1. More on the logarithmic small-country example. Consider the small-country Arrow- Debreu model with log preferences of section 5.1.6 and appendix 5B. Show that in general, when the current account need not be zero, the country's gross purchases of the individual Arrow-Debreu security purchases, B(1) and B(2) satisfy p(1) 1+r p(2)(2)(1) [p(1)^ p(1)] B(1): +(1)CA. 1+r Lp(2)^ P(2) p(2) B(2)= 1+r -p(2)(2)2(1) [p(1)^ 1+r p(1) +(2)CAL. Provide an intuitive interpretation. [Hint: Any date 2 expenditure (1+r)CA, above (below) p(1)Y2(1) + p2(2)Y2(2) goes to increase (reduce) state s consumption in the proportion (s)/p(s) with log preferences. The country then does any additional portfolio rebalancing it desires by a pure swap between state 1 and state 2 securities, as in the text.]