Suppose James has inter-temporal preferences given by u(c1,c2)=ln(c1)+ln(c2) with = 0.5 Let his income today be M1 = 100 and income tomorrow be M2 =105 . Suppose the price of consumption today is p1 = 1 and the price of consumption tomorrow is p2 =1.05. (Round the final result, but not the intermediate calculations, to the nearest 2 decimal points.)

(a): If the interest rate is i = 0.05 what is the most James can consume today. Alternatively, what is the most James can consume tomorrow?

(b): If the interest rate increases to i = 0.1 , what is the present value (today) of James' income in both periods? What is the most James can borrow? What is the level of consumption in each period at the zero savings point?

(c) [5 points] In general, how does the zero savings point depend on the interest rate? Please justify your answer.

(d): Suppose the interest rate is i =0.05 . What is the market price of an extra unit of period 1 consumption in terms of period 2 consumption? What is James's value of period 1 consumption in terms of period 2 consumption at the zero savings point? Use these two values to determine whether James is a borrower, or a saver. Explain your response.

(e): If the interest rate is i = 0.05 , how much will James want to consume in each period? If James is a saver, how much money will he save? If James is a borrower, how much money will he borrow? Make sure you derive these quantities based on James' goal of maximising his utility subject to his inter-temporal budget constraint.

(f) [10 points] What interest rate would make James want to consume at the zero savings point?