Now consider the following model and answer related questions. Y = C + I + G + X
ID: 1205513 • Letter: N
Question
Now consider the following model and answer related questions. Y = C + I + G + X- IM C = 49 + 0.9DI I = 300 - 2000r G = 800 T = 10 + 1/3(Y) X - IM = 60 If fed decides to set the interest rate at r = 0.05, how much will be the equilibrium GDP? At that rate how much is budget deficit or surplus? By how much GDP will change if government cuts tax rate from 1/3 to 0.20 and at the same time the Fed raises the interest rate from 0.05 to 0.06? Now suppose net exports drops by 20. In order to offset its contractionary impact on GDP, Fed decides to lower the rate of interest from 0.05 to 0.04 (just like during Asian crisis). How much is your prediction for a change in GDP?Explanation / Answer
Y=C+I+G+X-IM
C=49+0.9(Y-T)
I=300-2000r
G=800
T=10+Y/3
X-IM=60
a. r=0.05 so I = 300-2000*.05=200
Y = 49+0.9(Y-10-Y/3)+200+800+60 = 1100 - 3Y/5
Y = 1100*5/2 = 2750
b. T = 10+Y/3 = 926.67
G=800
So here government income is more than spending so there is a surplus.
c) Now
Y=C+I+G+X-IM
C=49+0.9(Y-T)
I=300-2000r
G=800
T=10+Y/5
X-IM=60
r=0.06 so I = 300-2000*.06=180
Y = 49+0.9(Y-10-Y/5)+180+800+60 = 1080 - 18Y/25
Y = 1080*25/7 = 3847.14
So GDP will increase by 1107.14
d) Now
Y=C+I+G+X-IM
C=49+0.9(Y-T)
I=300-2000r
G=800
T=10+Y/3
X-IM=40
a. r=0.05 so I = 300-2000*.04=220
Y = 49+0.9(Y-10-Y/3)+220+800+40 = 1100 - 3Y/5
Y = 1100*5/2 = 2750
So no change in GDP
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