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Homework answers / question archive / A small open economy is described by the following equations: C = 50 +
A small open economy is described by the following equations:
C = 50 + .75(Y-T)
I = 200 - 20r
NX = 200 -50e
M/P = Y -40r
G = 200
T = 200
M = 3000
P = 3
r* = 5
a. Derive and graph the IS* and LM* curves.
b. Calculate the equilibrium exchange rate, level of income, and net exports
c. Assume a floating exchange rate. Calculate what happens to the exchange rate, the level of income, net exports and the money supply if the government increases spending by 50.
d. Now assume fixed exchange rate. Calculate what happens to the exchange rate, the level of income, net exports and the money supply if the government increases spending by 50.
a) The IS* curve is given by C + G + I + NX = Y, i.e.,
which could be rearranged to be
The LM* curve is given by Y -40(5) = M/P = 3000/3 = 1000, so the LM* curve is Y = 1200.
b) Exchange rate is 2, income is 1200, and net export is 100. In equilibrium, IS* curve and LM* curve intersect, so we have Y = 1600 - 200e = 1200, which gives e = 2, Y = 1200, and NX = 200 - 50e = 200 - 50*2 = 100.
c) Exchange rate increases to 3, income remains the same, net export reduces to 50 and money supply remains the same. With the increase, now we have G = 250. The new IS* curve is Y = 1800 - 200e and the LM* curve remains the same: Y = 1200. . So equilibrium exchange rate increases to e = 3, income remains the same at 1200, net exports reduces to 200 -50*3 = 50, and money supply remains the same.
d) Exchange rate remains at 2, income increases to 16000, net export remains the same, money supply increases to 4200. With the fixed exchange rate, money supply has to adjust to maintain exchange rate at e = 2. Let the new money supply be M*, then we have
which give Y = 1600, M = 4200. Net exports remains the same.
