BUSF_A01.qxd

Appendix: Formal derivation of the separation theorem

curves of all rational individuals would therefore be broadly similar to those shown in

Figure 2.2.

If we combine Figures 2.1 and 2.2, the result of which is shown in Figure 2.3, we can

see that point P is the best combination of investment/consumption for our particular

Figure 2.2
Utility of present /
future consumption
for some individual

Each point along any particular curve represents a combination of present and future wealth

that a particular individual would find equally satisfactory: the higher the line the greater the

satisfaction which the combinations would give.

Figure 2.3
Utility of
consumption/
investment for
some individual

This person would invest along curve W 0 W 1 to the point where maximum utility would be

achieved. This would be at point P.