CHAPTER II -- Section 2

In this section Hicks returns to the study of the indifference diagram.  Figure 5, shown below, plays an important role in the discussion in this section.  For a given amount of income, the set of possible consumption choices (assuming income is fully spent) will be defined by the diagonal line (LM in the figure) that connects the two points that are defined by spending all the income on one of the two goods and none on the other.  The consumer will choose a point along this line that touches an indifference curve (this will be the highest-valued indifference curve that the consumer could achieve with that income).

If the consumer's income increases, the diagonal line (which we can think of as the consumer's budget constraint) will move to the right. (The line L'M' in the figure shows one such example.)  As long as the prices do not change, the new budget constraint will be parallel to the old one.

As the consumer's income continues to increase, the budget constraint line moves to the right, and the equilibrium consumption point traces out a curve (labeled as C in the figure).  Hicks calls this the income-consumption curve.  He explains that the income-consumption curve will ordinarily slope upward and to the right, but he shows in Figure 6 two cases where this does not hold.  Below I've tried to redraw Figure 6 as it appears in the text.

It is not obvious why income-consumption curves might look like curves C1 and C2, so I've drawn another graph that attempts to show how this might come about.  In this graph, which I call Figure 6a, I've shown the consumer's income increased to the line L'M' .

We are assuming there could exist cases in which either C1 or C2 intersects L'M'  at an equilibrium point.  These cases correspond to different shapes of the indifference curve.  The dotted curve is an indifference curve that causes C1 to intersect the budget constraint at an equilibrium point.  The dashed curve corresponds to the case where C2 intersects at an equilibrium point.  Note that both of these cases involve one of the goods being significantly more desirable than the other.