76

Irving Fisher—Mathematical investigations

26.

Fig. 26 shows the usual sort of indifference production curves.

B is here laid off to the left and A downward ;the line AB is the locus of production combina-tions of A and B which can be sold for thesame money, say $1,000. The point of tan-gency* I is the point at which the individual canproduce the required $1,000 worth of A and Bwith the minimum disutility. The curves aresuch that the points of tangency will be gener-ally at or near the axes, especially if the amountof production is large i. e. if the line AB is farfrom the origin. If B becomes cheaper (OB longer) the point oftangency will change but slowly until presently there are two pointsof tangency and if B becomes still cheaper the individual will changehis profession suddenly from the position I to a position in or nearthe A axis.

The numbers on the indifference curves for production increase in-definitely negatively. There is usually no maximum or minimumpoint.

§ 1 *.

Finally an article consumed may be competing or completing toanother produced. A blacksmith finds small utility in dumb bells,the production of horseshoes “ competes ” with the consumption ofdumb-bells.

The relations between competing articles and completing articlesare not always so simple, for articles may be competing at somecombinations and completing at others. Statistical inquiries alongthese lines might be made with profit, and have apparently attractedlittle attention.f

CHAPTER II.

THREE OR MORE COMMODITIES.

The foregoing methods extend very readily to three dimensions.Suppose the whole market to attain equilibrium. As before, let usas it were, freeze this equilibrium except for three commodities A, B,and C. Then as before, we obtain a fixed sum of money disposable

# The tangency must be such that the curve is on that side of the straight linetoward the origin. The other kind of tangency represents an unstable equilib-

t See Jevons, p. 136.

nun.