CHAPTER II -- Section 3

In contrast to the previous section, which examined the effects of changes in income (with prices fixed), this section begins by considering changes in price with income fixed.  As before, Hicks uses an indifference diagram representing a consumer's preferences for two goods, X and Y.  Letting one of the prices vary (the price of X) while holding the other fixed, he represents the consumption possibilities by the diagram in Figure 7.  The different prices of X determine diagonal lines, such as LM and L'M in the figure, defined by the consumer's income.  For each such diagonal, there will be an equilibrium point where the diagonal touches an indifference curve.  The set of all such equilibrium points defines a curve, represented by MPQ in the figure, that Hicks calls the price-consumption curve.
Hicks next compares the price-consumption curve with the income-consumption curve (defined in the previous section), using Figure 8 for illustration.  He notes that the point Q, where indifference curve I2 is tangent to a line through Q and M, lies to the right of P', where the indifference curve is tangent to a line parallel to LM.  He points out that this follows from the convexity of the indifference curves.  To spell that out a bit, let me note that convexity in this context implies that the slope of the indifference curve is increasing (specifically, becoming less negative) as we move from left to right.  The line L"M, where Q is tangent, has a less negative slope than LM (which has the same slope as L'M').  Thus the point where the indifference curve is tangent to L"M must occur to the right of the point where it is tangent to L'M'.

Hicks claims that this proposition is "quite fundamental to a large part of the theory of value" and discusses a few of its implications.  When the price of X falls, the consumer can afford more of it with the same income; thus he moves along the price-consumption curve from equilibrium P to equilibrium Q.  Hicks states that

We now see that this movement from P to Q is equivalent to a movement from P to P' along the income-consumption curve, and a movement from P' to Q along an indifference curve.  We shall find it very instructive to think of the effect of price on demand as falling into these two separate parts.

There are thus two effects of the change in price:  an effect that is similar to an increase in income, and an effect of substitution of the now-cheaper commodity for other commodities.  The total effect is the sum of these two effects.  Hicks notes that the relative importance of these two effects will depend on the proportion of income that the consumer was spending on the commodity whose price has changed.  If the consumer was not buying much of X, then a fall in its price may not gain him much, and the income effect will tend to be swamped by the substitution effect.  Hicks states that this point is the justification of Marshall's assumption of constant marginal utility.

Hicks goes on to note that the substitution effect will always happen and will always cause an increase in demand for a commodity when its price falls.  The income effect is less reliable.  Although it will ordinarily work similarly to the substitution effect, in the case of inferior goods, the income effect of a decrease in price may actually lead to a decrease in demand.