Question

1. Suppose that the following equations describe an economy.

Y = C^d + I^d + G

C^d = 180 + 0.8(Y – T)

I^d = 140 – 8r + 0.1Y

T = 400

G = 400

(M^d/P) = 6Y – 120i M^S = 6000 i = π^e + r

Assume expected inflation π^e = 0 and price level P = 1.

1. 1. Find the equation for the IS curve.
2. 2. Find the equation for the LM curve.
3. 3. Find the equilibrium values for output and the interest rate.
4. 4. At this equilibrium, what is the level of consumption and investment?
5. 5. If government purchases (G) increases to $440, everything else held constant, find the new equilibrium values for output and the interest rate.
   6. What are the effects of the fiscal expansion above on consumption and investment? That is, find the new levels of consumption and investment.
   7. Instead of increasing the government purchases G, find the new equilibrium values for output and the interest rate if the central bank increases the money supply to 6600. What are the effects of the monetary expansion above on consumption and investment (that is, find the new levels of consumption and investment)?
   8. Judging from your answers to the previous questions, what are the differences in the effects of expansionary fiscal and monetary policies above on Y, i, C and I ?

Answer 1

Since expected inflation is zero, i = r.

(Part 1)

In goods market equilibrium, Y = Cd + Id + G

Y = 180 + 0.8(Y - 400) + 140 – 8r + 0.1Y + 400

Y = 720 + 0.8Y - 320 - 8r + 0.1Y

(1 - 0.8 - 0.1)Y = 400 - 8r

0.1Y = 400 - 8r

Y = 4000 - 80r...........(IS equation)

(Part 2)

In money market equilibrium, (Md/P) = Ms/P

6Y - 120r = 6000/1

6Y = 6000 + 120r

Y = 1000 + 20r..........(LM equation)

(Part 3)

Setting IS = LM,

4000 - 80r = 1000 + 20r

100r = 3000

r = 30

Y = 1000 + 20 x 30 = 1000 + 600 = 1600

(Part 4)

When G = 440, (increase by 40), in new goods market equilibrium,

0.1Y = (400 - 8r) + 40

0.1Y = 440 - 8r

T = 4400 - 80r........(New IS equation)

Setting new IS = LM,

4400 - 80r = 1000 + 20r

100r = 3400

r = 34

Y = 1000 + 20 x 34 = 1000 + 680 = 1680

NOTE: As HOMEWORKLIB's Policy, 1st 4 parts are answered.