The general principles determining labour demand can be explained for the case of a firm that produces a single output (Q) using two inputs, capital (K), and labour (N). The technological possibilities relating output to any combination of inputs are represented by the production function:
Q 5 F(K,N) (5.1)
In the short run, the amount of capital is fixed at K 5 K 0 , so the production function is sim-
ply a function of N (with K fixed). The quantity of labour services can be varied by changing either the number of employees or hours worked by each employee, or both. For the moment, we do not distinguish between variations in the number of employees and hours worked; however, this aspect of labour demand is discussed in Chapter 6. Also discussed later is the possibility that labour may be a “quasi-fixed factor” in the short run.
The demand for labour in the short run can be derived by examining the firm’s short-run output and employment decisions. Two decision rules follow from the assumption of profit maximization. First, because the costs associated with the fixed factor must be paid whether or not the firm produces (and whatever amount the firm produces), the firm will operate as long as it can cover its variable costs (i.e., if total revenue exceeds total variable costs). Fixed costs are sunk costs, and their magnitude should not affect what is the currently most profitable thing to do. The second decision rule implied by profit maximization is that, if the firm produces at all (i.e., is able to cover its variable costs), it should produce the quantity Q * at which marginal revenue (MR) equals marginal cost (MC). That is, the firm should increase output until the additional cost associated with the last unit produced equals the additional revenue associated with that unit.
If the firm is a price-taker, the marginal revenue of another unit sold is the prevailing market price. If the firm is a monopolist, or operates in a less than perfectly competitive product market, marginal revenue will be a decreasing function of output (the price must fall in order for additional units to be sold). With capital fixed, the marginal cost of produc- ing another unit of output is the wage times the amount of labour required to produce that
LO1, 2 LO1, 2
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CHAPTER 5: Demand for Labour in Competitive Labour Markets
output. Expanding output beyond the point at which MR 5 MC will lower profits because the addition to total revenue will be less than the increase in total cost. Producing a lower output would also reduce profits because, at output levels below Q * , marginal revenue exceeds mar- ginal cost; thus, increasing output would add more to total revenue than to total cost, thereby raising profits.
The profit-maximizing decision rules can be stated in terms of the employment of inputs rather than in terms of the quantity of output to produce. Because concepts such as total reve- nue and marginal revenue are defined in terms of units of output, the terminology is modified for inputs. The total revenue associated with the amount of an input employed is called the total revenue product (TRP) of that input; similarly, the change in total revenue associated with a change in the amount of the input employed is called the marginal revenue product (MRP). Both the total and marginal revenue products of labour will depend on the physical productivity of labour as given by the production function, and the marginal revenue received from selling the output of the labour in the product market.
Thus the profit-maximizing decision rules for the employment of the variable input can be stated as follows:
• The firm should produce, providing the total revenue product of the variable input exceeds the total costs associated with that input; otherwise, the firm should shut down operations.
• If the firm produces at all, it should expand employment of the variable input to the point at which its marginal revenue product equals its marginal cost.
The short-run employment decision of a firm operating in a perfectly competitive labour market is shown in Figure 5.1. In a competitive factor market the firm is a price-taker; that is, the firm can hire more or less of the factor without affecting the market price. Thus, in a competitive labour market the marginal (and average) cost of labour is the market wage rate. The firm will therefore employ labour until its marginal revenue product equals the wage rate, which implies that the firm’s short-run labour demand curve is its marginal revenue product
Profit maximization requires labour to be employed until its marginal cost (the wage) equals its marginal benefit (marginal revenue prod- uct). For the wage, W 0 , the profit-maximizing employ- ment level is N*0 . At wages higher than W 1 , labour costs exceed the value of output, so the firm will hire no labour. The labour demand schedule is thus MRP N , below where ARP N reaches its maximum (the thicker part of the curve on the figure).
FIGURE 5.1 The Firm’s Short-Run Demand for Labour
MRPN ARPN N N W1 W0 Wage rate Employment 1 0 ben40208_ch05_140-172.indd 143 ben40208_ch05_140-172.indd 143 03/10/11 11:28 AM03/10/11 11:28 AM
144 PART 2: Labour Demand
of labour curve. For example, if the wage rate is W 0 , the firm would employ N*0 labour services.
However, the firm will shut down operations in the short run if the total variable cost exceeds the total revenue product of labour, which will be the case if the average cost of labour (the wage rate) exceeds the average revenue product of labour (ARP). Thus, at wage rates higher than W 1 in Figure 5.1 (the point at which the wage rate equals the average product of labour),
the firm would choose to shut down operations. It follows that the firm’s short-run labour demand curve is its marginal revenue product of labour curve below the point at which the average and marginal product curves intersect (i.e., below the point at which the ARP N reaches
a maximum).
The short-run labour demand curve is downward sloping because of diminishing marginal returns to labour. Although the average and marginal products may initially rise as more labour is employed, both eventually decline as more units of the variable factor are combined with a given amount of the fixed factor. Because the firm employs labour in the range in which its mar- ginal revenue product is declining, a reduction in the wage rate is needed to entice the firm to employ more labour. Similarly, an increase in the wage rate will cause the firm to employ less labour, thus raising its marginal revenue product and restoring equality between the marginal revenue product and marginal cost.
At this point, it may be worth highlighting a common misconception concerning the rea- son for the downward-sloping demand for labour. The demand is for a given, homogeneous type of labour; consequently, it does not slope downward because, as the firm uses more labour, it uses poorer-quality labour, and hence pays a lower wage. It may well be true that when firms expand their work force they often have to use poorer-quality labour. Neverthe- less, for analytical purposes it is useful to assume a given, homogeneous type of labour so that the impact on labour demand of changes in the wage rate for that type of labour can be ana- lyzed. The change in the productivity of labour that occurs does so because of changes in the amount of the variable factor combined with a given amount of the fixed factor, not because the firm is utilizing inferior labour.