We usually think of utility functions as always sloping upward(more is better) or downward (less is better — fewer nuclear power plant disasters, for example). But this is not always the case. In this problem, you must think about your utility function for coffee versus milk. Imagine that you are about to buy a cup of coffee. Let c (0 ≤ c ≤ 1) represent the proportion of the contents of the cup accounted for by coffee, and 1 – c the proportion accounted for by milk.
a. Assess your utility function for c for 0 ≤ c ≤ 1. If you like a little milk in your coffee, the high point on your utility function may be at a value of c strictly between 0 and 1.
b. Compare (A) the mixture consisting of proportions c of coffee and1 – c of milk in a cup and (B) the lottery yielding a cup of coffee with probability c and a cup of milk with probability 1–c. Are the expected amounts of milk and coffee the same in A and B? [That is, if you calculate E (c), is it the same in A and B?] Is there any value of c for which you are indifferent between A and B? (How about when c is 0 or1?) Are you indifferent between A and B for the value of c at the high point of your utility function?
c. How would you describe your risk attitude with respect to c? Are you risk-averse or risk-prone, or would some other term be more appropriate?