large number of competing products and Safelock is aware that if it wants to be successful in selling its product it cannot charge above a price of £30. Using this price information, the firm can move from an analysis of output to the revenue it can expect to earn from its product. Each worker’s MPPL can be considered in terms of MRPL.

MRPL – marginal revenue product of labour. This is the change in total revenue (price of output × number of units sold) generated by each additional worker. It is computed by multiplying the product price by the MPPL.

In Table 2.4 these additional estimations are shown for the Safelock example, with some blanks left for you to fill in. Table 2.4 shows how the first worker adds £750 to Safelock’s total revenue which is computed as the worker’s MPPL × P = 25 × 30. With the second worker, the total revenue (output × P) earned by the firm increases to £1650 which represents an MRPL of £900 (since £1650 − £750 = £900).

A final element in the firm’s decision on how many workers to employ is the cost to the firm of the workers (the cost to the firm is assumed here to be the wage rate only). If the firm knows it will only attract workers by paying £10 per hour, it can calculate its labour costs for varying numbers of workers as shown in Table 2.5 and Figure 2.11. When the working day is 8 hours and the wage rate is £10, it costs the firm £80 to employ each worker each day.

Hence, total labour costs per day rise steadily by £80 for each worker employed and the extra costs to the firm of employing each additional worker is computed as the daily wage. This is the marginal cost of labour for the firm.

All of the previous information on the output of workers, the revenue they generate for the firm and the costs of employing them enter into the firm’s decision about its demand for labour. In particular, the information regarding marginal revenue and marginal cost are central to the demand for labour.

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T A B L E 2 . 4 L A B O U R O U T P U T : E X T E N D E D

A N A L Y S I S

No. of workers	Output (per day)	MPPL	TR (P = £30)	MRPL
1	25	25	750	750
2	55	30	1650	900
3	82	27		810
4	102	20	3060	600
5	116	14	3480
6	124	8	3720	240
7	130	6		180
8	132	2	3960	60
9	130	−2	3900	−60
10	125	−5	3750	−150

A working day is assumed to consist of 8 hours.

T A B L E 2 . 5 L A B O U R C O S T S : W A G E S O F £ 8 0 P E R W O R K E R D A Y

Workers	1	2	3	4	5	6	7	8	9	10
Labour cost: total (£)	80	160	240	320	400	480	560	640	720	800
Labour cost: marginal (£)	80	80	80	80	80	80	80	80	80	80

It is possible to consider how many workers it makes economic sense for Safelock to hire at the (daily) wage rate of £80. Simply put, if the benefits to the firm outweigh the costs they should continue to hire additional workers:

•

•

•

•

First worker:	benefit = MRPL of £750	cost = £80	£750 > £80
Second worker:	benefit = MRPL of £900	cost = £80	£900 > £80
. . .	. . .	. . .	. . .
Eighth worker:	benefit = MRPL of £60	cost = £80	£60 < £80

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A										B
			Daily labour cost									Marginal labour cost
1000										100
800
										80
600										60
400										40
200										20
0										0
1	2	3	4	5	6	7	8	9	10	1	2	3	4	5	6	7	8	9	10
				Workers										Workers
F I G U R E 2 . 1 1 L A B O U R C O S T S : T O T A L A N D M A R G I N A L

When the decision of whether to hire the eighth worker is taken, the cost outweighs the benefit so the most efficient workforce for Safelock is seven workers. This solution could also be found graphically by drawing marginal cost and MRPL on the same graph and examining where they intersect.

The hiring decision would differ under different economic circumstances (another case of ceteris paribus). For example, at a wage rate of £25 per hour (£200 per day) it would make sense to keep hiring workers up to the sixth worker since the seventh worker would add more to the costs of Safelock (£200) than to the revenue (£180). The sixth worker will be hired as long as their MRPL is sufficient to cover their wage costs which means that once the wage rate does not rise above £30 per hour (£240 per day) it makes economic sense to hire the worker. This process shows that Safelock continues to hire workers once their MRPL (marginal revenue product of labour) is greater than or equal to the MLC (marginal labour cost), i.e. the wage rate. We can also see from Table 2.4 that it will never make economic sense to hire any more than eight workers (if price remains at £30) because after this level, MRPL is negative – given the available equipment and factory space more than eight workers leads to losses.

The above information allows us to conclude that Safelock’s demand for labour differs for different wage rates:

•at a wage rate of £10 demand is seven workers;

•at a wage rate of £25 demand would be six workers and at £30, five workers would be employed.

The demand for labour follows the general law of demand – the higher the price, the lower the quantity demanded, ceteris paribus. To find the demand for labour