Question

A small open Economy is described by the following equations:

C= 50 + 0.75(Y – T), I = 200-20r,

NX = 200-e, M/P = Y-40r, G= 200, T = 200, M = 3,000, P = 3, and r* = 5

A. Drive the IS* and LM* equations

B. Calculate the equilibrium Exchange Rate, level of income, and net exports

C. Assume a floating exchange rate, calculate what happens to exchange rate , the level of income, net exports, and money supply if if the government increases its spending by 50.

D. now assume a fixed exchange rate, calculate what happens to exchange rate , the level of income, net exports, and money supply if if the government increases its spending by 50.

Answer 1

a) For IS equation,

Y = C+I+G+NX

or, Y = 50+0.75(Y-T)+200-20r+G+200-e

or, Y = 50+0.75(Y-200)+200-(20*5)+200+200-e

or, Y-0.75Y = 50-150+200-100+200+200-e

or, 0.25Y = 400-e... (i)

Again, for LM equation,

M/P = Y-40r

or, 3,000/3 = Y-(40*5)

or, 1,000 = Y-200 ....(ii)

b) From (ii), 1,000=Y-200

or, Y=1,200  

Now, from (i), 0.25Y = 400-e

or, (0.25*1,200) = 400-e

or, e = 400-300

or, e = 100

and NX = 200-e = 200-100 = 100

c) With floating exchange rate if G increases by 50,

Y = C+I+G+NX

or, Y = 50+0.75(Y-T)+200-20r+G+200-e

or, Y = 50+0.75(Y-200)+200-(20*5)+250+200-e

or, Y-0.75Y = 50-150+200-100+250+200-e

or, 0.25Y = 450-e... (iii)

Again, for LM equation,

M/P = Y-40r

or, 3,000/3 = Y-(40*5)

or, 1,000 = Y-200

or, Y = 1,200

Then, putting the value of Y in (iii),

0.25Y = 450-e

or, 0.25*1,200 = 450-e

or, e = 450-300

or, e = 150

Then, NX=200-150 = 50

Thus, with floating exchange rate, exchange rate increases to 150, level of income remains at 1,200, NX falls to 50 and money supply remains the same

d) With fixed exchange rate at e=100,

from (iii), 0.25Y=450-e

or, 0.25Y = 450-100

or, 0.25Y = 350

or, Y = 1,400

Then, NX = 200-100 =100

Now, M/P = Y-40r

or, 3,000/P=1,400-(40*5)

or, P = 3,000/1,200

or, P = 2.5

Thus, under fixed exchange rate system, exchange rate remaining fixed at 100, level of income increases to 1,400, Net exports remaining the same, price level falls (money supply remaining the same).