I'll make a note that we look to revise this solution going forwards - it's not wrong - but could be simplified. However, Investor B is still risk averse (just to a lesser degree as wealth increases) whereas Investor A is not risk averse at all! This means, as Investor B becomes wealthier, he or she becomes less risk averse. For example if u(w) au(w)+b,a > 0, then Eu(X) > Eu(Y) is. A utility function need not,in fact can not be determined uniquely. It is a numerical description of existing preferences. However, I agree with your comment that Investor B exhibits decreasing absolute risk aversion. Observation about utility Utility theory is built on the assumed existed and consistency of preferences for probability distribution of outcomes. I'm not convinced that we need to consider A(w) and R(w) to answer this question. Investor B's utility curve is a graph of the square root of w, which has a concave shape. We can check that U'(w) = 1 and U''(w) = 0. Investor A's utility curve is a straight line. The graph of U(w) against w will be concave. For each additional $1 of wealth, the extra utility derived reduces. If 2 individuals have different CRRA utility functions, the one with the. Pages 10 to 12 in Chapter 2 show some illustrations of the shapes of the U(w) graphs for investors that are risk-averse, risk-neutral and risk-seeking.įor a risk-averse investor, we are looking for diminishing marginal utility of wealth. The parameter is often referred to as the coefficient of relative risk aversion. End nodes of the class implement value or utility functions that assign different value or utility functions to a nite set of attribute combinations. I wonder if an easier way of looking at it is to consider the utility function itself.Ĭan you visualise a plot of these two functions? End nodes of the class 2d imple-ment interpolated value or utility functions that are based on two attributes.
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