in the theory of value and prices. 73

§ 12 .

Since OA and OB represent quantities A and B of commodities(a) and (b) purchasable for the same sum ($25), they are inverselyproportional to the prices of (a,) and (6).

If prices remain the same but the individual grows richer and thesum he can afford to spend on (a) and ( b) is no longer $25 but $50>the line AB simply recedes twice as far remaining parallel to itself.As it changes, its varying point of tangency follows a tortuous linethe locus of all points at which the individual would arrange hiscombination of A and B at the given prices.

If the price of (a) increases, OA relatively diminishes and a newpoint of tangency is found. If the articles are completing (fig. 22)a change of price will not cause the tangent line to very greatlyalter the proportion of consumption of the articles for it will merelychange the position of I to (say) I', and it is clear that the coordin-ates of I' have nearly the same ratio as those of I; if substitutes(fig. 20) a slight relative change in price will cause an enormouschange in the proportions used (I and I'). This was found to be thecase in 1889 when a copper syndicate attempted to raise the priceof copper. Hardly any article exists which has not some substi-tute. This sort of dependence keeps manufacturers watchful.' Itis because of this dependence that some “ useful ” articles go out ofuse.

§ 13 .

Fig. 24 represents two “ grades ” of the same commodity, as brownand granulated sugar. The superior grade is laid off on the B (hor-izontal) axis, and the inferior on theA (vertical) axis. The point ol maxi-mum satisfaction is in or near the Baxis. If the individual is poor and canafford to spend little on the article hewill buy the poorer quality. The lineAB is tangent to an indifference curvein or near the A axis at I. If he growsricher the line AB recedes from theorigin and he purchases the combina-tion I' containing considerably more ofB; he uses this superior quality on Sun-days (say) while consuming A on week days. If he grows richerstill, he changes the position to I" using none of A or only a little.

24.