Question

Say there are two countries; Core and Periphery and two periods 1 and 2. In Core, each household has an endowment of Y_c1 and Y_c2 in the first and second period respectively, while in Periphery the analogous endowments are Y_p1 and Y_p2. Core has N_c households and Periphery has N_p households. Preferences are the same in the two households, given by (1 − β) log(C_i1) + β log(C_i2), i = C, P and there is an open world capital market with the gross world interest rate equal to 1 + r.

a) Derive the optimal saving of each country’s household given the world interest rate.

b) Since the sum of the current accounts of the two countries must equal zero, use this condition to derive an expression for the world interest rate.

c) Derive an expression for the current account to GDP for each country. How does each countries CA to GDP depend on a) the growth rate of its income and b) its size relative to the world economy?

Answer 1