Hi, can you shed light on solving this question? I am stuck once the tariff with terms of trade is included in this question. Thanks.

3. (Lack of credibility) This exercise, which follows Engel and Kletzer (1991), deals with a formalization of the idea of lack of credibility that we discussed in section 3.4. Consider a two-period endowment economy. The economy is endowed with a constant endowment, y, of an exportable good. It consumes an importable good, c. The terms of trade are equal to one. The domestic price of importables, however, may be greater than one if a tariff is imposed. The economy can borrow/lend at a fixed rate, r. In the first period, there is no tariff (i.e., the domestic relative price of importables is equal to one). In the second period, a tariff (p - 1) may be imposed with probability . Chapter 3 The consumer's problem is to maximize expected utility E(U) = logci + B(1 - 7) log c2 + Bu log cz, where B(1 + r) = 1, c1 is consumption in period 1, c2 is consumption in period 2 if the tariff is not imposed, and c is consumption in period 2 if the tariff is imposed. Using the exportable good as the numeraire, the consumer's flow constraints are given by (assume bo = 0) CI = y - b1. c2 = y+ (1+ r)b1. poz = y+ (1 + r)bi+ +*. where b, denotes end of period 1 (beginning of period 2) net foreign assets and r* denotes lump-sum transfers in case the tariff is imposed.?! (In general equilibrium, r* = (p - 1)c;.) In this context: a. Compute reduced forms for c1, c2, and c3. b. Compute consumer's welfare as a function of . c. Compare consumer's welfare when the tariff is p - 1 in both periods with certainty. d. What would you conclude about the desirability of trade reforms if you took the model at face value? e. How could you modify the model to yield a more sensible policy prescription