Question A. Consider a two-period small open economy populated by a...

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.

Explain in detail why budget constraint is W1 = (Ct1+Cn1)*pn1