Problem 2 - Portfolio Choice

Let's focus now on the problem of a single agent our OLG economy. As usual, she receives an endowment y = 100 when young and nothing when old. The agent has the option to buy 2 assets a and b in order to save for the future (there is no money). Asset a and b rates of return are ra, rb respectively. She has a typical log utility: u(c1, c2) = log(c1) + log(c2).

1. State the agent's budget constraints.

2. Suppose that ra = 2, rb = 1. What is the optimal demand for assets a and b?

3. What is the condition on ra and rb to make the agent accept to carry both assets?

4. If rb = 1 and the agent controls the returns of asset a such that raa = 2a 1/2 , what is the the optimal demand for a and b?

Please answer these 4 question ,Thanks