Consider a small open endowment economy without a government that is inhabited by a representative consumer...

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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 anticipates a revenue of Y (1 + g) in period 2 where g is the expected rate of future growth. The household consumes C1 in period 1 and C2 in period 2. Her/his intertemporal welfare is given by: A = C1C2. (2) 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: Y = C1 + B1 and C2 = (1 + r ? ) B1 + Y (1 + g). (a) Derive the intertemporal budget constraint. Next, derive the optimal trade-off between C1 and C2. (b) Give the value of the rate of time preference, p. (c) Derive optimal consumption in period 1, C ? 1, which must be expressed in terms of Y, r ? and g. (d) Derive the optimal NIIP, B? 1. Determine the condition under which the small open economy is a net debtor. Explain. 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 anticipates a revenue of Y (1 + g) in period 2 where g is the expected rate of future growth. The household consumes C1 in period 1 and C2 in period 2. Her/his intertemporal welfare is given by: A = C1C2. (2) 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: Y = C1 + B1 and C2 = (1 + r ? ) B1 + Y (1 + g). (a) Derive the intertemporal budget constraint. Next, derive the optimal trade-off between C1 and C2. (b) Give the value of the rate of time preference, p. (c) Derive optimal consumption in period 1, C ? 1, which must be expressed in terms of Y, r ? and g. (d) Derive the optimal NIIP, B? 1. Determine the condition under which the small open economy is a net debtor. Explain.

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