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Consider a two-period, small open economy populated by a large number of households with preferences described by the utility function lnC1 + lnC2, where Ct denotes consumption in period t = 1, 2, and = 0.8 denotes the subjective discount factor. Suppose that consumption is a composite of tradable and nontradable consumption, CTt and CNt , with the aggregation function Ct =CTt CNt ,for t = 1, 2. Households are endowed with 10 units of traded goods each period, QT1 = QT2 = 10. In period 1, they can borrow or lend by means of an internationally traded bond denoted B1 that pays the interest rate r = 0.1. Assume that households have no debts or assets outstanding at the beginning of period 1 (B0 = 0). Households supply h = 1 hours to the labor market inelastically each period. Nontradable goods are produced with labor, with the production function QNt = Ah^t , where QN t and ht denote nontradable output and hours worked in period t = 1, 2, A = 20 is a technological factor, and = 0.75 is a parameter. The foreign price of the tradable good, P T t , denominated in foreign currency, equals 1 for t = 1, 2. (a) Calculate the equilibrium level of consumption of tradables in periods 1 and 2. (b) Calculate the trade balance in periods 1 and 2 (T B1 and T B2). (c) Suppose the economy operates at full employment in period 1. Calculate the equilibrium value of the relative price of nontradables, p1 P N1 /E1, and the real wage, w1 W1/E1, where P N1 , E1, and W1 denote, respectively, the nominal price of the nontradable good, the nominal exchange rate, and the nominal wage in period 1. Suppose that W1 = 1. Calculate E1 and P N1 . (d) Suppose now that because of a drought the endowment of tradable goods in period 1 falls by 20 percent (QT 1 = 8). Suppose that prior to this shock, the nominal wage takes the value given in question 3c. Calculate consumption of tradables and the trade balance in periods 1 and 2. Calculate the relative price of nontradables, p1, the real wage, w1, unemployment, h h1, the nominal wage, W1, the nominal exchange rate, E1, and the nominal price of nontradables, P N1 , under the following two policy regimes: i. A fixed exchange rate regime with the nominal exchange rate, E1, equal to the value obtained in question 3c. ii. A floating exchange rate with the central bank pursuing the dual mandate of core-price stability and full employment. Provide an intuitive comparison of the adjustment under the two alternative regimes, emphasizing the effects on unemployment, currency depreciation, and core inflation.

(e) Finally, suppose that the endowment of tradable goods in period 1 is 10, as in the original situation, but that due to a pandemic part of the businesses in the nontraded sector (e.g., restaurants, hotels, movie theaters, hairdressers) shuts down. Lets capture this shock by a fall in the parameter A of the production function of nontradable goods. Specifically, suppose that A falls by 20 percent (A = 16). As before, suppose that prior to this shock the nominal wage takes the value given in question 3c. Calculate p1, w1, h h1, W1, E1, and P N1 under the following three policy regimes: i. A fixed exchange rate regime with the nominal exchange rate, E1, equal to the value obtained in question 3c. ii. A floating exchange rate with the central bank pursuing core-price stability. iii. A floating exchange rate with the central bank pursuing full employment. Provide an intuitive comparison of the adjustment under these three alternative regimes, emphasizing the effects on unemployment, currency depreciation, and core inflation.

3. (Droughts, Pandemics, and Exchange Rate Policy) Consider a two-period, small open economy populated by a large number of households with preferences described by the utility function In C1 + B In C2, where Ct denotes consumption in period t = 1, 2, and B = 0.8 denotes the subjective discount factor. Suppose that consumption is a composite of tradable and nontradable consumption, CT and CN, with the aggregation function Ce = VC CN, for t = 1, 2. Households are endowed with 10 units of traded goods each period, QT Q2 = 10. In period 1, they can borrow or lend by means of an internationally traded bond denoted B, that pays the interest rate r* = 0.1. Assume that households have no debts or assets outstanding at the beginning of period 1 (Bo = 0). Households supply h = 1 hours to the labor market inelastically each period. Nontradable goods are produced with labor, with the production function = QA = Ah, where QA and ht denote nontradable output and hours worked in period t = 1,2, A = 20 is a technological factor, and a = 0.75 is a parameter. The foreign price of the tradable good, PT*, denominated in foreign currency, equals 1 for t = 1,2. (a) Calculate the equilibrium level of consumption of tradables in periods 1 and 2. (b) Calculate the trade balance in periods 1 and 2 (TB, and TB2). (c) Suppose the economy operates at full employment in period 1. Calculate the equilibrium value of the relative price of nontradables, p1 = PN/E1, and the real wage, wi = W1/E1, where PN, E1, and W denote, respectively, the nominal price of the nontradable good, the nominal exchange rate, and the nominal wage in period 1. Suppose that W1 =1. Calculate &z and PN. (d) Suppose now that because of a drought the endowment of tradable goods in period 1 falls by 20 percent (Q1 = 8). Suppose that prior to this shock, the nominal wage takes the value given in question 3c. Calculate consumption of tradables and the trade balance in periods 1 and 2. Calculate the relative price of nontradables, P, the real wage, w1, unemployment, h h, the nominal wage, W1, the nominal exchange rate, E1, and the nominal price of nontradables, PN, under the following two policy regimes: i. A fixed exchange rate regime with the nominal exchange rate, E1, equal to the value obtained in question 3c. ii. A floating exchange rate with the central bank pursuing the dual mandate of core-price stability and full employment. Provide an intuitive comparison of the adjustment under the two alternative regimes, emphasizing the effects on unemployment, currency depreciation, core inflation 1 (e) Finally, suppose that the endowment of tradable goods in period 1 is 10, as in the original situation, but that due to a pandemic part of the businesses in the nontraded sector (e.g., restaurants, hotels, movie theaters, hairdressers) shuts down. Let's capture this shock by a fall in the parameter A of the production function of nontradable goods. Specifically, suppose that A falls by 20 percent (A = 16). As before, suppose that prior to this shock the nominal wage takes the value given in question 3c. Calculate pi, wi, h - h1, W1, E1, and PN under the following three policy regimes: i. A fixed exchange rate regime with the nominal exchange rate, E1, equal to the value obtained in question 3c. ii. A floating exchange rate with the central bank pursuing core-price stability. iii. A floating exchange rate with the central bank pursuing full employment. Provide an intuitive comparison of the adjustment under these three alternative regimes, emphasizing the effects on unemployment, currency depreciation, and core inflation. 3. (Droughts, Pandemics, and Exchange Rate Policy) Consider a two-period, small open economy populated by a large number of households with preferences described by the utility function In C1 + B In C2, where Ct denotes consumption in period t = 1, 2, and B = 0.8 denotes the subjective discount factor. Suppose that consumption is a composite of tradable and nontradable consumption, CT and CN, with the aggregation function Ce = VC CN, for t = 1, 2. Households are endowed with 10 units of traded goods each period, QT Q2 = 10. In period 1, they can borrow or lend by means of an internationally traded bond denoted B, that pays the interest rate r* = 0.1. Assume that households have no debts or assets outstanding at the beginning of period 1 (Bo = 0). Households supply h = 1 hours to the labor market inelastically each period. Nontradable goods are produced with labor, with the production function = QA = Ah, where QA and ht denote nontradable output and hours worked in period t = 1,2, A = 20 is a technological factor, and a = 0.75 is a parameter. The foreign price of the tradable good, PT*, denominated in foreign currency, equals 1 for t = 1,2. (a) Calculate the equilibrium level of consumption of tradables in periods 1 and 2. (b) Calculate the trade balance in periods 1 and 2 (TB, and TB2). (c) Suppose the economy operates at full employment in period 1. Calculate the equilibrium value of the relative price of nontradables, p1 = PN/E1, and the real wage, wi = W1/E1, where PN, E1, and W denote, respectively, the nominal price of the nontradable good, the nominal exchange rate, and the nominal wage in period 1. Suppose that W1 =1. Calculate &z and PN. (d) Suppose now that because of a drought the endowment of tradable goods in period 1 falls by 20 percent (Q1 = 8). Suppose that prior to this shock, the nominal wage takes the value given in question 3c. Calculate consumption of tradables and the trade balance in periods 1 and 2. Calculate the relative price of nontradables, P, the real wage, w1, unemployment, h h, the nominal wage, W1, the nominal exchange rate, E1, and the nominal price of nontradables, PN, under the following two policy regimes: i. A fixed exchange rate regime with the nominal exchange rate, E1, equal to the value obtained in question 3c. ii. A floating exchange rate with the central bank pursuing the dual mandate of core-price stability and full employment. Provide an intuitive comparison of the adjustment under the two alternative regimes, emphasizing the effects on unemployment, currency depreciation, core inflation 1 (e) Finally, suppose that the endowment of tradable goods in period 1 is 10, as in the original situation, but that due to a pandemic part of the businesses in the nontraded sector (e.g., restaurants, hotels, movie theaters, hairdressers) shuts down. Let's capture this shock by a fall in the parameter A of the production function of nontradable goods. Specifically, suppose that A falls by 20 percent (A = 16). As before, suppose that prior to this shock the nominal wage takes the value given in question 3c. Calculate pi, wi, h - h1, W1, E1, and PN under the following three policy regimes: i. A fixed exchange rate regime with the nominal exchange rate, E1, equal to the value obtained in question 3c. ii. A floating exchange rate with the central bank pursuing core-price stability. iii. A floating exchange rate with the central bank pursuing full employment. Provide an intuitive comparison of the adjustment under these three alternative regimes, emphasizing the effects on unemployment, currency depreciation, and core inflation

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