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a) Explain why a higher marginal tax ratereduces the size of the government expenditure multiplier.

b)b) Suppose government increases autonomoustaxes and defence expenditure by the same amount. Will real GDP increase in theshort run? Why?

Answered Same DayDec 20, 2021

Solution

The income determination equation is Y= C+I+G+X-M where Y= aggregate production/

income, C= consumption expenditure, I= autonomous investment, G= government expenditure

(exogenous), X-M= net exports. The functional form of consumption expenditure is C=

a+(c*disposable income) where a=autonomous consumption and c=marginal propensity to

consume. Yd (disposable income) = Y-(T+ tY) where (T+tY) is the tax function. T= autonomous

tax, t= marginal tax rate on income.

Therefore, the income determination equation is Y= (a+(c*(Y-T-tY))) +I+G+X-M which

can be further simplified to Y*(1-c (1-t)) = a-cT+I+G+X-M where each term on the right hand

side is exogenously given. Therefore now the expenditure multiplier is [1/ (1-c (1-t))]. Change in

aggregate production is [1/ (1-c (1-t))] times the change in government expenditure. An increase

in marginal tax rate i.e. t increases the denominator of the government expenditure multiplier and

hence reduces the multiplier value. With higher marginal tax rate, the size of government

expenditure multiplier reduces and vice versa. Higher tax rate in the...

The income determination equation is Y= C+I+G+X-M where Y= aggregate production/

income, C= consumption expenditure, I= autonomous investment, G= government expenditure

(exogenous), X-M= net exports. The functional form of consumption expenditure is C=

a+(c*disposable income) where a=autonomous consumption and c=marginal propensity to

consume. Yd (disposable income) = Y-(T+ tY) where (T+tY) is the tax function. T= autonomous

tax, t= marginal tax rate on income.

Therefore, the income determination equation is Y= (a+(c*(Y-T-tY))) +I+G+X-M which

can be further simplified to Y*(1-c (1-t)) = a-cT+I+G+X-M where each term on the right hand

side is exogenously given. Therefore now the expenditure multiplier is [1/ (1-c (1-t))]. Change in

aggregate production is [1/ (1-c (1-t))] times the change in government expenditure. An increase

in marginal tax rate i.e. t increases the denominator of the government expenditure multiplier and

hence reduces the multiplier value. With higher marginal tax rate, the size of government

expenditure multiplier reduces and vice versa. Higher tax rate in the...

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