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Answer to Question #65416 in Macroeconomics for andreas

Question #65416
Assume a model with no foreign sector, an income tax rate of 0.25, a consumption function defined as C = 680 + (0.8)YD and where autonomous investment, government spending and transfers are all equal to 100 and lump sum taxes are 200. What is the level of equilibrium income in this model economy?
Expert's answer
t=0.25
C = 680 + (0.8)Yd
I=G=T=100
TR=200
Equilibrium level of national income 
Y=C+I+G
Disposable income
Yd=(Y-T- t*Y+TR)
Therefore, substituting the values of various parameters and variables we have
Y = 680 + 0.8*(Y-T-t*Y+TR)+I+G
Y=680+0.8*(Y-200- 0.25*Y+100)+100+100
Y-0.8Y+0.2Y=680- 160+80+200
0.4Y=800
Y=2000
Answer: The equilibrium income in in this model economy is equal to 2000

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