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Econ457; March 9, 2017
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In all the exercises below assume that the world (market) interest rate is constant at 5% per annum.
Assume all transactions are in terms of a single homogenous good. Assume NUT = 0.
1. A country has a debt of 100 million units from its previous period. It must pay of its debt in two
periods: either in the current year or in the next. Suppose the country decides to pay of $50
million in the current year by running trade surplus. How much trade surplus or next year?
-W-1 (1+r*)= TB0 + TB1/(1+r*)
Since W-1 = -100
-(-100)(1+0.05) = 105 = 50 + TB1/(1+0.05)
TB1 = 55(1.05) = 57.75
2. What is the present value of an infinite stream of constant payoff of 100 starting from next
year?
100/0.05 = 2000
3. Suppose the GDP in the current year is 79 and thereafter it is constant every year at 100. What
is its present value?
79+100/0.05 = 2079
4. If a country wants to consume a constant consumption, C, what is the present value of its
consumption?
C + C/0.05 = 21C
5. An open economy’s output is expected to be 100 units forever and it can borrow and lend
freely from the rest of the world at an interest rate 5%. There is an unanticipated decrease
in output in the first period. That is, the economy’s output is 079, 100, 100, 100, 100…..
On t =0, 1, 2, 3, 4…..Assume initial wealth (W-1) is zero and NUT = 0. Assuming that the
economy always chooses a smooth consumption, what will be the consumption in the
first period and thereafter?
2079 = 21C; C = 99
6. What will be the trade balance in period 0 and thereafter? If the initial wealth is 0, what
will be the wealth level at the end of period 0? What is the trade balance, NFIA, Current
account, and wealth level at the end of period 1?
TB0 = GDP0 – GNE0 = 79- 99 = - 20; NFIA = r* W-1 =0; CA = NFIA0 +TB0 = -20; W0 - W-1 = CA = r* W-1
+TB0 = -20; W0 = -20;
TB1 = GDP0 – GNE0 = 100 – 99 = 1; NFIA = r* W0 =0.05*(-20) = -1; ; CA = NFIA1 +TB1 = -1+1 = 0; W1 - W0
= CA1 = r* W0 +TB1 = 0; W1 = W0 = 20. Thereafter, these values keep repeating in all the later periods.