19. substituting an expected value for a random variable Suppose we want to maximize the expected value of a a2, over a 0,

19. substituting an expected value for a random variable Suppose we want to maximize the expected value of θa − a2, over a ≥ 0, where θ is a random variable. So we want to solve max a≥0 E[θa − a2]

We now frame this by substituting the random variable’s expected value for the random variable. Let θ denote the expected value of θ.

Solving max a≥0

θa − a2 will of course locate the solution to the original problem. Discuss the principle of consistent framing that is being employed. What happens to the transparent substitution when risk aversion is present?