in the theory of value and prices.

71

to parallel straight lines whose intercepts on the A and B axes areinversely proportional to the fixed ratio of their marginal utilities.The point M is indeterminate on the line 99. “Lehigh” and

“Lackawanna” anthracite coal are nearly perfect substitutes. If itcost nothing the individual would indifferently consume the quan-

tity 09 (vertical) of one or 09 (horizontal) of the other or anycombination of the two on the straight line 99 inclined in this caseat 45°.

For perfect completing articles the whole family of curvesreduces to a straight line passing through the origin (fig. 23), Letus regard a pair of shoes as two distinct commodities : right shoesand left shoes. For any point in the line OM (fig. 23), the desirefor right shoes vanishes as long as no new left shoes are admitted,and yet the desire for a new pair may exist. The idea of marginalutility for right shoes has no application though that for pairs ofshoes has.

§ 11 .

There are endless points of view from which the primitive and itsderivatives may be approached and made to yield the economicrelations we seek.* Descriptions will be confined chiefly to the

* For instance we might take curves corresponding to the sections of the deriv-ative surfaces at various heights, or curveB orthogonal to the indifference curvesthese will be again referred to), or curves representing the locus of points atwhic h the marginal utilities of the two commodities have a given ratio.