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NOTE 1.06. Factors of Production: The Law of Returns

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6. FACTORS OF PRODUCTION, THE LAW OF RETURNS

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We have concluded that the value of each unit of any good is equal to its marginal utility

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at any point in time, and that this value is determined by the relation between the

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actor's scale of wants and the stock of goods available. We know that there are two types

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In the process of goods, consumers' goods, which directly serve human wants, and producers' goods, which aid in the process of production eventually to produce consumers' goods.

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It is clear that the utility of a consumers' good is the end directly served.

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The utility of a producers' good is its contribution in producing consumers' goods.

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With value imputed backward from ends to consumer's goods through the various orders of producer's goods, the utility of any producer's good is its contribution to its product, the lower stage producer's good or the consumer's good.

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As has been discussed above, the very fact of the necessity of producing consumer's goods implies a scarcity of factors of production.

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If factors of production at each stage were not scarce, then there would be unlimited

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quantities available of factors of the next lower stage.

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Similarly, it was concluded that at each stage of production, the product must be produced

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by more than one scarce higher-order factor of production.

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If only one factor were necessary for the process, then the process itself would not

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In other words he will evaluate each unit of a factor as equal to the satisfactions provided by its marginal unit, in this case the utility of its marginal product.

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of a factor as equal to the satisfactions provided by its marginal unit, in this case,

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the utility of its marginal product.

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The marginal product is the product foregone by a loss of the marginal unit, and its value

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is determined either by its marginal product in the next stage of production, or, if it

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is a consumer's good, by the utility of the end it satisfies.

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Thus, the value assigned to a unit of a factor of production is equal to the value of its marginal product, or its marginal productivity.

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Since man wishes to satisfy as many of his ends as possible, and in the shortest possible time, see above, it follows that he will strive for the maximum product from given units of factors at each stage of production,

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As long as the goods are composed of homogeneous units, their quantity can be measured in terms

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of these units, and the actor can know when they are in greater or lesser supply.

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Thus, whereas value and utility cannot be measured or subject to addition, subtraction, etc.,

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quantities of homogeneous units of a supply can be measured. A man knows how many horses or cows he

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has and he knows that four horses are twice the quantity of two horses. Assume that a product,

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P, which can be a producer's good or a consumer's good, is produced by three complementary factors,

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X, Y and Z. These are all higher order producer's goods. Since supplies of goods are quantitatively

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Therefore, P are free to vary.

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The value of A yielding the maximum P divided by A, that is, the maximum average return

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of product to the factor, is called the optimum amount of X.

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The law of returns states that with the quantity of complementary factors held constant, there

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always exists some optimum amount of the varying factor.

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As the amount of the varying factor decreases or increases from the optimum P divided by

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A, the average unit product declines.

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The quantitative extent of that decline depends on the concrete conditions of each case.

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As the supply of the varying factor increases just below this optimum, the average return

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of product to the varying factor is increasing.

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Under the optimum, it is decreasing. These may be called states of increasing returns

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and decreasing returns to the factor, with the maximum return at the optimum point.

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The law that such an optimum must exist can be proved by contemplating the implications

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of the contrary. If there were no optimum, the average product would increase indefinitely

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It could not increase indefinitely as the quantity decreases since the product will be zero when the quantity of the factor is zero.

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But if p divided by a can always be increased merely by increasing a, this means that any

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desired quantity of p could be secured by merely increasing the supply of x.

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This would mean that the proportionate supply of factors y and z can be ever so small.

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Any decrease in their supply can always be compensated to increase production by increasing

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and the Supply of X.

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This would signify that factor X is perfectly substitutable for factors Y and Z, and that

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the scarcity of the latter factors would not be a matter of concern to the actor so long

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as factor X was available in abundance.

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But a lack of concern for their scarcity means that Y and Z would no longer be scarce factors.

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Only one scarce factor, X, would remain.

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But we have seen that there must be more than one factor at each stage of production.

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Accordingly, the very existence of various factors of production implies that the average

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return of product to each factor must have some maximum or optimum value.

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In some cases, the optimum amount of a factor may be the only amount that can effectively

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cooperate in the production process.

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Thus, by a known chemical formula, it may require precisely two parts of hydrogen and

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one part of oxygen to produce one unit of water.

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If the supply of oxygen is fixed at one unit, then any supply of hydrogen under two parts

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will produce no product at all, and all parts beyond two of hydrogen will be quite useless.

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Not only will the combination of two hydrogen and one oxygen be the optimum combination,

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but it will be the only amount of hydrogen that will be at all useful in the production process.

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The relationship between average product and marginal product to a varying factor

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may be seen in the hypothetical example of the returns to a varying factor with other

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factors fixed.

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The average unit product increases until it reaches a peak of 8 at 5 units of x.

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This is the optimum point for the varying factor.

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The marginal product is the increase in total product provided by the marginal unit.

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At any given supply of units of factor X, a loss of one unit will entail a loss of total

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product equal to the marginal product.

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In this hypothetical example, with three units of factor Y and zero units of factor X, total

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product is zero units, average unit product is zero units, and marginal product is inapplicable.

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With three units of factor Y and one unit of factor X, total product is four units,

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average unit product is four units, and marginal product is four units.

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With three units of factor Y and two units of factor X, total product is ten units, average

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unit product is five units, and marginal product is six units.

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With three units of factor Y and three units of factor X, total product is eighteen units.

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Average unit product is six units and marginal product is eight units.

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With three units of factor Y and four units of factor X, total product is thirty units.

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Average unit product is seven and a half units and marginal product is twelve units.

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With 3 units of factor Y and 5 units of factor X, total product is 40 units, average unit

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product is 8 units and marginal product is 10 units.

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With 3 units of factor Y and 6 units of factor X, total product is 45 units, average unit

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product is 7 and a half units and marginal product is 5 units.

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And with 3 units of factor Y and 7 units of factor X, total product is 49 units, average

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unit product is 7 units, and marginal product is 4 units.

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Thus if the supply of X is increased from 3 units to 4 units, total product is increased

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from 18 to 30 units, and this increase is the marginal product of X with a supply of

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4 units. Similarly, if the supply is cut from 4 units to 3 units, the total product must

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be cut from 30 to 18 units, and thus the marginal product is 12. It is evident that the amount

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of X that will yield the optimum of average product is not necessarily the amount that

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maximizes the marginal product of the factor. Often the marginal product reaches its peak

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before the average product. The relationship that always holds mathematically between the

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average and the marginal product of a factor is that as the average product increases,

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increasing returns, the marginal product is greater than the average product. Conversely,

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As the average product declines, diminishing returns, the marginal product is less than

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the average product.

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It follows that when the average product is at a maximum, it equals the marginal product.

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It is clear that with one varying factor, it is easy for the actor to set the proportion

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of factors to yield the optimum return for the factor, but how can the actor set an optimum

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Optimum combination of factors if all of them can be varied in their supply.

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If one combination of quantities of x, y and z yields an optimum return for x, and another

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combination yields an optimum return for y, etc., how is the actor to determine which

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combination to choose?

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Since he cannot quantitatively compare units of X with units of Y or Z, how can he determine

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the optimum proportion of factors?

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This is a fundamental problem for human action, and its methods of solution will be treated

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in Subsequent Chapters.