Answer to Question #196916 in Macroeconomics for John

Question

A small open economy is described by the following equations:

C=50+0.75 (Y-T) I=200-20r NX=200-50e M/P=Y-40r

G=100 T=100 M=2,000 P=2 r*=4

(a) Derive and graph the IS* and LM* curves (Mundell-Fleming model)

(b) Calculate (i) the equilibrium rate and (ii) output

(c) Assume a floating exchange rate. Calculate what happens to (i) the exchange rate, (ii) income, (iii) net exports, and (iv) the money supply if the government raises taxes by 50. Use a graph to explain what you find.

Answer 1

A small open economy is described the following equations.

$C = 50 + 0.75 (Y - T) \\ T = 200 \\ I = 200 - 20r\\M/P = Y - 40r \\ M = 3000 \\ P = 3 \\ r = 5 \\ G = 200 \\ NX = 200 - 50E$

a).

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

$Y - 40r = 3000 \\ Y = 40r + 1000$

(b) When $r = 0, Y = 2000-200E$

$0=2000-80r-200E \\ 80r=2000-2.5e$

$LM\Rightarrow y=3000+40r$

     When $r=0, y=3000$

     When $y=0, r=\dfrac{-3000}{40}=-75$

(c) At Equilibrium, IS=LM

  $2000-80r-200E=3000+40r$

   At r=5, 

  $2000-80(5)=3000+40(5)\\1400=200E\\E=7 \\[9pt] Y=2000-80(5)-200(7)=200$

(d) 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. Multiplier 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