Problem 2 (20 points) Assume that Mary has an initial wealth of $2,800. Mary needs to make a decision on whether to purchase a lottery or not. If Mary buys this lottery, she has 0.2 probability of winning $1,000 and 0.8 probability of losing $400. Mary's utility function is given by U (w)= Vw. Where w denotes Mary's total wealth. a. Assume that the price of the lottery is $420.0. What would be Mary's expected wealth if she chooses to purchase the lottery? (4 points) b. What would be Mary's utility if she chooses NOT to purchase the lottery? (4 points) c. Continue with the assumption in part a. What would be Mary's expected utility if she chooses to purchase the lottery? (4 points) d. What is the certainty equivalence wealth level of purchasing this lottery? That is, what is the certain amount of wealth that would give Mary the same utility level as her expected utility of purchasing the lottery? (4 points) e. What is the expression of Mary's coefficient of absolute risk averse (in terms of w )? (4 points)