mutually perpendicular axes from an origin 0 called respectivelyOX', OX”, OX'”, and represent the income combination orincome stream for the particular individual by the point P,whose coordinates c', c", and d” are the three years’ income in-stallments with which the individual is initially endowed. Thenthrough the point P draw, instead of the straight line in the pre-vious representation, a plane ABC cutting the three axes inA, B, and C. This plane has a slope with reference to the twoOB
axes OX’ and OX” of equal to 1 + i' (unity or 100 per cent
plus the rate of interest connecting the first and second years),and has a slope with reference to the axes OX” and OX'"OC
represented by ^ equal to 1 + i" (unity plus the rate of inter-est connecting the second and third years). Now suppose thespace between the axes to be filled with willingness surfaceslaminated like the coats of an onion, such that for all points onthe same surface, the total desirability or wantability of thetriple income combination or income position represented byeach of those points will be the same. These surfaces will besuch as to approach the three axes and the planes between them,and also such that the attached numbers representing theirrespective total wantabilities shall increase as they recede fromthe origin. The plane ABC drawn through P at the slope fixedby the rates of interest just indicated will now be tangent tosome one of the willingness surfaces at a point Q, which is thepoint at which the individual will, under these conditions, fixhis income situation, for every point on the plane ABC willhave the same present value, and every point on this plane isavailable to him by borrowing and lending (or buying andselling) at the rates i' and i", but not all of them will have thesame desirability, or wantability. He will select that one whichhas the maximum wantability, and this will evidently be thepoint Q, at which the plane is tangent to one of the family ofwillingness surfaces. This point will be such that the rates oftime preference will be equal to the rate of interest.
[ 509 ]