7.02. Determination of the Discounted Marginal Value Product

0:002. Determination of the Discounted Marginal Value Product a. Discounting If the DMVP schedules determine the prices of non-specific factor services, what determines the shape and position of the DMVP schedules? In the first place, by definition it is clear that the DMVP schedule is the MVP schedule for that factor, discounted. There is no mystery about the discounting, as we have stated, the MVP of the factor is discounted in accordance with the going pure rate of interest on the market. One of the determinants of the DMVP schedule is the rate of discount, and we have seen b.

1:12The Marginal Physical Product What then determines the position and shape of the MVP schedule? What is the marginal value product? It is the amount of revenue intake attributable to a unit of a factor. And this revenue depends on two elements. One, the physical product produced, and two, the price of that product. If one hour of factor X is estimated by the market to produce a value of 20 gold ounces, this might be because one hour produces 20 units of the physical product which are sold at a price of 1 gold ounce per unit, or the same MVP might result from the production of 10 units of the product sold at 2 gold ounces per unit, etc.

2:09In short, the marginal value product of a factor service unit is equal to its marginal physical product times the price of that product. This is not strictly true, but the technical error in the statement does not affect the causal analysis in the text. In fact, this argument is strengthened, for MVP actually equals MPP times marginal revenue, and Marginal Revenue is Always Less Than or Equal to Price. Let us then investigate the determinants of the Marginal Physical Product, MPP. In the first place, there can be no general schedule for the MPP as there is for the MVP, for the simple reason that physical units of various goods are not comparable.

3:06How can a dozen eggs, a pound of butter and a house be compared in physical terms? Yet the same factor might be useful in the production of any of these goods. There can be an MPP schedule, therefore, only in particular terms. That is, in terms of each particular production process in which the factor can be engaged. For each production process there will be for the factor a marginal physical production schedule of a certain shape. The MPP for a supply in that process is the amount of the physical product imputable to one unit of that factor, that is, the amount of the product that will be lost if one unit of the factor is removed.

3:59If the supply of the factor in the process is increased by one unit, other factors remaining the same, then the MPP of the supply becomes the additional physical product that can be gained from the addition of the unit. The supply of the factor that is relevant for the MPP schedules is not the total supply Supply in the Society, but the supply in each process, since the MPP schedules are established for each process separately. 1. The Law of Returns In order to investigate the MPP schedule further, let us recall the Law of Returns set forth in Chapter 1.

4:47According to the law of returns and eternal truth of human action, if the quantity of one factor varies and the quantities of other factors remain constant, there is a point at which the physical product per factor is at a maximum. Physical product per factor may be termed the average physical product, APP. The law further states that with either a lesser or a greater supply of the factor, the APP must be lower. 2. Marginal Physical Product and Average Physical Product What is the relationship between the APP and MPP?

5:33The MPP is the amount of physical product that will be produced with the addition of of One Unit of a Factor, Other Factors Being Given. The APP is the ratio of the total product to the total quantity of the variable factor, other factors being given. To illustrate the meanings of APP and MPP, let us consider a hypothetical case in which all units of other factors are constant and the number of units of one factor is variable. With zero units of the variable factor, the total product is zero, the average physical product is zero, and the marginal physical product is zero.

6:20With one unit of the variable factor, the total product is three, the average physical product is three, and the marginal physical product is three. With 2 units of the variable factor, the total product is 8, the average physical product is 4, and the marginal physical product is 5. With 3 units of the variable factor, the total product is 15, the average physical product is 5, and the marginal physical product is 7. With four units of the variable factor, the total product is 22, the average physical product is 5.2, and the marginal physical product is 7.

7:07With five units of the variable factor, the total product is 27.5, the average physical product is 5.5, and the marginal physical product is 5.5. With 6 units of the variable factor, the total product is 30, the average physical product is 5, and the marginal physical product is 2.5. And with 7 units of the variable factor, the total product is 28, the average physical product is 4, and the marginal physical product is minus 2. In the first place, it is quite clear that no factor will ever be employed in the region where the MPP is negative.

7:57In our example, this occurs where 7 units of the factor are being employed. 6 units of the factor, combined with given other factors, produced 30 units of the product. An addition of another unit results in a loss of 2 units of the product. The MPP of the factor when seven units are employed is minus two. Obviously, no factor will ever be employed in this region, and this holds true whether the factor owner is also owner of the product or a capitalist hires the factor to work on the product. It would be senseless and contrary to the principles of human action To expand either effort or money on added factors, only to have the quantity of the total product decline.

8:49We follow here the law of returns, in that the APP, beginning, of course, at zero, with zero units of the factor, rises to a peak and then falls. We also observe the following. 1. When the APP is rising, with the exception of the very first step, where TP, APP and MPP are all equal, MPP is higher than APP. 2. When the APP is falling, MPP is lower than APP. 3. At the point of maximum APP, MPP is equal to APP. In other words, if APP is increasing, then the marginal physical product is greater than the average physical product in this region, and where APP is decreasing, the marginal physical product is lower than the average physical product.

9:55But if MPP is greater than APP when the latter is rising, and is lower than APP when the latter is falling, then it follows that when APP is at its maximum, MPP must be neither lower nor higher than, but equal to, APP. Now let us explore further the area of increasing APP. Let us take another hypothetical, in which 2 units of the variable factor yield a total product of 10 and an average physical product of 5, while 3 units of the variable factor yield a total product of 18 and an average physical product of 6.

10:44Let us stipulate further that four units of the variable factor yield a total product of 25 and an average physical product of 6.2. This is a segment of the increasing section of the average physical product schedule, with the peak being reached at 4 units and 6.2 APP. The question is, what is the likelihood that this region will be settled upon by a firm as the right input-output combination? Two units of the variable factor plus a bundle of all the other factors yield 10 units of the product. On the other hand, at the maximum APP for the factor, four units of it plus other factors yield 25 units of the product.

11:37We have seen that it is a fundamental truth in nature that the same quantitative causes produce the same quantitative effects. Therefore, if we have the quantities of all the factors, we shall get half the product. In other words, two units of the factor combined with the other factors will yield 12.5 units of the product. Consider this situation. We see that 2 units of the variable factor plus given factors yield 10 units of the product. But we see that 2 units of the variable factor plus given factors yield 12.5 units of the product. Obviously, no one would want to spend more in effort or money on factors, the other factors, and obtain less total output, or for that matter, the same total output.

12:34It is evident that such a producer is in an area of negative marginal physical productivity of the other factors. He would obtain a greater total product by throwing away some of the other factors. A region of increasing APP for one factor, then, signifies a region of negative MPP for other factors, and vice versa. Thus, the variable factor will be set so that it has zero marginal productivity, only if it is a free good. There is, however, no such thing as a free good. There is only a condition of human welfare not subject to action, and therefore not an element in productivity schedules.

13:23Conversely, the APP is at its maximum for the variable factor only when the other factors are free goods and therefore have zero marginal productivity at this point. Only if all the other factors were free and could be left out of account could the producer simply concentrate on maximizing the productivity of one factor alone. However, there can be no production with only one factor, as we saw in Chapter 1. The conclusion, therefore, is inescapable. A factor will always be employed in a production process in such a way that it is in a region of declining APP and declining but positive MPP.

14:14In every production process, therefore, every factor will be employed in a region of diminishing MPP and diminishing APP, so that additional units of the factor employed in the process will lower the MPP and decreased units will raise it. 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.

15:02What 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 consumer's demand, 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. For each specific production process, any factor will be employed in the region of diminishing MVP. This law applies to all factors, specific and non-specific.

15:48This 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.

16:34This 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 are used 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 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.

17:36Thus, 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 non-specific or is a single residual specific factor in a process.

18:36The MVP in question is determined by the general MVP schedule covering the various uses of the 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, setteris paribus, the price of the factor will rise.

19:31To 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 firms using the product, since it equals the value product that is foregone 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 cooperate in producing a product, and therefore it is impossible to establish any sort of imputation of part of the product to various cooperating factors.

20:28Hence, 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 cooperate in producing goods, But the fact that most factors, and all labor factors, are non-specific, 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 is not just bargaining, but tends to be set strictly in accordance with its discounted marginal value product.

21:22The 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, 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 non-monetary desires of the producers themselves. In the free market process, therefore, there is no separation between production and distribution.

22:11There 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 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 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 consumer's product is produced.

23:13It 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 non-specific factors among various productive stages of the same or of different goods. Thus, if the DMVP of a factor is 6 gold ounces, and if the factor is employed on a process practically instantaneous with consumption, its MVP will be 6. Suppose that the pure rate of interest is 5%. If the factor is at work on a process that will mature in final consumption 5 years from now, a DMVP of 6 signifies an MVP of 7.5.

24:06If it is at work on a 10-year process, a DMVP of 6 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 are 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.