: Suppose that your initial wealth is 200 and you consider a risky investment (like buying a stock or a company). If the investment succeeds, your final wealth will be 400. If the investment fails, your final wealth will be 100. Both of these possibilities happen with probability 1/2. If you decide to not invest, your final wealth will be equal to your initial wealth, i.e., 200.

a) Would you invest if you were risk-neutral, risk-loving, risk-averse?

b) Now suppose that your utility of final wealth is given by u(w) = w. What sort of risk attitude does this utility function imply? Would you invest?

c) Now suppose that if you do not invest, you can deposit your money in a bank that pays an interest or r (for example, a 5% interest is represented by r = 0.05). As a result, your final wealth in this case is (1 + r)200 instead of 200. In other words, the original setup implicitly assumed r = 0.

d) Assuming that your utility of final wealth is as given in part (d), for what values of r would you decide to not invest, for what value you would be indifferent and for what values would you decide to invest?