¹ These curves may be interpreted either as long- or as short-run cost curves.

² The concept of an advertising factor may appear a bit strange since salesmen, billboards, etc., add nothing to the physical product of the firm, but it should be remembered that from the point of view of the firm, any good or service, the purchase and/or employment of which increases profits is a productive agent, i.e. a factor.

³ It may seem odd that the marginal profits curve should have a rising branch, but this assumption merely implies that the units in which the advertising factor can be purchased are so small that the first few units are not likely to have much effect and that a certain minimum amount must be used before the advertising becomes subject to “diminishing returns.” This assumption appears to be plausible to the writer, but the argument does not require it, and if the facts should prove to be different, the curve can be redrawn without changing the argument.

⁴ Our technique of handling advertising costs approaches the problem from a different angle from Chamberlin, E. H. in The Theory of Monopolistic Competition (Cambridge, Mass., 1933).Google Scholar Dr. Chamberlin adds advertising costs into the cost function of the firm whereas we draw the marginal value product curve (the marginal profits curve) for one advertising factor and the intersection of this curve with the marginal cost curve (to the firm) of the factor determines the amount of the factor that will be hired. By our technique we.may determine not only the amount to be spent on advertising, but also the amount to be spent on each particular kind of advertising (i.e., on each advertising factor) by means of drawing a diagram similar to Figure 2 for each advertising factor. Dr. Chamberlin's technique is not, I think, able to solve this problem. It should not be supposed, however, that the author is the originator of this technique. Actually the technique is adapted from an excellent but little known, article by Zeuthen, F., “Effect and Cost of Advertising from a Theoretic Aspect,” published in the 09, 1935, issue of the Nordisk Tidsskrift for Teknisk Okonomi, pp. 62–72.Google Scholar Professor Zeuthen's technique is quite complicated and the version of it here presented is considerably simpler than his.

⁵ We shall adopt the conventions that a schedule “increases” when it shifts in such a way that, at given ordinates, all abscissae (over the relevant range) will be further to the right than they were prior to the shift. A schedule will be said to “decrease” when (over the relevant range) the abscissae of the schedule, at given ordinates, are further to the left than before the schedule is shifted.

⁶ The ordinates of the marginal net value productivity schedule for a given factor measure the addition to the value of the firm's output due to the addition of a unit of the factor minus the additional expense involved in hiring the additional quantities of other factors in those quantities which make their marginal net value products proportional to their marginal prime costs at the given volume of employment of the factor for which the schedule is drawn.

⁷ Assuming that the labourers are homogeneous with respect to physical productivity.

⁸ Strictly speaking, marginal productivity analysis can only be applied when there is a sufficient number of units to make it possible to determine the marginal contribution of a unit (of a given factor) by variation about the margin and hence a person can only have a marginal productivity (in the strict sense), if his services are homogeneous with the services offered by a large number of other persons. However, in many cases, e.g. salesmen, each person has a different value productivity, and this productivity cannot be determined in a precise manner. But the value produced by the person in conjunction with the co-operating factors gives an upper limit to the wage rate he could possibly get and this upper limit is reduced by the formation of economic pressure groups (of which the person is not a member) in just the same way that the marginal net value product functions are shifted to the left and down.

⁹ As might be expected, the members of a trade or profession are only too anxious to keep their competitors out of social clubs, etc., in order not to have to share the business of the club members. In many cases, the trade unions refuse to admit more members, since, it is argued (correctly) that the existence of unemployed members tends to cause “chiseling” on the union wage scale, but none the less closed unions simply force non-union members to work for lower wages than they would have accepted if the union did not exist.

¹⁰ Because there is little or no homogeneity among the various persons engaged in these occupations, it is impossible to classify them into factors of production and apply marginal productivity analysis, but in spite of this, they may be said to have a value productivity. This value productivity is the upper limit to the wage rate an individual could possibly be paid (see n. 8), and we can tell when it increases and when it decreases. Of course, owing to changes in the bargaining power of the various factors and of the employer, an increase in the value productivity of a person could conceivably result in the diminution of his wage rate, but if we make a ceteris paribus assumption about relative bargaining strength, the argument will hold without further qualification.

¹¹ The marginal net value productivity of factory workers and other “anonymous” employees of big corporations depends largely upon their physical productivity in the sense that they, as members of groups (other than trade unions), cannot attract business to the firm which employs them, since the complexity of a large-scale production process makes it impossible for a prospective buyer to discriminate in favour of the employers of the members of a particular ethnic or social group. Of course, salesmen are in an entirely different position since their contact with the customer is personal, and here large as well as small enterprises must consider the contribution which an individual's “connections” makes to his value productivity; with salesmen, an individual's “connections” may be the major determinant of his value productivity, since his only function is to sell, i.e. he has no “physical” productivity.

¹² When the union is in a strong enough position to insist upon a closed shop, the additional value productivity of union workers due to the “goodwill” they bring is an “over-head contribution,” i.e. the “goodwill” of the union is conditional upon exclusive employment of union men and not upon the absolute amount of employment offered (although there are exceptions to this) and hence the employment of additional men does not shift the demand curves for the products to the right. This means that the marginal net value productivity function of union labour is the same as it would be if the union were completely powerless to affect the demand curves for an employer's products, but the average net value productivity function will be higher owing to the “overhead” contribution and hence the union is able to demand (with some prospects of getting) a total reward in excess of the marginal value product multiplied by the number of units employed. However, this additional reward must be collected in a lump sum since it cannot be received in the form of higher wage rates, for an attempt to collect it in this form will merely diminish the volume of employment and will not yield the union (or its members) a total payment in excess of the marginal net value product multiplied by the number of units employed. The additional payment is, of course, indeterminate in size (it has an upper limit) and its amount can be settled only by bargaining.

¹³ We shall not consider the consequences of the fact that a store owned by the company has a smaller risk and uncertainty cost than a store owned by an individual because the company has access to knowledge of the future demand curves for the store's products, which the individual does not, i.e. a knowledge of the future output and hence employment plans of the factory. Furthermore, the wage-bill of the factory will always be larger if the store is owned by the firm that owns the factory (see p. 32), hence the expected yield of the store will be higher if it is owned by the factory.

¹⁴ The marginal propensity to consume the products of the company store is defined in a manner similar to Mr. Keynes's definition of the marginal propensity to consume; it is the ratio of a marginal increase in expenditure on the products sold at the company store to a marginal increase in income.

¹⁵ In the case of highly perishable products, the demand schedule in one period will tend to be independent of the amount previously purchased, since the previously purchased products will have been either consumed or destroyed. However, as individuals may be willing to forgo temporarily the consumption of certain goods if they have recently consumed some, this statement may not always be true even in the case of perishable goods.

¹⁶ As drawn, the cost function is a short-period cost function, i.e. not all costs are prime costs; however, this is not essential to the argument. It is essential to the argument, however, that the period to which the demand and cost functions refer be of shorter duration than the period for which the entrepreneur has output and price plans, for otherwise it would be impossible to distinguish “the present” from “the next” period.

¹⁷ Throughout this section of the paper, we have assumed that the entrepreneur is only concerned with two periods: the present period and one future period, which we have called the “next” period. These periods may be as short or as long as we desire. However, during the period the price charged for a product and the prices paid for the factors remain constant and the entrepreneur is indifferent as to the precise moment in the period at which he sells the product or buys (hires) the factors.

¹⁸ Actually, as we shall see below, the cost functions are also affected by the price charged for the product in the present period. This effect takes place through shifting of the supply functions of the factors as indicated below. Consequently the P ₂ curve should be interpreted to indicate the maximum profit that can be earned when the factors are combined in the optimum manner (from the point of view of the firm).

¹⁹ As can be seen, we are assuming that the firm maximizes its profits in the next period without regard to the effect of its output on the demand curves for periods still further in the future, but if we wish we may extend the analysis to include additional periods, i.e. demand in the period after the “next period” might be a function of the output in the present and the “next” periods, but this can be done more easily by calculus than by clumsy geometry—analytically the problem presents no difficulty.

²⁰ We are here concerned only with inter-relations between the demands for the products of the firm and we are assuming that the cost functions of the two products are completely independent. Later we shall examine the case of joint production.

²¹ This is so only by assumption—in fact the demand curve for X ₂ might just as well decrease as increase due to an increase in the output of X ₁.

²² We actually discuss only the two variable cases, but it is obvious that the analysis could be extended to include any number of variables. However, as previously indicated, it is better to handle multi-variable cases by means of calculus.