6. Future productivity shocks when current accounts are initially unbalanced. Let Home have the production function \( Y = A F^*(K) \), and Foreign the function \( Y^* = A^* F^*(K^*) \), on each of two dates. Let the corresponding lifetime utility functions of residents be \( U_1 = u(C_1) + \beta u(C_2) \) and \( U^*_1 = u(C^*_1) + \beta u(C^*_2) \), where \( u(\cdot) \) is isoelastic. On date 1 the countries may borrow (lend) at the world interest rate \( r \), determined by \( S_1 + S^* = I_1 + I^*_1 \). A Walras-stable world market with a single equilibrium is assumed.