Question

Consider an economy represented by the following expenditure equations (in $ trillion):

Y = C + I + G + NX

C = 2 + ⅔(Y – T)

I = 6 – r

G = 4, T =3, NX = -1

1. What is the equation for the IS curve, Y=f(r)?
2. For the short run, consider the inflation rate fixed at π = 2. The Central Bank wants to target the real interest rate r = 2. What should be the target for the nominal interest rate, i? What is the equilibrium Y?
3. The money demand equation is M = Y – i. What should the Money supply be in order to achieve the interest rate target?
4. There is an adverse shock and the new investment function is I’ = 4 – r. What happens to GDP Y if the Central Bank maintains the interest rate target in part b?
5. There is an adverse shock and the new investment function is I’ = 4 – r. What happens to GDP Y if the Central Bank lets the market determine the equilibrium interest rate and keeps the money supply fixed at the amount you found in part c?
6. Which causes a deeper recession, the monetary policy in part d or e?
7. What monetary policy will keep GDP to the level found in part b? What should r, i and M_S be?
8. Graph the IS-MP and the Money Market for part d, e and g.

Answer 1

A) IS EQUATION = Y = C+I+G+NX

Y = 2+2/3(Y-3) +6-r +4+(-1)

Y =2+2/3(Y-3) +9-r

Y =11+2/3(Y-3) - r

Y =33+2(Y-3)-3r/3

3Y=27+2Y -3r

Y=27-3r REQUIRED Y=F(R)

B)FOR short run

, Real interest rate = 2

NOMINAL INTEREST RATE = REAL INTEREST RATE +

= 2+2=4

The government should target the nominal interest rate to 4%

equilibrium Y = IS model equilibrium equation

= Y= 27 - 3r= 27-3x4= 15

C)money demand = money supply  

M=Y-i= 15-4= 11.

here we will consider the i as a nominal interest rate

D)with new investment function I'= 4-r and with the nominal interest rate of 4 the eqilibrium GDP (y)=

C+I+G+NX

=2+2/3(Y-3)+4-r+(-1)

Y= 21-3r

as r= 4 than Y = 21-(3X4)= 9