1. Current account sustainability and the intertemporal budget constraint. Suppose that a country has negative net foreign assets and adopts a policy of running a trade balance surplus sufficient to repay a constant small fraction of the interest due each period. It rolls over the remaining interest. That is, suppose it sets its trade balance according to the rule TB, = -Er B,, > 0.

(a) Using the current account identity and the definition of the trade balance, show that under this policy, net foreign assets follow the equation B+1 = [1 + (1)r] B.

(b) Show directly that the intertemporal budget constraint is satisfied for any > 0. [Hint: Show why?