Ms. Ants "intertemporal" endowment consists of $270 in period 1 and $90 in period 2. The prices are normalized to be 1 in either period. Ms. Ants preferences are represented by period utility function v (x) = ln x and the discount factor = 4 5

1. Assuming that Ms. Ant can borrow or save money at an interest rate of r, solve for her optimal consumption levels in the two periods as functions ofr.

2. Show that Ms. Ant would save money in the first period for any positive interest rate r.

Now consider Mr. Grasshopper, who has the same intertemporal preferences as Ms. Ant. But Mr. Grasshoppers income is zero in the first period. He only makes an income of $180 in the second period

3. Find out how much money Mr. Grasshopper would borrow as a function of the interest rate r.

4. Suppose Ms. Ant and Mr. Grasshopper are the only two participants in the credit markets. Find the equilibrium value of the interest rate r that would equate the quantity demanded for borrowing to the quantity supplied of funds. What are the equilibrium consumption levels of the two agents in the two periods?