If the increase in government purchases is $15 billion with MPC 2/3, the change in the equilibrium level of GDP will be the third option, an increase of $45 billion.
It is given that the government has increased its purchases by $15 billion. This implies that the Government Expenditure, i.e G has increased by $15 billion.
This would lead to a multiplier effect, increasing Y, or the equilibrium GDP by an amount much greater than $15 billion.
We know that the Government Expenditure multiplier
= 1/(1 - MPC)  X ΔG
where,
MPC = Marginal propensity to Consume
ΔG = Change in Government Expenditure.
It is given that
MPC = 2/3
ΔG = $ 15 billion.
Hence, the change in the equilibrium level of GDP will be
1/(1 - 2/3) Â X Â $15 billion
= 1/(1/3) Â X Â $15 billion
= $45 billion
The equilibrium level of GDP will increase by $45 billion
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