Question A.

Consider a two-period small open economy populated by a large number of identical households with preferences described by the utility function

lnCT 1 + lnCN 1 + lnCT 2 + lnCN 2

where CT 1 and CT 2 denote consumption of tradables in periods 1 and 2, respectively, and CN 1 and CN 2 denote consumption of nontradables in periods

1 and 2. Households are born in period 1 with no debts or assets and are

endowed with L1 = 1 units of labor in period and L2 = 1 units of labor in

period 2. Households oer their labor to rms, for which they get paid the

wage rate w1 in period 1 and w2 in period 2. The wage rate is expressed in

terms of tradable goods. Households can borrow or lend in the international nancial market at the world interest rate r. Let pN 1 and pN 2 denote the

relative price of non tradable goods in terms of tradable goods in periods 1

and 2, respectively.

Firms in the traded sector produce output with the technology QT 1 = aTLT 1 in period 1 and QT 2 = aTLT 2 in period 2, where QT t denotes output in period t = 1,2 and LT t denotes employment in the traded sector in period t = 1,2.

Similarly, production in the nontraded sector in periods 1 and 2 is given by

QN 1 = aNLN 1 and QN 2 = aNLN 2 .

1. Write down the budget constraint of the household in periods 1 and 2.

2. Write down the intertemporal budget constraint of the household.

3. State the household's utility maximization problem.

International Macroeconomics, Chapter 9 299

4. Derive the optimality conditions associated with the household's maximization problem.

5. Derive an expression for the optimal levels of consumption of trade

ables and non tradables in periods 1 and 2 (CT 1 , CN 1 , CT 2 , and CN 2 ) as functions of r, w1, w2, pN 1 , and pN 2 .

6. Using the zero-prot conditions on rms, derive expressions for the real wage and the relative price of nontradables (wt and pN t , t = 1,2),

in terms of the parameters aT and aN.

7. Write down the market clearing condition for nontradables.

8. Write down the market clearing condition for labor.

9. Using the above results, derive the equilibrium levels of consumption ,

the trade balance, and sectoral employment (CT 1 , CT 2 , CN 1 , CN 2 , TB1, TB2, LT 1 , and LT 2 ) in terms of the structural parameters aT, aN, and r.

10. Is there any sectoral labor reallocation over time? If so, explain the

intuition behind it.

Part ii.

How will each of the following changes in demand and/or supply affect equilibrium price and equilibrium quantity in a competitive market; that is, do price and quantity increase or decrease, or are the answers indeterminate because they depend on the magnitudes of the shifts?

a. Supply decreases and demand is constant.

Price?

Quantity?

b. Demand decreases and supply is constant.

Price?

Quantity?

c. Supply increases and demand is constant.

Price?

Quantity?

d. Demand increases and supply increases.

Price?

Quantity?

e. Demand increases and supply is constant.

Price?

Quantity?

f. Supply increases and demand decreases.

Price?

Quantity?

g. Demand increases and supply decreases.

Price?

Quantity?

h. Demand decreases and supply decreases.

Price?

Quantity?