a) Explain why a higher marginal tax rate
reduces the size of the government expenditure...

Question

a) Explain why a higher marginal tax rate
reduces the size of the government expenditure multiplier.
b)
b) Suppose government increases autonomous
taxes and defence expenditure by the same amount. Will real GDP increase in the
short run? Why?

David · Accepted Answer

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.

a) Explain why a higher marginal tax rate reduces the size of the government expenditure multiplier. b) b) Suppose government increases autonomous taxes and defence expenditure by the same amount....

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