Chapter 2 • A framework for financial decision making
EW 0 and consume amount 0D. This can be done by borrowing the shortfall (ED).
Obviously this amount will have to be repaid (with interest) next year, but, nonethe-
less, consumption of 0D now and 0C next year represents a more attractive (higher
utility) prospect than consuming 0B now and 0A next year. Thus the introduction of
borrowing/lending has increased utility. Note that GC (the amount that must be
repaid next year out of 0G to leave the individual with 0C) is equal to ED (the amount
borrowed now) plus interest on ED, that is, ED (1 +r). This is evident from Figure 2.5
if we bear in mind that the slope of the borrowing/lending line is (1 +r).The separation theorem
An examination of Figure 2.5 reveals an important point. Irrespective of the indi-
vidual’s time preferences (shape of utility curve), all investors faced with the product-
ive investment opportunities depicted in Figure 2.5 would invest up to point R and
then achieve their personal highest level of utility by use of the borrowing/lending
opportunity. Those investors whose highest utility curve would be tangential to
the borrowing/lending line above R would invest up to R and lend that part of the
remainder of their wealth that they wish not to consume. In Figure 2.5, UxUxis a util-
ity curve of a different investor from the one whose preferences are represented by
U 1 U 1 and U 2 U 2. This second individual would choose to invest up to point R on the
productive investment curve and then lend amount FE, leaving 0F for consumption.
An individual whose highest utility curve coincides with point R will obviously
wish to invest up to that point but will not need to use the borrowing/lending
opportunity.
Irrespective of the personal preferences of various investors, all the investors agree
that it is best to invest up to point R, which is the point where the slope of the pro-
duction curve W 0 W 1 is equal to that of the borrowing/lending line. This unanimity
among investors as to the optimum level of productive investment is quite interesting
in the context of individuals. In the context of businesses where managers should try
to make investments that most benefit all their shareholders, the unanimity becomes
of major importance.
The assumptions on which the above is based and their implications were each
discussed in the main body of this chapter.