Question

Exercise:

A small open economy is described by the following equations:

C = 50 + .75(Y-T)

I = 200 – 20r

NX = 200 – 50e

MD = Y – 40r

G = 200, T = 200, M = 3000, r* = 5

a. Derive the IS* and LM* functions;

b. Based on a, graph the IS* and LM* curves.

c. Calculate the equilibrium exchange rate e*, output/income Y*.

d. Suppose G increases to 250, redo a, b, c.

Answer 1

Answered:-

A small open economy is described the following equations.

C = 50 + 0.75 (Y - T)

T = 200

I = 200 - 20r

G = 200

NX = 200 - 50E

M/P = Y - 40r

M = 3000

P = 3

r* = 5

a. 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 its spending by 50. Use a graph to explain what you find.

Equation for IS is given by Y = C + I + G + NX

Y = 50 + 0.75 (Y - 200) + 200 - 20r + 200 + 200 - 50E

Y = 2000 - 80r - 200E

Equation for LM is

Y - 40r = 3000/3

Y = 40r + 1000

When r* = 5, Y* = 1200 and E* = 2.

When G becomes 250, equation of IS becomes

Y = 550 + 0.75Y - 20r - 50E

Y = 2200 - 80r - 200E

LM equation does not change so we still have Y = 40r + 1000. Multipleir is 1/1-0.75 or 4 so income rises by 50*4 = $200. If Y = 1200 + 200 = 1400, we have

1400 = 40r + 1000, r = 10%. Hence at r = 10% and Y = 1400, we see that

1400 = 2200 - 80*10 - 200E

E* = 0.

At these levels, net exports = 200 - 50*0 = 200. There is no change in money supply

b. Now assume a fixed exchange rate. Calculate what happens to the exchange rate, the level of income, net exports, and the money supply if the government increases its spending by 50. Use a graph to explain what you find.

Now E is fixed at 2. This suggests that Y is now 1400, interest rate is 10% but E should stay at 2. Then

Y = 2200 - 80r - 200*2

Y = 1800 - 80r and Y = 40r + 1000

r* = 6.67 and Y* = 1266.4

Net exports are 200 - 50*2 = 100.