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7. Production: General Pricing of the Factors > 2. Determination of the Discounted Marginal Value...

C. Marginal Value Product

As we have seen, the MVP for any factor is its MPP multiplied by the selling price of its product. We have just concluded that every factor will be employed in its region of diminishing marginal physical product in each process of production. What will be the shape of the marginal value product schedule? As the supply of a factor increases, and other factors remain the same, it follows that the total physical output of the product is greater. A greater stock, given the consumers’ demand curve, will lead to a lowering of the market price. The price of the product will then fall as the MPP diminishes and rise as the latter increases. It follows that the MVP curve of the factor will always be falling, and falling at a more rapid rate than the MPP curve. For each specific production process, any factor will be employed in the region of diminishing MVP.8 This correlates with the previous conclusion, based on the law of utility, that the factor in general, among various production processes, will be employed in such a way that its MVP is diminishing. Therefore, its general MVP (between various uses and within each use) is diminishing, and its various particular MVPs are diminishing (within each use). Its DMVP is, therefore, diminishing as well.

The price of a unit of any factor will, as we have seen, be established in the market as equal to its discounted marginal value product. This will be the DMVP as determined by the general schedule including all the various uses to which it can be put. Now the producers will employ the factor in such a way that its DMVP will be equalized among all the uses. If the DMVP in one use is greater than in another, then employers in the former line of production will be in a position to bid more for the factor and will use more of it until (according to the principle of diminishing MVP) the DMVP of the expanding use diminishes to the point at which it equals the increasing DMVP in the contracting use. The price of the factor will be set as equal to the general DMVP, which in the ERE will be uniform throughout all the particular uses.

Thus, by looking at a factor in all of its interrelations, we have been able to explain the pricing of its unit service without previously assuming the existence of the price itself. To focus the analysis on the situation as it looks from the vantage point of the firm is to succumb to such an error, for the individual firm obviously finds a certain factor price given on the market. The price of a factor unit will be established by the market as equal to its marginal value product, discounted by the rate of interest for the length of time until the product is produced, provided that this valuation of the share of the factor is isolable. It is isolable if the factor is nonspecific or is a single residual specific factor in a process. The MVP in question is determined by the general MVP schedule covering the various uses of the factor and the supply of the factor available in the economy. The general MVP schedule of a factor diminishes as the supply of the factor increases; it is made up of particular MVP schedules for the various uses of the factor, which in turn are compounded of diminishing Marginal Physical Product schedules and declining product prices. Therefore, if the supply of the factor increases, the MVP schedule in the economy remaining the same, the MVP and hence the price of the factor will drop; and as the supply of the factor dwindles, ceteris paribus, the price of the factor will rise.

To the individual firm, the price of a factor established on the market is the signal of its discounted marginal value product elsewhere. This is the opportunity cost of the firm's using the product, since it equals the value product that is forgone through failure to use the factor unit elsewhere. In the ERE, where all factor prices equal discounted marginal value products, it follows that factor prices and (opportunity) “costs” will be equal.

Critics of the marginal productivity analysis have contended that in the “modern complex world” all factors co-operate in producing a product, and therefore it is impossible to establish any sort of imputation of part of the product to various co-operating factors. Hence, they assert, “distribution” of product to factors is separable from production and takes place arbitrarily according to bargaining theory. To be sure, no one denies that many factors do co-operate in producing goods. But the fact that most factors (and all labor factors) are nonspecific, and that there is very rarely more than one purely specific factor in a production process, enables the market to isolate value productivity and to tend to pay each factor in accordance with this marginal product. On the free market, therefore, the price of each factor is not determined by “arbitrary” bargaining, but tends to be set strictly in accordance with its discounted marginal value product. The importance of this market process becomes greater as the economy becomes more specialized and complex and the adjustments more delicate. The more uses develop for a factor, and the more types of factors arise, the more important is this market “imputation” process as compared to simple bargaining. For it is this process that causes the effective allocation of factors and the flow of production in accordance with the most urgent demands of the consumers (including the nonmonetary desires of the producers themselves). In the free-market process, therefore, there is no separation between production and “distribution.” There is no heap somewhere on which “products” are arbitrarily thrown and from which someone does or can arbitrarily “distribute” them among various people. On the contrary, individuals produce goods and sell them to consumers for money, which they in turn spend on consumption or on investment in order to increase future consumption. There is no separate “distribution”; there is only production and its corollary, exchange.

It should always be understood, even where it is not explicitly stated in the text for reasons of exposition, that the MVP schedules used to set prices are discounted MVP schedules, discounting the final MVP by the length of time remaining until the final consumers’ product is produced. It is the DMVPs that are equalized throughout the various uses of the factor. The importance of this fact is that it explains the market allocation of nonspecific factors among various productive stages of the same or of different goods. Thus, if the DMVP of a factor is six gold ounces, and if the factor is employed on a process practically instantaneous with consumption, its MVP will be six. Suppose that the pure rate of interest is 5 percent. If the factor is at work on a process that will mature in final consumption five years from now, a DMVP of six signifies an MVP of 7.5; if it is at work on a 10-year process, a DMVP of six signifies an MVP of 10; etc. The more remote the time of operation is from the time when the final product is completed, the greater must be the difference allowed for the annual interest income earned by the capitalists who advance present goods and thereby make possible the entire length of the production process. The amount of the discount from the MVP is greater here because the higher stage is more remote than the others from final consumption. Therefore, in order for investment to take place in the higher stages, their MVP has to be far higher than the MVP in the shorter processes.9

  • 8. This law applies to all factors, specific and nonspecific.
  • 9. See the excellent discussion in Böhm-Bawerk, Positive Theory of Capital, pp. 304–12. For a further discussion of DMVP as against MVP, see Appendix B below, “Professor Rolph and the Discounted Marginal Productivity Theory.”