Value & Capital, CHAPTER VII -- TECHNICAL COMPLEMENTARITY AND TECHNICAL SUBSTITUTION, Section 1

This chapter begins right where Chapter VI leaves off, by asking "what happens when a firm which has been at equilibrium at certain prices of products, and prices of factors, experiences a change in those prices."  How will those price changes affect the quantities of input factors it uses and the quantities of products it produces?  Hicks notes the similarity of the question to those addressed in Chapters II and III for the private individual.

Considering the simplest case, discussed in the last chapter, of an entrepreneur employing a single factor to produce a single product, the equilibrium is as shown in Figure 19 in the last chapter and can be seen in Figure 20 below -- in both figures denoted by P.  If the price of the factor falls, the most immediate effect (before any change is made in production) is that the entrepreneur's surplus increases from OK to OK1.  The reason for this is that the dashed line that represents the exchange of product for factor after the price change, will not decrease as much in moving from point P back to the vertical axis as did the prior exchange line PK;  this is because the quantity ON of factor consumed in production is not as costly in terms of product as before the price change.)  But the line PK1 is not tangent to the production curve, so OK1 is not the maximum surplus that the entrepreneur can achieve under the new conditions.  He will be better off at the new equilibrium P' on the production curve where the tangent P'K2 has the same slope as PK1.

We assume the production curve is concave down, so "the point P', where the tangent slopes upwards less steeply than at P, must lie to the right of P."  Therefore the fall in the price of the factor results in an increased use of the factor as an input to production and an increased output of the product.  As Hicks notes, a rise in the price of the product will also cause a decreased slope of the tangent, with the same effects.

In comparing these results with the earlier results for the private individual, Hicks notes that here the change in price leads to a new point where the tangent line touches the same (production) curve as before the price change, rather than a different curve.

Therefore, in the case of production, we do not have anything similar to the income effects which gave us so much trouble in utility theory. The only 'production effect' is something similar in character to the substitution effect; it is a movement along the curve (in this case a production curve, as in that case an indifference curve), the curve whose properties we know from the stability conditions.

Hicks notes another complexity within the production effect, however:  that of complementarity.  It turns out that complementarity is more complicated in production theory than in utility theory, because we have to consider the relations between two kinds of commodities -- the factors and the products.  Hicks closes with a brief glimpse of upcoming sections, saying "Their mutual relations and their cross-relations will take a little disentangling."