15. Consider a two-period, small, open economy. Households are endowed with 10 units of tradables in period 1 and 11 units in period 2 (Q17 = 10 and Qar= 11). The country interest rate is 10 percent, or r = 0.1, the nominal exchange rate is fixed and equal to 1 in both periods (S1 = $2= 1), and the nominal wage equals 5.5 in both periods (W1 = W2 = 5.5). Nominal wages are downwardly rigid. Suppose the economy starts period 1 with no assets or debts carried over from the past (By= 0). Suppose that the household's preferences are defined over consumption of tradable and non-tradable goods in periods 1 and 2, and are described by the following utility function, In CIT +In CIN +In C27 +In C2N, where Cit and Car denote consumption of tradables in periods 1 and 2, respectively, and CIN and C2N denote consumption of non-tradables in periods 1 and 2. Let p1 and p2 denote the relative prices of non-tradables in terms of tradables in periods 1 and 2, respectively. Households supply inelastically h= 1 units of labour to the market each period. Finally, firms produce non-tradable goods using labour as the sole factor input. The production technology is given by QIN = F(h1) = hq Q2N = F(h2) = hq in periods 1 and 2, respectively, where Qin and hidenote, respectively, non-tradable output and employment in period i = 1, 2. The parameter a is equal to 0.5. (a) Assume that, in any circumstances, the sum of labour income and profit for firms that the households get from the non-tradable sector are equal to the endowment of non- tradable in each period. [This assumption turns out to be true]. This means that in addition to QT, the households obtain Qin in each period i = 1, 2. Also, notice that the market of non-tradable good must clear every period. Given the information above, write down the intertemporal budget constraint in terms of tradable goods. (3 marks) (b) Derive the optimal consumption of tradable in period 1 and in period 2. Given the optimal consumptions, what is the trade-balance in the two periods? Provide an intuition for the result. (5 marks)(c) We are now looking for the equilibrium level of employment in period 1 h;. (d) (e Let us start from the demand side. Assume that the price of foreign tradable goods is normalized to 1 and that the law of one price holds, i.e. P;; = S;inperiodi=1, 2. The revenue for the non-tradable goods firms in terms of tradable goods is p;F (h;) while its cost % in periodi=1, 2. Write down the firm problem in period 1 and derive the L labour demand equation of the firm, which is a relationship between p, and h;. Let us now derive the demand schedule for non-tradable for the household in period 1. To do so, first, find out the household's optimality condition that links consumption of tradable and non-tradable in period 1; second, use the fact that the consumption of non-tradable clears in each period, that is Cin=F (h,), and also use the equilibrium value of Cir found above. This will give you another relationship between p, and h;. Use the two equations found in the previous steps to determine the equilibrium level of employment in period 1, h,, and the non-tradable output produced in period 1, Q1n- (8 marks) Now assume that instead the interest rate is 20 percent. Recompute optimal non- tradable consumption in the two periods, the trade-balance, the equilibrium level of employment in period 1, and the non-tradable production in period 1. Provide an intuition for the results in how they differ from the case where the interest rate is 10 percent. (8 marks) Still assume the interest rate is 20 percent. What is the devaluation rate of the currency that the country should set to obtain full employment? Explain your results. (6 marks) 15 ( a ) (10 + 5.5 + 1/p1) + (11 + 5.5 + 1/p2) = Cir + 1.1 (b) CIT = 15.25 Cy = 16.75 TB, =- 5.25 TB2 =- 5.775 (c) Maximize