4. L the period utility functi homogeneous. In this case, we say that households have homothetic prefer- ences for tradable and nontradable goods. Exercise 10.10 (Equilibrium in the TNT Model with Production) Consider a two-period, small open economy that produces and consumes tradable and non- tradable goods. In periods t = 1, 2, the production possibility frontier (PPF) is of the form QN = 2- (Q7), where Q and Q denote, respectively, tradable and nontradable output in periods t = 1,2. Preferences are described by the utility function In (C) +In (C) + In (C) + In (C), where C and C+ denote, respectively, tradable and nontradable consumption in periods t = 1,2. Let pt = P/P denote the relative price of nontradable goods in terms of tradable goods in periods t = 1,2. 1. Suppose that p is equal to 1 (i.e., 1 unit of nontradable goods sells for 1 unit of tradable goods). Using the information provided by the PPF, and assum- ing that firms producing tradables and nontradables are profit maximizers, calculate output of tradables and nontradables in period 1 (Q and QN). 2. Using the results obtained thus far, and the market-clearing condition in the nontraded sector, calculate consumption of nontradables in period 1 (CN). 3. Assuming that households are utility maximizers, use the information given above and the results of the previous two questions to calculate consumption of tradables in period 1 (CT). 4. Calculate the country's trade balance in period 1 (TB1). 5. Suppose that the initial net foreign asset position, Bo, is nil. Calculate the current account in period 1 (CA1). 6. Suppose that the world interest rate, denoted r*, equals 0 percent (r* = 0). Assume further that households have access to the world financial market. Calculate consumption of tradables in period 2 (C). 7. Calculate tradable output in period 2 (Q). To this end, use the economy's intertemporal resource constraint for tradables. 8. Now calculate output of nontradables in period 2 (QN). 9. Calculate the relative price of nontradables in terms of tradables in period 2 (P2). 10. Is the initial guess for p, namely, p = 1, an equilibrium? Be explicit about what must be verified for this to be the case. Exercise 10.11 (The Trade Balance in the TNT Model with Sectoral Production) State whether the following claims about the equilibrium in the TNT model with sectoral production of Section 10.5 are true, false, or uncertain and explain why. In answering this question, assume that the initial international investment position Bo, is zero. 1. If (1+r)=1, then the trade balance in both periods is nil, TB = TB = 0. 2. If (1+r)>1, then the trade balance is positive in period 1, TB1 > 0. 3. If 80 in the world interest rate leads to a trade