You are the financial advisor for Max Zorin and are tasked with deciding on how to allocate Mr. Zorins fortune. Mr. Zorin lives in the island nation of San Monique, and thus is required by law to only invest in bonds issued by the national James Bank, which have an interest rate of 50% over 10 years. Mr. Zorins utility function is logc1+3/4logc2, where c1 is his consumption over the next ten years and c2 is his consumption afterwards; his current wealth is $21 million.

1. Determine how much you should invest in bonds to maximize Mr. Zorins utility. (15 points)

2. Now suppose that San Monique imposes a capital gains tax of 50% on your gains over those 10 years. How does this change your decision about how much to invest in bonds? Please explain in terms of income and substitution effects. (10 points)

Now suppose that you discover another investment opportunity on the island in agribusiness. Unfortunately, the return on this investment is very risky: there is a 50% chance of the value of the investment returning nothing. But if the investment is successful, you will get back 5 times your principal plus the principal itself.

3. Return to the assumption that there are no capital gains taxes. To maximize Mr. Zorins expected utility, how much of Mr. Zorins assets should you invest in bonds, and how much in the agribusiness opportunity? (15 points)
4. Now again suppose that San Monique imposes a capital gains tax of 50% on your gains over those 10 years. (Note that even if the agribusiness fails, San Monique will still levy a 50% tax on gains from your investment in bonds.) How does this change your decision about how much to invest in bonds versus investing in the agribusiness? Why does your investment portfolio change in this way? (20 points)