Value & Capital, CHAPTER VII, Section 3

This brief section begins the discussion of production in cases more complex than the simple cases treated in the previous two sections.  Those sections derived results about the necessary effects resulting from a factor or product price change in the one factor, one product case and in the fixed output, two factor case.

This section opens by discussing an analogy with utility theory, and how similar necessary results were obtained in simple cases. Thus the expectation is stated that we are getting these necessary results for the simple cases in production because we are working with only two variables -- one factor and one product, or two factors.  In more complex cases we may expect this "definiteness" to disappear.

This section considers the case of a firm producing a fixed output, using three factors A, B, and C.  Suppose the price of factor A falls; then, because the ratio of the prices of B and C stays the same, they can actually be considered as a single factor.  So we can conclude that the price drop for A will cause an increase in demand for A, and the demand for the combined factor of B and C must decrease.  As Hicks puts it, "There must be a substitution in favour of A at the expense of the other factors taken together."

Things change in the presence of complementarity. If B is complementary with A, the increased demand for A will cause an expansion in demand for B as well and therefore a substitution in favor of A and B, and against C.  Hicks explains that, as in utility theory, A and B are considered complementary when a substitution of A for C (B remaining unchanged) moves the marginal rate of substitution of B for C in favor of B.  Thus for a constant output, if we consider only substitutions among factors, the same rules emerge as for substitutions in a consumer's budget.

Practically the same thing would happen if the quantities of factors were kept constant and the firm varied its production of various products in response to changes in prices.  The only difference is that a rise in price of product X would lead to a substitution in favor of product X, as opposed to a price rise in a factor leading to a substitution against that factor.