An important concept in the theory of wages is the elasticity of demand for labour. It measures the degree of responsiveness of the quantity of labour demanded to a change in the wage rate, ceteris paribus. There are four determinants of elasticity of demand for labour, known as the Hicks-Marshall laws of derived demand. The laws say that, other things being equal, the price elasticity of demand for labour is higher.
a. When the other factors of production can be easily substituted for labour;
b. When the supply curves of other factors of production (such as capital) are highly elastic;
c. When the cost of labour is a large proportion of the total cost of production; and
d. When the price elasticity of demand for the product of the firm is high.
These four important determinants of the elasticity of derived demand may now be discussed one by one:
1. Elasticity of Factor Substitution:
The elasticity of factor substitution is denoted by the symbol a.
In case of two variable factors, viz., labour and capital it is expressed as;
It shows the percentage change in the capital to labour ratio for a given percentage change k. factor-price ratio, holding the level of output constant. The ability to substitute labour by capital (or another other variable factor) is reflected in the elasticity of substitution between the two factors. If σ = 1, a 10% fall in r/w results in a 10% increase in K/L. A high value of elasticity indicates that the two factors are close substitutes in production.
Now if a close substitute is available, then, when the price of labour rises (other things remaining constant), the firm can simply substitute labour by the other input. So if labour and capital are close substitutes, then, when the wage rate rises, firms will substitute capital for labour, and the fall in employment will be greater. Hence the demand for labour will be more elastic when close substitutes are available.
2. Elasticity of Supply of Other Factors:
The demand for labour will be more elastic if the supply curves of other factors (such as capital) are more elastic. Suppose the wage rate rises. This will induce a firm to substitute capital for labour. However, if the supply of capital (machines) is inelastic, then the firm would have limited ability to substitute labour by capital profitably. This is because a small increase in demand for capital will cause a large increase in the rate of interest. Thus the fall in the demand for labour will be smaller and the demand for labour will be less elastic.
Short-Run vs. Long-Run:
It may be noted that the possibilities of substitution are higher in the long run than in the short run. In the long run, the producers of capital goods such as plant, equipment and machinery can expand their capacity and new producers can enter the market. Thus the long-run elasticity of supply of other factors will be higher than the short-run elasticity. Consequently the long-run elasticity of demand for labour would be higher than the corresponding short-run elasticity.
3. The Share of Labour Cost in Total Cost:
The proportion of labour cost in total cost is also an important determinant of the elasticity of demand for labour. If the proportion of labour costs is only 10% of total costs then a 10% rise in the wage rate, cet. par., would raise total costs by only 1%.
However if the share of labour cost is 90% of total cost, a 10% rise in the wage rate would increase total cost by 9%. Since marginal cost will increase faster in the latter case than in the former price will increase faster in the latter case and output, and hence, employment will fall faster in the latter case. Thus the larger the share of labour cost in total costs, the higher the wage elasticity of demand for labour tends to be.
This law may not always hold in reality. This argument suggests that the quantity of labour use per unit of output is independent of the wage rate. In other words, the ‘law’ is necessarily true only in the case where inputs are to be combined in fixed proportions (i.e., as in the case of Leontief-type production function where we have L-shaped isoquants).
4. Elasticity of Demand for the Product of a Firm:
An increase in the price of labour (wage rate) leads to an increase in the output price and the greater the price elasticity of demand for the product of the firm, the larger will be the fall in industry output for a given increase in price. The larger the fall in output, the greater the decrease in the usage of labour (other things being the same). Thus the stronger the elasticity of demand for the product of the firm, the greater will be the elasticity of demand for labour.
It may be added that the individual firm’s demand for an input will be more elastic than the industry demand. However, the difference between the two elasticities is not large if the elasticity of demand for the output is high. Finally the long-run elasticity of demand for output is higher than the short-run elasticity. Correspondingly the long-run price elasticity of demand for labour will be higher than its short-run elasticity.
By way of conclusion we may make three comments on the derived demand for labour:
1. Skilled vs. unskilled labour:
Labour is not homogeneous as we have assumed so far. Labour is of two broad categories, viz., skilled and unskilled. So there will exist two wage rates — one for skilled and another for unskilled labour. Thus when we speak of elasticity of demand, we mean the own wage elasticity.
2. Labour-labour substitution:
Furthermore we have to consider not only capital-labour substitution but also labour-labour substitution, or the substitution possibilities between skilled labour and unskilled labour. Also, like capital, skilled labour will be in limited supply in the short run, because skill formation takes time. It takes time to train up the required number of doctors or pilot.
3. Role of unions:
Trade unions also limit the scope of substitution of labour by capital or any other input. Since the bargaining power of a trade union depends on the elasticity of demand for labour (the higher this elasticity, the weaker the bargaining power), unions try to adopt necessary measures for lowering the elasticity of demand for labour.
The elasticity of demand for the final product depends largely on the availability of substitutes. It is quite common for this substitute product to be an imported item. So it is quite logical for trade unions to put pressure on the government to impose tariffs or quotas so that there is not much competition from foreign goods and prices of domestic goods do not fall.
Determinants of the demand for a variable factor by an individual firm:
In short, the demand for a variable factor (such as labour) depends on the following factors:
i. The price of the factor:
This remains constant in a competitive labour market.
ii. The marginal physical product of the factor:
This is derived from the production function.
iii. The price of the commodity produced by the factor:
If there is perfect competition in the commodity market (VMPL = P.MPPL = MR.MPPL = MRPL).
iv. The amount of other factors which are combined with labour:
An increase in the collaborating factors will shift the MPPL outwards to the right and hence will raise its VMPL curve (and vice-versa).
v. The prices of other factors:
Since these prices will determine the demand for those (competitive) factors and hence the demand for labour.
vi. Technological progress:
Technological progress changes the marginal physical product of all inputs and hence their demand.
Responsiveness of factor demand to change in factor prices: A summary view:
To sum up the extent to which fall in wage rate affects a profit-maximisation firm’s demand for labour depends on substitution and output effects. First, we consider the substitution effect. The increase in the demand for labour will depend on how easy it is for firms’ to substitute other factors of production for labour.
In other words, the size of the substitution effect will depend on the elasticity of substitution of the firm’s production function. Some firms will find it relatively easy to substitute capital by labour (in the event of a fall in w) and for other firms the quantity of labour demanded does not increase much. And substitution is virtually impossible in case of firms using a fixed-proportions technology.
The time factor:
Apart from the technical properties of the production function, the size of the substitution effect will depend on the time required to make necessary adjustment. In the short run, not much substitution of capital by labour is possible because the firm may have a fixed number of machines which have to be used with a fixed number of workers.
In the long run some machines will wear out and may not be replaced. More workers can therefore, be used. Since, in the long, the firm may be able to adopt its machinery so as to use more labour per machine, the possibilities of substitution may be quite substantial.
The output effect:
A fall in the wage rate will also reduce a firm’s costs. This will cause the price of the good being produced to fall, too and consumers will increase their purchase of that good. This increase in purchase is called the output effect. Since more output is being produced, more labour will be demanded. Thus the output effect reinforces the substitution effect.
The size of output effect, in its turn, depends on two things:
(1) The proportion of labour cost in total cost and
(2) Price elasticity of demand for the product of the firm.
In those industries where labour costs are a major portion of total costs and for which demand is very elastic, output effects will be quite large. The converse is also true.