Question

In the two-period model reviewed in class, both the Current Account and the Trade Balance in period 1 worsen (i.e., decrease) with an anticipated increase in the endowment of period two (ΔQ1=0 and ΔQ2>0)'' Use equations of the optimal allocation of consumption in periods 1 and 2, the trade balance in period 1 and the current account in period 1 to support your answer. No credit without explanation. For simplicity, assume the following lifetime utility function: U(C1,C2)= ln(C1) +β ln(C2) Note that the subjective discounting factor is 0<β<1, which is different from the case reviewed in the textbook

Answer 1

Step 1 Some part of the question is not clear "In the two period model reviewed in class" are you referring to dynamic models of economic fluctuation ten which one?. What is Q1 and Q2? I suppose they are outputs which in my problem I assumed Y1 and Y2

Step 2 According to my understanding.

Identifying an open economy that exists for 2 periods. Output in each period Y1 and Y2 respectively is given exogenously.

Consumer maximises his lifetime utility U=u(C1)+u(C2) where C1 and C2 are consumption in the two periods and is subjective factor, 0<<1. The country is able to lend and borrow in internation market at a given real interest rate, r. The initial asset is 0. Hence, the budget constraint is

C1+C2/1+r=Y1+Y2/1+r

First order condition for optimal consumptiom and interpretation

Solving the budget contraint for C2

C2=Y1(1+r)+Y2-(1+r)C1...........................(1)

and substitute the constraint into the objective function

U=u(C1)+u(Y1(1+r)+Y2-(1+r)C1)................(2)

Maximise the objective function wrt C1.The FOC is

u'(C1)-(C2)(1+r)=0

or, u'(C1)1/1+r=u'(C2)

or, u'(C2)/u'(C1)=1/1+r.................................(3)

(3) is the marginal rate of substitution(MRS) between consumption in period 1 and period 2. It means how much C1 I am willing to trade for one more unit of C2 (given constant utility). The right hand side is the relative price of consumption in period 2 which means how much C1 I have to give up to get one more unit C2. In optimum MRS(C1,C2) relative price. If MRS >1/1+r I can increase utility by trading C1 for C2 and vice versa if MRS<1/1+r.