Brief history and main reactions

1 So far, we have been using the abbreviated notation
V to denote the aggregate of the valuations created by the project over time to its terminal period T, omitting, for the time being, the discounting or compounding procedure necessary to reduce the
V to a single figure.

However, we may write Vt = (v^b_t − v^c_t), where Vtis the net benefit in the year t (which could be positive or negative), v_t^bis the valuationof the benefit inyear t, while v_t^cis the valuationof the cost inthe year.¹

The calculationof v_t^bpresents no problem, at least in so far as the goods produced by the project are marketable. Inthe earlier chapters inPart II, we perforce had to adopt, as an adequate measure of consumer surplus, the area under the demand curve for a good x less the amount the consumers have to pay for the amount, OQ, they buy. Thus, the full valuationfor the total value OQ amount of x is the area under the demand curve (without any subtraction of the sum paid by the consumers). And it is from this valuation v_t^bof the benefit of the project’s output of the good x that we now have to subtract the real cost, the v^c_t.

In a cost–benefit calculation, however, costs are not, in general, equal to the costs of the materials and productive factors used by the project in the ordinary sense; say, as they would be calculated by a private enterprise from their market prices. The relevant costs in a CBA are what are known as ‘opportunity’ costs – a term which serves to indicate the valuations forgone when the materials or factors are transferred from other employments.

2 In general, then, this key concept of opportunity cost to the project is the worth of that particular input in some alternative use. Yet, so defined, there will be ambiguity wherever there is more than one alternative use. In such cases, the definition adopted may refer to the alternative use that yields the highest value.

1 It will be convenient, nonetheless, to continue to use
V as shorthand for the aggregate of valuations (both positive and negative to the end of the period T), although it is more revealing to use notation

Vtor

(v^b_t−v_t^c). Ineither case, if the aggregate is positive – at least whenreduced by discounting to a present sum – it must be concluded that all the factors and materials used in the project over time have a higher value inaggregate thanthe value they created inthe uses from which they are transferred.

QUAH: “CHAP11” — 2007/1/25 — 07:59 — PAGE 65 — #2 Opportunity cost of labour 65 And were the economist at liberty to choose from which use the material or factor should be transferred, such a definition would be valid. In so far as the economist is, in this respect, subject to political constraints, he has no choice but to calculate the opportunity cost of anything as the value it created in that particular (politically determined) use from which it is to be transferred. It will simplify the exposition if, henceforth, we think of opportunity cost in terms of a particular designated alternative use.

Although the concept of opportunity cost, using this definition, can be extended to any material or productive factor that is to be used in a project, either for its initial construction or for its operation upto some terminal year T, nothing is lost in our understanding of its nature and method of calculation if, in the main, we confine our treatment of it to labour or to labour of a particular skill.

Inrespect of labour, however, we should be aware that the calculationof its opportunity cost must also take into account any occupational preference the worker has when comparing the employment conditions offered by the project and those in his existing occupation. We may also have to take account of any costs of movement the worker may have to incur in moving from his present employment to employment in the new project.

In the absence of either of these, however, the opportunity cost of a unit of labour – say, a 40-hour working week of that labour – to the project is no more thanthe value it cancreate inthe productionof the amount of a good x from which it is to be transferred. In more familiar jargon, its opportunity cost is equal to the value of its marginal product in x, abbreviated to VMPx, this being the value forgone when the unit of labour is moved from producing x to producing alternative goods – say, y and/or z – inthe project.

In a cost–benefit calculation, this VMPxfigure must, ingeneral, be adjusted to make allowance for any externalities associated with the production or consump-tion of the amount of good produced by the unit of labour. If, in that labour’s unit of productionof good x, a positive externality of $50 is conferred on the community, this $50 is added to the VMPx. Conversely, if the community suffers a loss valued at $80, that much has to be subtracted from VMPx. The adjusted VMPx may be referred to as the social value of the marginal product of labour in producing the good x, or SVMPx, and is therefore the appropriate opportunity cost of that labour to the project.

3 In order to fix our ideas, we may suppose that a unit of labour is to be transferred from the productionof good x to producing something else in the project. If this unit of labour produces 10 units of x during a week, each unit of x having a social value of $50, its SVMPxis $500, which is thenthe appropriate opportunity cost per week to the project – provided the worker is indifferent between producing good x and working in the project and provided also there are no costs of movement when he transfers his labour from producing good x to working for the project.

If the worker is not indifferent between occupations; if, say, he would require no less than $75 per week additional to his wage in x to induce him to work for the project, the opportunity cost of his labour to the project becomes $575

QUAH: “CHAP11” — 2007/1/25 — 07:59 — PAGE 66 — #3 or SVMPxplus op (op being shorthand for the occupational preference premium of the worker). Were the reverse to be the case, the opportunity cost, SVMPx

minus op, becomes $425 per week.

A further adjustment to the opportunity cost is required if the worker incurs costs inmoving from the productionof x into the project, where the costs include both the money costs of relocation and the less tangible ‘psychic’ costs experienced by him, his family and friends, when he departs from an area in which he had settled. Although the physical costs of the relocationare easily ascertained, the ‘psychic’ costs can be estimated only from the worker himself.

Consequently, there can be difficulties in eliciting the true figure. Whatever the total of these costs is, however, they will occur only once and they are, there-fore, to be spread over the entire period of the worker’s employment in the project.

It will be noticed that, in the above examples, no mention has been made of the wage rate or the worker’s rent either inthe productionof x or inthe project.

Calculation of their magnitudes is unnecessary in estimating the opportunity cost, for the wage paid and the worker’s rent are properly conceived as transfer payments from the rest of the community to the worker.

4 Calculating the opportunity cost of the entire output produced by all the fac-tors during a period of, say, a year, is a straightforward business. If the only factor used during the year in project w were 2,000 workers transferred from x, their opportunity cost to project w would be equal to the social value of the amount of the good x they produce ina year, say $25 million, corrected, however, for their occupational preference for working in x rather thaninw (which we may suppose to be measured by anaverage of $75 a week). The full opportunity cost is therefore equal to this $25 million plus the measure of occupational preference, which is equal to (2,000 × 50 × $75) for a 50-week working year.

This social value of x, assumed above to be $25 millionis, of course, equal to the most the community is willing to pay for it, adjusted for externalities in its production or consumption. And the most people are willing to pay for that annual amount is adequately measured by the area under the demand curve for x. Nor is there any difficulty if the workers employed in project w are transferred from the production of a number of different goods. If, say, 1,200 workers are transferred from producing good x and the remaining 800 from producing good y, the social value forgone is simply the sum of the area under the demand curve for the amount of x produced by 1,200 workers over the year plus the area under the demand curve for the amount of y produced by the 800 workers over the year – again, adjusted for any incidental externalities.²

2 No problem arises if the economist wishes to calculate opportunity costs in terms of goods rather than interms of factors. For example, the opportunity cost of a good w is simply equal to the opportunity cost of a unit of of labour (or other x-producing factor) divided by the number of w goods it produces.

QUAH: “CHAP11” — 2007/1/25 — 07:59 — PAGE 67 — #4 Opportunity cost of labour 67 5 Nor is any revision required if the inputs required by the project are materials imported from abroad (as we shall see inChapter 14) or materials that have to be transferred from a domestic non-augmentable stock.

An example of a non-augmentable stock would be the total oil reserves in a country that has no prospect of increasing the amount of oil at home or abroad in the forseeable future. The opportunity cost of the amount of oil required by the project is equal to the domestic social value of the oil currently being used in the economy.

As for the opportunity costs of other inputs such as plant, equipment and machin-ery, their calculationfollows that of labour. They are not, that is, the prices that are paid for them, but calculated by reference to the social value forgone when they are transferred to the project in question.

If, for example, some particular equipment has to be produced specifically for the project, its opportunity cost, say it comes to $10,000, is calculated by reference to the opportunity cost of labour and other inputs required, whether imported or not.

Investment in such a piece of equipment would, of course, be made in anticipation of its contributing to the social value of the project’s annual product.

However, the required equipment may not be specific to the project, but one that currently has a social value of other goods being produced in the economy.

Its opportunity cost is then calculated as the social value it contributes annually in producing these other goods. This opportunity cost could, for example, be $1,500 per annum for for ten consecutive years.

6 As for the opportunity cost of a significant area of land required by the pro-ject, this is sometimes entered as the DPV of the expected net benefits over the future that would otherwise accrue to this area of land if it remained in its current use; or sometimes, and this is worth, simply as the market value of the land.

It may thenseem that its opportunity cost may be properly calculated as the DPV or, rather, the compounded terminal value (CTV),³of the net contribution of the land to the annual social value since these annual contributions have to be forgone when the land is transferred to the project. However, the contribution made to the social value of the product by the land itself may not be possible where it is combined in fixed proportion with the other inputs. In addition, transferring the land from its current use to the project entails a dismantling of the whole of the existing concern and also, therefore, the disposal of the various sorts of labour, machinery and equipment used in producing its goods. Such losses must also be counted. Yet, it would be erroneous to cost such losses arising, say, from the disposal of labour or machines once used by the concern as equal to their resulting opportunity costs. For it may well be that the machines have only scrap value, and the discarded labour has no use, or little use, elsewhere.

3 As will be indicated in Part V on ‘Investment Criteria’, our critique of the popular DPV for evaluating net benefit streams is a prelude to our proposal that it be supplanted by our proposed CTV.

QUAH: “CHAP11” — 2007/1/25 — 07:59 — PAGE 68 — #5 On such a reckoning, the cost to the project of taking over the land, and therefore the consequent disposal of the labour and machinery involved, would be under-stated. For these other factors would, if the land remained in its original use, continue to contribute to the full social value there.

It must be concluded that, wherever a significant area of land is involved (signif-icant in that the area of land has value in some other use), it is virtually impossible to assignto it anopportunity cost. The only valid procedure thenavailable to the economist entrusted with the cost–benefit analysis of a project is that of comparing the social value of the land in its current use with its use in the proposed project.

In each of the two alternative uses to be considered, the fixed factor, land, is combined with other factors to yield a stream of net social benefits – the social value of the annual benefits less the opportunity costs of the other inputs required.

The project meets the economist’s criterion if the DPV, or preferably the CTV, of the net social benefits from using the land for the project exceeds that from continuing the current use of the land.

In the particular case where the project being mooted is that of restoring an area of land to its original wilderness state or creating a designed wilderness area, additional costs may be incurred if demolition has to be employed; apart, that is, from the opportunity costs of labour and other inputs required initially in restoring or designing a wilderness area and, subsequently, in maintaining and monitoring the area.

QUAH: “CHAP12” — 2007/1/25 — 08:02 — PAGE 69 — #1

12 Opportunity cost of unemployed