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Given information:
Assume that the marginal propensity to consume is 0.8.
=>MPC= 0.8
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The economy's output increases by $10 billion
=> ΔY = $10 billion
--
The tax revenue decreases by $6 billion
=> ΔTaxes = -$6 billion
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The government budget deficit increases by $2 billion
=> ΔGovernment budget deficit = $2 billion
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(a) Government deficit = Government spending - Taxes
=> ΔGovernment deficit = ΔGovernment spending - ΔTaxes
Note: tax revenue decreases by $6 billion, and the government budget deficit increases by $2 billion.
=> $2 billion = ΔGovernment spending - (-$6 billion)
=> $2 billion = ΔGovernment spending + $6 billion
=> ΔGovernment spending = $2 billion - $6 billion
=> ΔGovernment spending = -$4 billion
The government spending will decrease by $4 billlion (or change by -$4 billion)
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(b) Public saving = taxes - government spending
=> ΔPublic saving = ΔTaxes - ΔGovernment spending
=> ΔPublic saving = -$ billion - (-$4 billion)
=> Δ Public saving = -$6 billion + $4 billion
=> ΔPublic saving = -$2 billion
The public saving will decrease by $2 billion (or change by -$2 billion)
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(c)
The economy output increases by $10 billion
=> ΔY = $10 billion
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MPC = ΔC / ΔY
=> 0.8 =(ΔC / $10 billion)
=> ΔC = 0.8 * $10 billion
=> ΔC = $8 billion
The consumption increase by $8 billion (or change by $8 billion)
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Private saving = Y - C - T
Where T is taxes
=> ΔPrivate saving = ΔY - ΔC - ΔT
=> ΔPrivate saving = $10 billion - $8 billion - (-$6 billion)
=> ΔPrivate saving = $2 billion + $6 billion
=> ΔPrivate saving = $8 billion
The private saving will increase by $8 billion (or change by $8 billion)
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(d) National saving = Private saving + Public saving
=> ΔNational saving = ΔPrivate saving + ΔPublic saving
=> ΔNational Saving = $8 billion + (-$2 billion)
=> ΔNational saving = $6 billion
The national saving will increase by $6 billion (or change by $6 billion)
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(d) Due to increase in national saving, the equilibrium real interest will decrease.