Answer to Question #154314 in Macroeconomics for Dulmini

Question

Explain carefully why the tax multiplier [ΔY/ ΔT = -b/ (1-b)] is negative and why it is 

smaller in absolute value than the government expenditure multiplier [ΔY/ ΔG = 1/ (1-

b)].

Answer 1

The tax multiplier [ΔY/ΔT = -b/(1-b)] is negative because an increase in taxes will reduce the personal disposable income of the household, which in turn reduces the consumption expenditure. For instance, a one dollar increase in tax reduces the personal disposable income by one dollar but also lowers the consumption spending component of aggregate demand by factor of b dollars. The remaining part of the decline is fetched by the fall of (1-b) dollars in savings.

It is smaller in absolute value than the government expenditure multiplier because not whole of the tax increase represents income which otherwise might have been consumer by the households. Since the marginal propensity to consume is less than one, some fraction of each dollar earned gets saved, which does not get added to aggregate demand. So, the initial change in consumption because of one dollar tax increase is

-MPC×(-$1) = -MPC

Thus, this amount highlighted is the change in autonomous expenditure that results from $1 tax increase and hence, we multiply this by the government spending multiplier and get

Tax Multiplier = -MPC/(1-MPC)