Question

Consider the Mundel-Fleming small open economy model: Y=C(Y-T)+1(1) + G Y = F(K,L) (M/P) L(r+z® Y) Goods Money C = 50+0.8(Y- T) M 3000 I = 200-20r r*=5 NX = 200-508 P = 3 G=T= 150 L(Y, r) Y - 30r 1- find the IS* equation (hint : y as a function of e) 2- find the LM* equation (hint, also relates y and maybe e) 3-draw the IS-LM curve I y 4- find the equilibrium interest rate (trick question!) income Y. indicate them in previous graph. 5- Also find cquilibrium exchange rate e and net exports NX: 5- find the values of consumption C and investment I: 6-FISCAL POLICY: G increases by 30 i.e. G 180 rewrite the IS and LM* equations from part 1 to reflect this change:

Answer 1

1. IS equation (as a functin of $\epsilon$)

Y =C(Y - T) + I(r) + G + NX

=> Y = 50 + 0.8(Y - T) + 200 -20r + 150 + 200 - 50$\epsilon$

=>Y = 50 + 0.8(Y - 150) + 200 -20(5) + 150 + 200 - 50$\epsilon$

=> Y - 0.8Y = 50 - 120 + 200 - 100 + 150 + 200 - 50$\epsilon$

=> 0.2Y = 380 - 50$\epsilon$

=> Y = 1900 - 250$\epsilon$

2. LM equation

(M/P) = L(Y, r)

=> (3000/3) = Y - 30r

=> 1000 = Y - 30(5)

=> Y = 1000 + 150

=> Y = 1150

3. Graph

2.6 1 M ti so t400

4. Equilibrium interest rate

We already have the interest rate is given, i.e., r = 5

5. $\epsilon$ and NX

Equating the IS-LM curve we get,

=>1900 - 250$\epsilon$ = 1150

=> 250$\epsilon$ = 750

=> $\epsilon$ = 3

We know that, NX = 200 - 50$\epsilon$

Puttting the value of $\epsilon$ = 3, we get

=> NX = 200 - 50(3)

=>NX = 200 - 150

=> NX = 50

Consumption and investment

C = 50 + 0.8(Y - T)

=> 50 + 0.8(1150 - 150)

=> 50 + 0.8(1000)

=> 50 + 800

=> 850

I = 200 - 20r

=> 200 - 20(5)

=> 200 - 100

=> 100

6. G increase by 30

Now, G = 150 + 30 = 180

IS: Y =C(Y - T) + I(r) + G + NX

=> Y = 50 + 0.8(Y - T) + 200 -20r + 180 + 200 - 50$\epsilon$

=> Y = 50 + 0.8(Y - 150) + 200- 20(5) + 180 + 200 - 50$\epsilon$

=> 0.2Y = 50 - 120 + 200 - 100 + 180 + 200 - 50$\epsilon$

=> 0.2Y = 410 - 50$\epsilon$

=> Y = 2050 - 250$\epsilon$

LM:

(M/P) = L(Y, r)

=> (3000/3) = Y - 30r

=> 1000 = Y - 30(5)

=> Y = 1000 + 150

=> Y = 1150

Equating IS-LM, we get

=> 2050 - 250$\epsilon$ = 1150

=> 250$\epsilon$ = 900

=> $\epsilon$ = 3.6