ACCOUNTING PRICES FOR LABOR
6.2 The Efficiency Price of Labor
From the "efficiency" analysis perspective, it is of interest to know the sum of the CVs of the effects attributable to the increase in the demand for labor gener-ated by a project. The efficiency price of labor for this additional demand will be the quotient between this sum of CVs and the additional demand in question. In most cases, however, the efficiency price of labor can be calculated as the sum of the CVs attributable to a unitary excess demand. As the previous analysis showed, if a project increases the demand for labor by L, - Ls (Figure 6.2) when there is no "involuntary unemployment", the workers will come from a reduction in employment in other jobs (L0 - Ls) and from an increase in workers who join the market due to the wage increase (L, - £0). As indicated in the previous section, the cost at efficiency prices of the latter will be given by their willingness to receive. However, jobs L0 — Ls in the project will be filled at the cost of employment in other sectors, which will see their costs rise because of the wage increase. The effects of such a situation are shown in Figure 6.3 in which, for the sake of simplicity, it is assumed that in the without project situation, labor L0 is used only to produce the quantity q0 of consumer good q. If in addition it is assumed that Aw is sufficiently small not to bring about substitution between labor and the other inputs (the average long-run technical coefficients are equal to the marginal coefficients)2, and
2. This assumption does not seem very restrictive if we consider that the long-run effect of the price increase produced by Aw will most probably be limited to postponing the entry sequence of a given set of plants.
Copyright © by the Inter-American Development Bank. All rights reserved. For more information visit our website: www .iadb.org/pub
ACCOUNTING PRICES FOR LABOR
that the prices of the remaining inputs are equal to their efficiency prices and are not affected, the difference between long-run average costs C(wj) and C(w0) will be
[6.2]
The increase in the market value of quantity q} of the consumer good will be [6.3]
Substituting [6.2] in [6.3] we see that
[6.4]
The complement of the C V of the consumers of q will be
[6.5]
Substituting [6.2] in [6.5] we see that
[6.6]
The sum of the consumers' CVs can then be obtained as the sum of [6.4]
and [6.6], that is
[6.7]
If we now compare [6.1] with [6.7] we can see that the difference between the sum of the CVs of workers Lj and that of the consumers will be
equal to the area ACB in Figure 6.2. In other words, an important part of the gain to workers L{ is offset by the loss to the consumers.
76
Copyright © by the Inter-American Development Bank. All rights reserved. For more information visit our website: www .iadb.org/pub
It is now possible to summarize the effects of the additional demand for labor and to identify the sectors affected (see Table 6.1). The workers em-ployed in the without project situation Ls + (L0 — Ls) gain the equivalent of wage increase w, — vv0 for this volume of employment. The additional work-ers L, — L0 gain the difference between their wage income and their willing-ness to receive or the minimum income they are willing to accept. The total effect on the workers is equal to the sum of their CVs. As shown in [6.4], the additional income of employment Ls corresponds, under the simplifying as-sumptions adopted, to the loss to the consumers through greater expenditure on quantity q[1 of the consumer good. The consumers also lose the difference between their valuation of q0 — g, and what they actually pay. The project pays the hired workers wage w, and the firms producing the consumer good no longer receive revenue from sales q0 — q{ and at the same time stop paying for the resources required to produce that quantity. If the market prices of these resources are acceptable approximations of their efficiency prices, the value of these resources at market prices is taken as a gain.
The reader can imagine that data in Table 6.1 could have been disaggrega-ted at the level of each worker, consumer and owner of the project and of the other firms, in which case the columns could have been added up vertically without resorting to interpersonal comparisons. However, it should be noted that any horizontal sum requires a value judgment regarding the contribution to "total welfare" of the changes in individuals' income. From the point of view of the potential compensation criterion, the comparison of the vertical totals indicates that the gain of workers CVL is insufficient to compensate the consumers (CVcons) and the employers (the project). Consequently, the
"total" loss that can be attributed to hiring Lt — Ls workers is recorded in the Total column and shows the minimum income that their employment ought to generate to make compensation possible.
Application of the value judgment that assigns equal weights to all marginal income changes allows for columns in Table 6.1 to be added up, and the total in the last column to be interpreted according to efficiency analysis. This total consists of the cost of the additional employment for the workers, their will-ingness to receive (WR), equal to
plus the consumers' willingness to pay (WP) for the quantities q0 — q^ of consumer goods that they will stop consuming
Copyright © by the Inter-American Development Bank. All rights reserved. For more information visit our website: www .iadb.org/pub
Table 6.1. Economic Valuation of the Additional Demand for Labor (Consumption Numeraire)
CVL
Increase in Income for Ls
Income of (L0LS) with the Project Income of (L0LS) without the Project Income of (L} L0) with the Project Willingness to Receive for (/., /.„)
Copyright © by the Inter-American Development Bank. All rights reserved.
For more information visit our website: www.iadb.org/pub
78
less the value of the resources released (VRR) by this reduction in consump-tion and which remain available for use in the rest of the system, which consequently excludes quantity L0 — Ls used by the project,
Thus, looked at from the "value of resources" angle, the cost at efficiency prices (CEP) of jobs Lj — Ls will be3
It is worth recalling here that the previous example, although illustrative of the logic of the valuation of labor, is based on the assumption that the wage increase does not lead to any substitution of inputs in the production of consumer goods. If such a substitution existed or if the average long-run technical coefficients were different from the marginal coefficients, the change in the unit costs of production of q would not be equal to the wage change multiplied by the labor requirements per unit of product. Conversely, income from other "primary factors" would be affected and the identification and quantification of these effects per group would not be practicable.4 How-ever, whenever the labor demand of the project Lt — Ls is small in relation to the respective employment, the change in wages will be insignificant and, as a consequence, the change in the price of the goods using this labor will be negligible. In this case, the cost of labor Lj - Ls at efficiency prices (CEP) will simply be
[6.8]
Table 6.2 presents its breakdown in terms of the effects on various sectors.
Finally, this line of reasoning enables us to arrive at the criterion normally used in practice. If all the labor employed by the project (Lj — Ls) is taken from alternative occupations, the cost at efficiency prices of the additional employment will be
[6.9]
3. The expression —WP(q0 — qt) + VRR substitutes for the value of the marginal product of labor withdrawn from the production of consumer goods.
4. See Mishan (1982, Chapter 10 and 1981, Part V)
Copyright © by the Inter-American Development Bank. All rights reserved. For more information visit our website: www .iadb.org/pub
Table 6.2. Economic Valuation of the Additional Demand for Labor When Changes in Wages Are Negligible (Consumption Numeraire)
CVL
Increase in Income for Ls
Income of LQLS with the Project Income of L0LS without the Project Income of ^ /.„ with the Project Willingness to Receive of ^ /.„
Consumers
Willingness to Pay for q0q.
Paid for q0q^
Resources Released Total
Workers Consumers
w(L0Ls)
w(L0Ls) w(L,L0)
w(L,L0)
p(qQq,) PtioQi)
Project
w(L0Ls)
w(L,L0)
w(L,Ls)
Other Firms Total
w(L0Ls)
w(L,L0)
p(90^)
p(q0<ii)
p(q0qi) p(qaqj
w(L,Ls)
Copyright © by the Inter-American Development Bank. All rights reserved.
For more information visit our website: www.iadb.org/pub
80
the consumers' valuation of the loss in consumption Aq less the value of the resources released, excluding the labor used by the project. On the other hand, if all the jobs created by the project were to be done by workers joining the market because of higher wages, and provided employment in the remain-ing sectors were not affected, the efficiency value of the additional employ-ment would be
[6.10]
the willingness to receive for these jobs.5
It should be noted that when the wage is the variable that adjusts the labor market, and the distributional value judgments of efficiency analysis are made, the economic cost of labor is always w AL. However, when labor is withdrawn from alternative jobs (expression [6.9]), use of the valuation w AL requires the following additional assumptions: (a) the market price of the good in the production of which it would be used in the without project situation is accepted as its accounting price; and (b) the market prices of the remaining resources released (VRR) are also accepted as their accounting prices. Assumption (a) does not present any problems if the good in question, q in the example given, is a non-traded consumer good. However, if q were a traded good it would be necessary to correct its market price in the manner indicated in Chapter 4. This case will be dealt with in Section 6.4. If on the other hand, q were a non-traded intermediate good, use of the valuation wAL would require assumptions (a) and (b) to be valid along the entire inter-industrial chain up to the non-traded consumer goods or the traded goods.