We now have $5,000 in assets and are given a choice between investment 1 and investment 2. With investment 1, we increase our asset position by $295,000 with a 80% probability and by $95,000 with a 20% probability. With investment 2, we increase our asset position by $595,000 with a 50% probability and by $5,000 with a 50% probability. Our utility function for final asset position x is u(x). We are given the following values for u(x): u(0)=0, u(90,000)=0.3, u(490,000)=0.7, u(640,000)=0.8, u(810,000)=0.9 , u(1,000,000)=1.
Part (a): Will we prefer investment 1 or investment 2? (Hint: In general, you need to approximate u(x) for some of those x’s whose utility values are not given. This approximate interpolation can be done with the help of Excel, through your trial-and-error guess values of the x’s. A good set of approximate utility values of the x’s together with the given utility values should lie approximately on a smooth curve. However, for this particular problem, the given utility values are consistent with a utility function of a special form.)
Part (b): Are we risk-averse, risk-seeking, or risk-neutral? Explain.