Shape of utility function

Question

I have read in a paper (http://www.public.asu.edu/~kirkwood/DAStuff/refs/risk.pdf) that the shape of the utility function depends on the attitude towards risk. My question is does not it also depend on the underlying optimization problem. For example, if it is a minimization problem then if my attitude is risk aversing then utility function should be convex, whereas if it is a maximization problem and my attitude is risk aversing then utility function should be concave. Am I correct. Any suggestion will be useful.

Answer 1

There is no reason to make your utility function convex just because you are faced with a minimization problem. It is true that minimization problems often have convex objective functions, but you are not minimizing your utility, are you? More likely, you will be minimizing some cost function, and the utility function will appear in the constraints.

At a more conceptual level, utility functions are to be set before you decide what to do with them. The utility function is a complete description of the individual agent, and you cannot change the utility function without altering the person behind it. For example, my dislike for peanut butter does not depend on prices, or of whether I'm maximizing utility or minimizing costs, and my utility function should respect this in all cases.