# 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....

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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

David answered on Dec 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...
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