7 You have $100 (thousand ) in the bank. You have the opportunity to buy Bitcoin for $40 (thousand ) per Bitcoin. (I am denominating everything in thousands to keep the numbers smaller. $40,000 is roughly the current price of Bitcoin. Assume Bitcoin is perfectly divisible) Your trusted financial advisor estimates that in the next month, Bitcoin will either go up to $60 or go down to $30, with equal probability. (That is, the probability that it will go up is 1/2 and the probability it will go down is 1/2.) In either case you will sell your Bitcoin and move to Costa Rica. Your utility for money is U(c) = 2c1/2. (Risk aversion = 1/2.)

(a) If you buy x units of Bitcoin:

(i)how much money will you have left in the bank?

(ii)if Bitcoin goes up, how much money will you have in total and what will your utility be?

(iii)if Bitcoin goes up, how much money will you have in total and what will your utility be?

(iv)what will your expected utility be?

(b) What is your optimal purchase of Bitcoin?

8 Your (fraternal) twin is in exactly the same position as you (the same amount of money in the bank, the same financial advisor, the same opportunity, the same plan to move to Costa Rica in one month) - except that your twin's utility for money is U (c) = ln c. (Risk aversion = 1.) Answer the same questions as above for your twin.