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ECON 7520

SEMESTER 1, 2023

Tutorial 10

Problem 1 (Sudden Stops with Downward Wage Rigidity)

Consider a two-period, small open economy with two types of goods, trad- ables and nontradables. The economy is populated by a represenative household and a representative, perfectly competitiveirm. The household’s preferences over consumption of tradable and nontradable goods in periods 1 and 2 are described by the utility function

lnC1(T) + lnC1(N) + lnC2(T) + lnC2(N) ,

where Ct(T)  and Ct(N)  denote, respectively, consumption of tradables and nontrad- ables in period t = 1, 2.  The household is endowed with 10 units of tradables in period 1 and 12 units of tradables in period 2 (Q1(T)   = 10 and Q2(T)   = 12) and owns the irm. The household inelastically supplies  = 1.2 units of labour to the market in each period. The irm produces nontradables using labour as the sole input. The production technology is given by

Q1(N)  = h1(α)      and   Q2(N)  = h2(α)

in periods 1 and 2, respectively, where Qt(N)  and ht  denote, respectively, nontrad- able output and hours employed in period t = 1, 2. The parameter α is equal to 0.50.

The economy starts period 1 with no assets or debts carried over from the past (B0  = 0). The economy’s interest rate is 20 percent (r1  = 0.20). Nominal wages are downwardly rigid. Speciically, assume that the nominal wage in the economy in periods 1 and 2 is W1  = W2  = 5. The nominal exchange rate is ixed and equal to 1 in both periods (E1  = E2  = 1). Assume that PPP holds for tradable goods and that the price of tradables in the rest of the world is equal to 1 (PtT*  = 1). Let p1 and p2  denote the relative prices of nontradables in terms of tradables in periods 1 and 2, respectively.

(a) Solve for the equilibrium values of C1(T) , C2(T) , C1(N) , C2(N)  and employment in periods 1 and 2 (h1 and h2 ).

(b) Suppose now that the country’s interest rate increases to 50 percent. Calculate the level of unemployment for period 1.