3. Catching-Up Economy and Foreign Borrowing. Consider a small open endowment economy without a government that is inhabited by a representative consumer who lives two periods indexed by '1' and '2', respectively. The representative consumer receives exogenously a revenue of Y in period 1 and 2 .Y in period 2. The household consumes C₁ in period 1 and C₂ in period 2. Her/his intertemporal welfare is given by: A = ln C₁ + In C₂. (3) To transfer consumption across time, the household holds a stock of foreign bonds B₁ in period 1. We impose the following condition B₂ = 0. The stock B₁ represents the net international investment position (NIIP). When B₁ < 0 (B₁ > 0), it means that the country is a net debtor (creditor) as it borrows (lends) from (to) abroad. The (exogenous) world interest rate is denoted by r*. Period 1 and period 2 budget constraints are given by, respectively: Y = C₁ + B₁, C₂ = (1+r) .B₁ +3.Y. (4) (a) Derive the intertemporal budget constraint. (b) Derive optimal consumption in period 1, C, which must be expressed in terms of Y and r*. (c) Derive the optimal NIIP, B. We assume that r* < 2. Explain the reason why the small open economy borrows abroad.
