Question

Consider the closed-economy market-clearing model. Assume that the marginal propensity to consume is 0.8. The economy's output increases by $10 billion, tax revenue decreases by $6 billion, and the government budget deficit increases by $2 billion.

(a) Calculate the dollar change in government spending. (b) Calculate the dollar change in public saving. (c) Calculate the dollar change in private saving. (d) Calculate the dollar change in national saving. (e) Would the equilibrium real interest rate increase, decrease, or stay the same?

Answer 1

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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

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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.