Consider the following small open economy model with production. At dates 1 and 2, the home country receives exogenous fixed endowments y1 and y2 respectively. The home country has access to the international capital market at a fixed interest rate r* at which it can save or borrow. Let the net saving of the home country be s1 and its consumption stream in two periods be given by
c1 and c2 respectively.the following maximization problem:
Max ln c1 + ln c2
s.t. C1 + S1 = Y1
C2 = C1(1+r*) + Y2
Derive optimal consumption and current account functions and carefully interpret it in terms of a two-period Fisherian graph.
Refer to (a). Suppose the home country also has an access to an investment
technology which means that if it invests k units at date 1, it produces y2 = Aka units of output
in the next period where A >0 and 0 < a< 1 . Modify budget constraints for (a)Derive the optimal investment and saving rules for this
economy assuming the same logarithmic utility function as in (a). Interpret your results
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