Question

Consider the following economy:

Y = AK^0.5N^0.5

A = 1

K = 100

N = 100

T = 15

G = 15

C = 10 = 0.5(Y-T) - 0.5r

I = 25-2r

L = 50 + 0.5y - 10r

M = 225

Pi^e = 0

1. Derive the equation for the IS curve

2. Derive the equation for the LM curve

3. General equilibrium values of output, real interest rate, and price level

4. G increases by 6 to 21, what are the new short run equilibrium values of output, consumption, investment , real and interest rate?

5. After G increases to 21, gov't prints money to pay for deficit. M goes up by 6 to 231. What will be the short run impact of this policy on output, consumption, investment, and the real interest rate?

Answer 1

1)Is equation;Y=C+I+G

Y=0.5(Y-15)-0.5r+25-2r+15=0.5Y-7.5-0.5r+25-2r+15=32.5+0.5Y-2.5r

Y=65-5r{ Is equation}

2) LM equation;L=M/p

50+0.5Y-10r=225/p

r=5+0.05Y-22.5/P{ LM equation}

3)Y=65-2.5r

C=10=0.5(Y-15)-0.5r

17.5=0.5Y-0.5r

Y=35+r

35+r=65-2.5r

3.5r=30

r=30/3.5=8.5

Y=65-2.5*8.5=43.75

8.5=5+0.05*43.75-22.5/p

P=22.5/1.3125=17.14

4) multiplier=1/(1-mpc)=1/(1-0.5)=1/0.5=2

∆G=6

∆Y=∆G*multiplier=6*2=12

New Y=43.75+12=55.75

New IS equation;Y=77-2.5r

r=55.75-77)/-2.5=-21.25/-2.5=8.5

New C=0.5(40.75)-0.5*8.5=16.125

Investment=25-2*8.5=25-17=8