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  1. Suppose GDP is $1,500, consumption is $900, investment is $200, government purchases are $300, and taxes are $100. The marginal propensity to consume is 0.8. Is this economy in equilibrium? If so explain why, if not explain how it gets to an equilibrium.
  2. In problem 1, what is the equilibrium level of output?
  3. Explain why an increase in government purchases of 100 million dollars causes national income rise by more than 100 million dollars?

Question 1
Aggregate expenditure (Y) = C +G+I
But C= a+ b (Y-T)
A is autonomous consumption
b is the marginal propensity to consume.
I is investment
G is government purchases
T is taxes
Y=900+0.8(Y-100) +200+300
Y=900+0.8Y-80+500
Y=0.8Y+1320
Y-0.8Y=1320
0.2Y=1320
Y= $660
This economy is not in equilibrium since the potential GDP ($1,500) is not equal to the calculated DGP ($600).
The output gap is given by Y p -Y
1500-660=$840
The economy will get to the equilibrium by increasing the aggregate expenditure by $840, this will entail either increasing consumption, government expenditure or investments.
Question 2
The equilibrium level of output is $660
From the solution
Aggregate expenditure (Y) = C +G+I
But C= a+ b (Y-T)
A is autonomous consumption
b is the marginal propensity to consume.
I is investment
G is government purchases
T is taxes
Y=900+0.8(Y-100) +200+300
Y=900+0.8Y-80+500
Y=0.8Y+1320
Y-0.8Y=1320
0.2Y=1320
Y= $660
Question 3
Through the multiplier effect, government purchases leads to an increase in consumption and hence $100million government purchases will lead to more than $100 million raise in national income. Government purchases adds up consumption, which also leads to an addition in the national income.