need help with this problem

Consider a two period small open economy, where the representative con- sumer has the following utility function loge + log C2 Assume also that consumption in each period t (t = 1, 2) is a composite of consumption of the domestic good (car) and the foreign good (GR) such that A = CHAR Assume that the economy has zero initial assets (on = 0), and that the real exchange rate in each period is denoted by e. Assume also that income in each period is given by y. The economy can borrow or lend at the international interest rate r. (a) Write down the lifetime budget constraint and the Lagrangian. (b) Solve for the optimal consumption of home and foreign goods in each period. (c) What is the net asset position of this economy? (d) Suppose now that y1 = 100, and y2 = 1000. # = 0.95 and r = 5 percent (0.05). Suppose also that en = ez = 1. From your answer to part (c), calculate numerically the net asset position of the economy. Is the economy a net borrower or lender? (e) For the numbers given above, calculate also the optimal consumption of all goods in each time period. (f) Now suppose that the economy is restricted from borrowing abroad, and net assets must always be non negative. (a1 2 0). What is the optimal consumption of each good? (g) Comparing parts (e) and (f), which situation gives the consumer the highest utility? (Hint: Evaluate the lifetime utility function in each case)