a) A hypothetical economy is given by the following identities:
C = 3000
I = 2000
G = 2500
T = 0.2Y
MPC = 0.5
X=6500
Z=5500 + 0.2Y
i. Find the equilibrium level of income.
Y=3,000+0.5(Y−0.2Y)+2,000+2,500+6,500−5,500−0.2YY=3,000+0.5(Y−0.2Y)+2,000+2,500+6,500−5,500−0.2YY=3,000+0.5(Y−0.2Y)+2,000+2,500+6,500−5,500−0.2Y
Y=3,000+0.4Y+2,000+2,500+6,500−5,500−0.2YY=3,000+0.4Y+2,000+2,500+6,500−5,500−0.2YY=3,000+0.4Y+2,000+2,500+6,500−5,500−0.2Y
Y=14,000−5,500+0.2YY=14,000−5,500+0.2YY=14,000−5,500+0.2Y
Y=8,500+0.2YY=8,500+0.2YY=8,500+0.2Y
0.8Y=8,5000.8Y=8,5000.8Y=8,500
Y=10,625Y=10,625Y=10,625
Equilibrium level of income =10625= 10625=10625
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