(1) You are given 2 choices: (a) getting $500,000 tax-free for sure, and (b)taking a chance on a gamble that has a probability p of getting $1 million tax-free and probability 1-p of getting nothing. Clearly, if probability p is 100% in the gamble, as a rational and sane person, you will choose the gamble because you will have a 100% chance of getting $1 million; on the other hand, if p is 0%, you will choose $500,000 for sure. Now, by gradually reducing the probability p of getting $1 million in the gamble from 100% towards 0, find the probability p* for you will feel choice
(b) has about the same degree of attractiveness or desirability as (a) to you. Use p* to compute your utility of $500,000.
(2) Repeat (1) by changing choice (a) to getting $200,000 tax-free for sure. Note: the probability p* for the case will generally be smaller than the one for (1).