Question

Assume the following equations summarize the structure of an open economy:

          C= 500 + .9 (Y – T)                  Consumption Function

          T = 300 + .25 Y                         Tax

          I = 1000 – 50 i Investment equation

          G = 2500                                   Government Expenditures

          NX = 505 Net Export

          (M/P)d = .4 Y -37.6 i Demand for Money (i= interest rate)

          (M/p) s = 3000                          Money Supply

5- Derive the equation for the LM curve.

6- Compute the equilibrium interest rate (i) and real GDP (Y).

7- If government spending increases by $400:

a- Derive the new equation for the new IS curve.

b Computer the new equilibrium interest rate and real GDP.

c- Compute the amount of crowding out.

Answer 1

5) LM equation represent money market equilibrium,

(M/p)d=(M/p)s

0.4y-37.6i=3000

i=0.01y-79.78 { LM equation}

6) Y=11,413.33 -1.33i{ IS equation}

Putting LM equation into IS.

Y=11,413.33-1.33(0.01y-79.78)

Y=11413.33-0.0133Y +106.1074

1.0133y=11,519.4374

Y=11,368.24

i=0.01*11,368.24-79.78=113.68-79.68=33.9% or 0.339

7) a)Y=4280-50i+0.675y+400

Y=(4680-50i)/0.375

Y=12,480-1.33 { new IS equation}

B) multiplier=1/(1-mpc+mpc*t)=1/(1-0.9+0.225)=1/0.375=3.077

∆G=400

∆Y=∆G*multiplier=400*3.077=1230.8

New Y=11,368.24+1230.8=12,599.04

NEW i=0.01*12,599.04-79.78=125.99-79.78=46.21% or 0.4621

C) Initial Investment=1000-50*0.339=983.05

New investment=1000-50*0.4621=976.895

Crowding out effect=983.05-976.895=6.154