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Figure 2.3Utility ofconsumption/investment forsome individualThis person would invest along curve W0W1 to the point where maximum utility would beachieved. This would be at point P.Chapter 2 • A framework for financial decision making38Figure 2.4The borrowing/lending opportunityavailable to anindividual withan amount ofwealth (W0)This amount could be lent at an interest rate r so that it would grow to W0 + rW0 afterone time period. Alternatively, an amount W0 borrowed at an interest rate r would leadto W0 + rW0 being owed after one time period.investor as it gives the highest level of utility. No other point along the productioncurve will enable this person to achieve as high a level of satisfaction as will the investment/consumption decision implied by point P. Therefore the amount investedshould be BW0 (which will yield 0A after a year), and 0B should be consumed now,giving 0A to consume next year. Suppose that our individual in fact only invests topoint Z, which is a feasible possibility. Whilst this would give some consumption, bothnow and next year, it does not give what this person would regard as the most satisfyingcombination of present and future consumption. We know this because Z coincideswith a lower utility curve. Given our individual’s preferences (represented bythe shape of the utility curve) and the state of the world as far as investment is concerned(represented by the investment line W0W1), P is clearly the most satisfying levelof investment for our individual.This is not necessarily the same as would be chosen by other individuals becausethey are unlikely to have the same views on the trade-off between present and futureconsumption. So there would be no unanimity as to the desirable level of investment –it would vary from person to person.The borrowing/lending opportunityAt this point let us introduce a further factor into the analysis and so make it morerealistic. That factor is the opportunity available to individuals for borrowing andlending through banks and other financial institutions (the financial market).Figure 2.4 shows another possibility, which could be used alone or in conjunctionwith the production opportunities. If the investor were to lend all of the wealth (W0)Appendix: Formal derivation of the separation theorem39now, it would, with interest at rate r, become W0 rW0 after a year. Thus the slope ofthe borrowing/lending line is (W0 rW0)/W0 1 r.The existence of borrowing/lending opportunities enables levels of investment tobe undertaken in excess of the amount of wealth left after a desired level of consumptionhas been undertaken. This is achieved by borrowing the required amount nowand repaying it (with interest) next year. Similarly, not all of the present wealth leftafter consuming the desired amount need be invested in production; some of it can belent, to be received back (again with interest) next year. This broadening of the possibilitiesmay well enable the investor to achieve higher levels of satisfaction (utility).