Q2: Insurance (1.5 points) Suppose you have been given a crypto wallet filled with new SBF inspired Oopscoin. The wallet is currently worth about $100.00. Based on past experience you know that this wallet will go straight to the moon if you hodl for a year, at which point you could trade the coin for $100,000.00. But if you happen to lose/forget the crypto wallet key you won't be able to access the funds in the future. If this happens the value of the wallet will fall to $0.00. Based on a recent cognitive test, you know there is a % chance you will lose or forget the wallet key. Use Cr and Cr to denote your potential consumption when you remember or forget the crypto key respectively. Use this information to answer the following prompts: A. Start by marking the endowment point in the commodity space (C'g,Cr). Then assume you can buy insurance that pays $N in the event you are unable to access your crypto wallet. The cost of this insurance is a premium of $0.40N. Draw your budget constraint in the commodity space. (1/2 point) B. Suppose your Von Neumann-Morgenstern utility function is given by U(Cgr,Cr) = %ln(C'R) + 110111(6'1;!). What is your marginal rate of substitution at the endowment point (1/4 point) C. If you are maximizing your expected utility, how much insurance will you purchase and how much money will you have to spend in each of the two contingencies. Will you insure fully? (1/2 point) D. Now suppose the price of insurance rises to a premium of $0.50N. Now how much insurance will you purchase and how much money will you have to spend in each of the two contingencies. Will you insure fully? (1/4 point) Jichael Mordan is famous for his love of gambling. His utility over money is U($) = $28z$ = $3. That is to say his utility over money is the cube of however much money he has. Suppose Jichael is out golfing with his friend Bharles Carkley and currently has $4,000,000.00 in his wallet. Bharles offers Jichael a $2,000,000.00 bet on the flip of a fair coin: 50% probability he loses $2,000,000.00 (walks away with $2,000,000.00) and 50% probability he wins $2,000,000.00 (walks away with $6,000,000.00). Use this information to answer the following: A. Plot Jichael's Bernoulli utility function. Is Jichael risk-loving, risk-averse, or risk-neutral? (1/4 point) B. Will Jichael take this bet? Show that his expected utility is higher/lower if he accepts/declines this gamble. Mark the expected utility of the gamble on the graph from (A). (1/4 point) C. What is the expected value of this gamble? Mark this number on the graph from (A). (1/2 point) D. How much money will make Jichael indifferent between taking the gamble or walking away (what is the certainty equivalent of this gamble)? Is it greater or smaller than the expected value of the lottery? Write an economic interpretation of this number. (1/2 point)