10
suppose (a) and ( b ) are two brands of flour. If I consumes duringthe period X units of one brand and 20 units of the other his desirefor a 21st unit of the latter will depend on how much he has ofthe former (how large X is). If he has much of the first kind hisdesire is small.
A similar pair of curves may be found by moving P horizontally.
If the supposition in Part I were true the two strange curves (viz:connecting marginal utilities of A and B with quantities of B andA, respectively), would reduce to straight lines parallel to the planeof the paper.
§ 10 .
The relations indicated hv these three surfaces are really allincluded in one of them—the primitive. Consequently, to avoidtroublesome transitions from one mode of representation to anotherwe shall hereafter confine ourselves to this primitive surface.
Consider horizontal sections of this surface, that is sections par-allel to the plane of the A and B axes. Each section forms a curvewhich may be called an indifference curve. It is the locus of pointsrepresenting all consumption-combinations of A and B which have agiven total utility. In fig. 18 the attached number to each curverepresents the amount of this utility. They in general form afamily of concentric curves vanishing finally at the point M of max-imum satisfaction. M is the point at which the individual wouldarrange his consumption-combination of A and B if they cost noth-ing. There may be two or more maxima. For competing articlesthese maxima may lie in the axes (fig. 19), for one may prefer not toconsume both.
The ordinates may of course have any units of length. Suppose19- this unit to he indefinitely reduced from an
inch to a millimeter, etc. Then our surface-becomes a layer. Its thickness may he fig-ured as a density (rather than an ordinate),distributed over the plane of the paper aselectricity over a conductor. Each indif-ference curve is the locus of points wherethe density (formerly ordinate), is a givenamount. This idea of density will be hence-forth used though the necessity for its usedoes not come till the next chapter.
Fig. 20 shows the curves for competing articles and fig. 22 forcompleting. For “perfect” substitutes the curves (fig. 21) reduce