Front Page Titles (by Subject) Chapter II: THE DEFINITION OF MARGINAL SOCIAL AND PRIVATE NET PRODUCTS - The Economics of Welfare
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Chapter II: THE DEFINITION OF MARGINAL SOCIAL AND PRIVATE NET PRODUCTS - Arthur Cecil Pigou, The Economics of Welfare 
The Economics of Welfare (4th ed.) (London: Macmillan, 1932).
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THE DEFINITION OF MARGINAL SOCIAL AND PRIVATE NET PRODUCTS
§ 1. CONCERNED as we are with the national dividend as a continuing flow, we naturally understand by the resources directed to making it, not a stock of resources, but a similarly continuing flow; and we conceive the distribution of these resources among different uses or places on the analogy, not of a stagnant pond divided into a number of sections, but rather of a river divided into a number of streams. This conception involves, no doubt, many difficulties in connection both with the varying durability of the equipment employed in different industries and with the dynamic, or changing, tendencies of industry as a whole. In spite of these difficulties, however, the general idea is exact enough for the present purpose. That purpose is to provide a suitable definition for the concepts which are fundamental throughout this Part, namely, the value of marginal private and the value of the marginal social net product. The essential point is that these too must be conceived as flows—as the result per year of the employment per year of the marginal increment of some given quantity of resources. On this basis we may proceed to work out our definition.
§ 2. For complete accuracy it is necessary to distinguish between two senses in which the term marginal increment of resources may be employed. It may be conceived either as being added, so to speak, from outside, thus constituting a net addition to the sum total of resources in existence, or as being transferred to the particular use or place we are studying from some other use or place. If the effect on production in a particular use or place of adding an increment of resources is independent of the quantity of resources employed elsewhere, the net products of these two sorts of marginal increment will be the same. It often happens, however, that this condition of independence is not satisfied. Thus, as will be shown more fully in a later chapter, the nth unit of resources employed in a particular firm will yield different quantities of produce according as the quantity of resources employed in other firms in the same industry is larger or smaller. The net products derived from marginal increments of resources, interpreted in the above two ways, might perhaps be distinguished as additive marginal net products and substitutive marginal net products. In general, however, the net products derived from the two sorts of marginal increment of resources in any use or place are not likely to differ sensibly from one another, and for most purposes they may be treated as equivalent.
§ 3. Waiving, then, this point, we have next to define more precisely what is meant when we speak of the marginal net product of the resources employed in any use or place as the result of the marginal increment of resources employed there. This is tantamount to saying that the marginal net product of a given quantity of resources is equal to the difference that would be made to the total product of these resources by adding to or subtracting from them a small increment. This, however, is not by itself sufficient. For the addition or subtraction of a small increment can be accomplished in several different ways with correspondingly different results. We are here concerned with a particular way. For us the marginal net product of any flow of resources employed in any use or place is equal to the difference between the aggregate flow of product for which that flow of resources, when appropriately organised, is responsible and the aggregate flow of product for which a flow of resources differing from that flow by a small (marginal) increment, when appropriately organised, would be responsible. In this statement the phrase when appropriately organised is essential. If we were thinking of marginal net product in the sense of the difference between the products of two adjacent quantities of resources, we should normally imagine the resources to be organised suitably to one of these quantities and, therefore, not to the other. Since, however, our interest is in the difference between the products of two adjacent flows of resources, it is natural to conceive each of the two flows as organised in the manner most appropriate to itself. This is the conception we need. It is excellently illustrated by Professor J. B. Clark. The marginal increment of capital invested in a railway corporation is in reality, he writes, "a difference between two kinds of plant for carrying goods and passengers. One of these is the railroad as it stands, with all its equipment brought up to the highest pitch of perfection that is possible with the present resources. The other is the road built and equipped as it would have been if the resources had been by one degree less. A difference in all-round quality between an actual and a possible railroad is in reality the final increment of capital now used by the actual corporation. The product of that last unit of capital is the difference between what the road actually produces and what it would have produced if it had been made one degree poorer."8
§ 4. One further point must be made clear. The marginal net product of a factor of production is the difference that would be made to the aggregate product by withdrawing any (small) unit of the factor. The marginal unit is thus not any particular unit. Still less is it the worst unit in existence—the most incompetent workman who is employed at all—as some writers have supposed! It is any (small) unit out of the aggregate of units, all exactly alike, into which we imagine this aggregate to be divided. Though, however, the marginal unit is thus any unit, it is not any unit however placed. On the contrary, it is any unit conceived as placed at the margin. The significance of this is best understood with the help of an illustration. To withdraw a man attending a new machine or working in an easy place in any industry and to do nothing else would, of course, affect aggregate output more seriously than to withdraw a man attending an obsolete machine or working in a difficult place would do. The marginal net product of work in that industry is then the difference that would be made to aggregate output by withdrawing for a day any (similar) man and redistributing, if necessary, the men that are left in such wise that the machine consequently left unattended or place of work left unfilled is the least productive machine or place of work of which use has hitherto been made.
§ 5. So much being understood, we have next to distinguish precisely between the two varieties of marginal net product which I have named respectively social and private. The marginal social net product is the total net product of physical things or objective services due to the marginal increment of resources in any given use or place, no matter to whom any part of this product may accrue. It might happen, for example, as will be explained more fully in a later chapter, that costs are thrown upon people not directly concerned, through, say, uncompensated damage done to surrounding woods by sparks from railway engines. All such effects must be included—some of them will be positive, others negative elements—in reckoning up the social net product of the marginal increment of any volume of resources turned into any use or place. Again an increase in the quantity of resources employed by one firm in an industry may give rise to external economies in the industry as a whole and so lessen the real costs involved in the production by other firms of a given output. Everything of this kind must be counted in. For some purposes it is desirable to count in also indirect effects induced in people's tastes and in their capacity to derive satisfaction from their purchases and possessions. Our principal objective, however, is the national dividend and changes in it as defined in Part I. Chapters III. and V. Therefore psychical consequences are excluded, and the marginal social net product of any given volume of resources is taken, except when special notice to the contrary is given, to consist of physical elements and objective services only. The marginal private net product is that part of the total net product of physical things or objective services due to the marginal increment of resources in any given use or place which accrues in the first instance—i.e. prior to sale—to the person responsible for investing resources there. In some conditions this is equal to, in some it is greater than, in others it is less than the marginal social net product.
§ 6. The value of the marginal social net product of any quantity of resources employed in any use or place is simply the sum of money which the marginal social net product is worth in the market. In like manner the value of the marginal private net product is the sum of money which the marginal private net product is worth in the market. Thus, when the marginal social net product and the marginal private net product are identical and the person responsible for the investment sells what accrues to him, the value of both sorts of marginal net product in respect of a given volume of resources is equal to the increment of product multiplied by the price per unit at which the product is sold when that volume of resources is being employed in producing it.9 For example, the two sorts of marginal net product per year of a million units of resources invested in weaving being assumed to be identical, the value of both is equal to the number of bales of cloth by which the output of a million plus a small increment, say a million and one, exceeds the output of a million units, multiplied by the money value of a bale of cloth when this output is being produced.10 This, it should be observed in passing, is different from, and must by no means be confused with, the excess—if there is an excess—of the money value of the whole product when a million and one units of resources are being employed over the money value of the whole product when a million units are being employed.
[8.] The Distribution of Wealth, p. 250. I have substituted "produced" for "earned" in the sentence quoted above.
[9.] This definition tacitly assumes that the realised price is equal to the (marginal) demand price. If government limitation of price causes it to be temporarily less than this, the value of the marginal net product will need to be interpreted as the marginal (physical) net product multiplied by the marginal demand price, and the marginal demand price in these conditions will not be equal to the actual selling price.
[10.] Cf. Marshall, Principles of Economics, p. 847. It will be noticed by the careful reader that, even when the additive marginal net product and the substitutive marginal net product are equal, the value of the marginal net product will be different according as marginal net product is interpreted as additive and as substitutive marginal net product. The difference will, however, in general, be of the second order of smalls.