# Figure 23 utility of consumption investment for some

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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. Chapter 2 A framework for financial decision making 38 Figure 2.4 The borrowing/ lending opportunity available to an individual with an amount of wealth (W 0 ) This amount could be lent at an interest rate r so that it would grow to W 0 + r W 0 after one time period. Alternatively, an amount W 0 borrowed at an interest rate r would lead to W 0 + r W 0 being owed after one time period. investor as it gives the highest level of utility. No other point along the production curve 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 invested should be BW 0 (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 to point Z, which is a feasible possibility. Whilst this would give some consumption, both now and next year, it does not give what this person would regard as the most satisfying combination of present and future consumption. We know this because Z coincides with a lower utility curve. Given our individual’s preferences (represented by the shape of the utility curve) and the state of the world as far as investment is concerned (represented by the investment line W 0 W 1 ), P is clearly the most satisfying level of investment for our individual. This is not necessarily the same as would be chosen by other individuals because they are unlikely to have the same views on the trade-off between present and future consumption. So there would be no unanimity as to the desirable level of investment – it would vary from person to person. The borrowing/lending opportunity At this point let us introduce a further factor into the analysis and so make it more realistic. That factor is the opportunity available to individuals for borrowing and lending through banks and other financial institutions (the financial market). Figure 2.4 shows another possibility, which could be used alone or in conjunction with the production opportunities. If the investor were to lend all of the wealth (W 0 ) Appendix: Formal derivation of the separation theorem 39 now, it would, with interest at rate r , become W 0  r W 0 after a year. Thus the slope of the borrowing/lending line is (W 0  r W 0 )/W 0  1  r . The existence of borrowing/lending opportunities enables levels of investment to be undertaken in excess of the amount of wealth left after a desired level of consumption has been undertaken. This is achieved by borrowing the required amount now and repaying it (with interest) next year. Similarly, not all of the present wealth left after consuming the desired amount need be invested in production; some of it can be lent, to be received back (again with interest) next year. This broadening of the possibilities may well enable the investor to achieve higher levels of satisfaction (utility).