Assume a two-period small open economy where the representative agent receives endowments Q1 and Q2 in periods 1 and 2, respectively. In addition, assume that this representative agent receives an initial wealth of (1+r0)B0*, where B0* are bonds that pay interest rate ro. In period 1, the representative agent chooses consumption C1 and bond holdings B1* which pay interest rate r1. (a) assuming that the transversality condition is satisfied, derive the two-period budget constraint and discuss its implications (20 marks) (b) Assume that the inter-temporal utility function of the representative agent is given by U=lnC1+lnC2. Write the inter-temporal optimization problem, and derive the optimal consumption levels, trade balance and current account expressions. Discuss how these depend on the endowment levels and global interest rate. (30marks) (c) using the expressions derived in (b) discuss the implications of permanent and temporary shocks to the endowments. Discuss how you would introduce terms of trade in this framework and how the inter-temporal budget constraint changes in this case (50 marks).