The Demand for a Factor of Labour | Factor Pricing | Microeconomics

In case of a single variable factor (such as labour) the value of the marginal product (VMP) curve is a firm’s demand curve of the factor. But when more than one (or several) variable factors are involved in the production process the VMP curve of labour is not its demand curve. This is because various resources are used simultaneously in the production of goods. So a change in the price of one factor leads to changes in the employment (use) of the others. The latter, in its turn, shifts the MPP curve of labour when the wage rate initially falls.

(a) Three Effects of a Fall in Factor Price and a Firm’s Demand Curve for Labour:

The change (fall) in the wage rate has in general three effects:

i. A substitution effect,

ii. An output expansion (scale) effect, and

iii. Profit-maximisation effect.

The first two effects are examined in Fig. 25.2.

Let us suppose that initially the firm produces the profit-maximising output Q₁ with the combination of factors K₁, L₁, given the initial factor prices r₁ and w₁, whose ratio defines the slope of the iso-cost line AB. Now the wage rate falls to w₂ and the new iso-cost line is AC. The firm, having the same fixed budget, can now produce a higher output denoted by the isoquant Q₂, using K₂ and L₂ units of capital and labour, respectively, as shown by point F (the tangency of new iso-cost line AC with the higher isoquant Q₂).

1 & 2. Substitution Effect and Scale Effect:

The movement from E to F can be divided into two separate effects: an input substitution effect and an output expansion (scale) effect. To separate the two effects we draw an imaginary iso-cost line (A’C’) parallel to the new one (AC) so that it reflects the new factor price ratio, but is tangent to the old isoquant Q₁.

Now tangency occurs at point E’. The movement from E to E’ constitutes the input substitution effect: the firm substitutes the cheaper labour for the relatively more expensive capital while producing the same level of output Q₁. So the employment of labour increases from L₁ to L’₁. However, the firm will not stay at point E’ on the same isoquant.

Since the wage rate falls the firm, with the same budget, can buy more of labour, more of capital or more of both the factors. Consequently the firm can produce the higher level of output Q₂, employing K₂ units of capital and L₂ units of labour. The increase of employment from L’₁ to L₂, corresponding to a movement from E’ to F, is the output expansion effect.

3. Profit-Maximising Effect:

However point F is not the final equilibrium of the firm. The reason is that a fall in the wage rate reduces cost and induces the firm to increase its profit-maximising output level further. This point is illustrated in Fig. 25.3. Here the firm’s initial equilibrium is at point A where its MC is equal to the fixed price of the product under perfect competition.

The fall in the wage rate shifts the MC curve downward and to the right and the profit-maximising output of the perfectly competitive firm increases to Q₃. This requires an increase in cost outlay equal to rectangle Q₂ABQ₃ in Fig. 25.3. This will lead to a parallel rightward shift of the iso-cost line to A”C” in Fig. 25.4. The final equilibrium of the firm will be at the point of tangency of the new iso-cost line A”C” with the isoquant Q₃, denoting a higher profit- maximising level of output (point G in Fig. 25.4).

Thus we see the simultaneous operation of both pull and push forces. Here the substitution effect of a decrease in the wage rate causes a fall in the MPP_L, because labour has a smaller quantity of capital to work with. However, output expansion and profit-maximisation effects together result in an increase in the usage of both inputs.

Thus the two effects together cause the MPP_L curve to shift upward to the right. In general the output and profit- maximising effects together more than offset the substitution effect. So the end result of a fall in the wage rate is a shift of the MPP_L curve to the right.

Given the fixed price of the final commodity, P, the VMP_L curve shifts to the right when several variable factors are used in the production process. The shift is shown in Fig. 25.5. The new equilibrium demand for labour is denoted by point F on VMP_L2.

If we repeat the above exercise with alternative wage rates we can generate a series of points such as E, F, G, etc. The locus of all such points is a firm’s demand curve for labour when several factors are variable. This may be called the long-run demand curve for labour of the firm.

In short, the demand curve of the firm for a single variable factor (such as labour) is its VMP curve. The demand curve tor labour when several variable factors are used by the firm is the locus of points belonging to shifting VMP curves. This long run demand curve for labour is negatively sloped because, on balance, the three effects of an input price (wage) change must cause the quantity of labour demanded to vary inversely with the wage rate.

(b) The Market Demand Curve for Labour:

The demand curves for labour of all individual firms are added to derive the market demand curve for labour. However, the market demand curve for labour is not just the horizontal summation of such demand curves of individual firms. This is because output expansion by all the firms at the same time when the wage rate falls creates a problem.

A fall in the wage rate reduces the cost of production of each firm and improves its profit prospects. In order to make more profit each firm expands output. When all firms increase their output levels at the same time the aggregate supply of the commodity increases and the market supply curve shifts to the right, leading to a fall in the price of the product.

Since MR = P under perfect competition, a fall in P leads to a fall in MRP = VMP. So the VMP curve, which is the demand curve for labour of an individual firm, shifts to the left. In Fig. 25.6 (a) d_l1 is the individual firm’s initial demand curve for labour.

It shows that when the wage rate is W₁ the firm is at point e on its demand curve and employs l₁ units of labour. Summing over all firms, we arrive at the total demand for labour at the wage rate w₁. Point E in Fig. 25.6 (b) is one point on the market demand curve for labour.

Now let us suppose the wage rate falls to W₂. Ceteris paribus, the firm would be moving along its demand curve d_l1, to point g, increasing the usage of labour to l₃. But due to fall in price of the product the VMP_L also falls at all levels of employment and all the VMP_L curves (the demand curves for labour of individual firms) shift downward.

In Fig. 25.6(a) the new demand curve is d_l2. When the wage rate falls to W₂ the firm is in equilibrium not at point g (on the original demand curve), but at point f on the new demand curve d_l2. Summing horizontally over all firms we arrive at point F of the market demand curve.

If the fall in the market price of the product was not taken into account, we would overestimate the demand for labour following a fall in the wage rate. In Fig. 25.6(b), point G represents the demand for labour in the market when the price of the product remains unchanged. However, when the price of the product falls this point does not belong to the market demand curve for labour.

In short while deriving an individual firm’s demand curve for labour we assume that all other things remain constant. Thus when the wage rate falls the demand for labour vanes inversely with the wage rate. But in reality other things do not remain constant.

When the wage rate falls, all firms tend to demand more labour, and increased employment leads to an increase in total output. The market supply curve of the product shifts right and the price of the product (its demand remaining the same) falls. The fall in the price of the product reduces the value of the marginal product of labour (VMP_L).

This is why in the face of falling price the market (industry) demand curve for labour is the not simply the horizontal sum of the demand curves of individual firms. However, if the price of the product of the firm remains constant, this generalisation is valid.