The government is attempting to stimulate the economy via a discretionary expansion of the fiscal deficit. The private market orientated advisors tell them to cut taxes and 'privatise' the expansion whereas the more civic-minded advisors argue that there is a need for improved public infrastructure which requires increases in government spending. So imagine that the government is choosing between a tax cut that will reduce tax revenue at the current level of national income by $x and a spending increase of $x. Which policy option will have the greater initial impact on aggregate demand?
Answer: Spending increase
The answer is Spending increase.
The question is only seeking an understanding of the initial injection into the spending stream rather than the fully exhausted multiplied expansion of national income that will result. It is clear that the tax cut approach will have two effects: (a) some initial demand stimulus; and (b) it increases the value of the multiplier, other things equal.
We are only interested in the first effect rather than the total effect. But I will give you some insight also into what the two components of the tax result might imply overall when compared to the stimulus motivated by an increase in government spending.
To give you a concrete example which will consolidate the understanding of what happens, imagine that the marginal propensity to consume out of disposable income is 0.8 and there is only one tax rate set at 0.20. So for every extra dollar that the economy produces the government taxes 20 cents leaving 80 cents in disposable income. In turn, households then consume 0.8 of this 80 cents which means an injection of 64 cents goes into aggregate demand which them multiplies as the initial spending creates income which, in turn, generates more spending and so on.
Government spending increase
An increase in government spending (say of $1000) is what we call an exogenous injection into the spending stream and stimulates aggregate demand by that amount. So it might be an order of $1000 worth of gadget X which advances human welfare immeasurably! The firm that produces gadget X thus increases production of the good or service by the rise in orders ($1000) and as a result incomes of the productive factors rises by $1000. So the initial rise in aggregate demand is $1000.
This initial increase in national output and income then stimulates (induces) further consumption by 64 cents in the dollar so in Period 2, aggregate demand increases by $640. Output and income rises by the same amount to meet this increase in spending. In Period 3, aggregate demand rises by 0.8 x 0.8 x $640 and so on. The induced spending increase gets smaller and smaller because some of each round of income increase is taxed away, some goes to imports and some is saved.
Tax-cut induced stimulus
The stimulus coming from a tax-cut does not directly impact on the spending stream in the same way as the rise in government spending.
First, imagine the government worked out a tax cut that would increase its initial fiscal deficit by the same amount as would have been the case if it had increased government spending (so in our example, $1000).
In other words, disposable income at each level of GDP rises initially by $1000. What happens next?
Some of the disposable income is saved (20 cents in each dollar that disposable income increases). So immediately some of the tax increase is lost from the spending stream.
In this case the injection into aggregate demand is $800 rather than $1000 in the case of the increase in government spending.
What happens next depends on the parameters of the macroeconomic system. The multiplied rise in national income may be higher or lower depending on these parameters. But it will never be the case that an initial fiscal equivalent tax cut will be more stimulatory than a government spending increase.
Note in answering this question I am disregarding all the nonsensical notions of Ricardian equivalence that abound among the mainstream doomsayers who have never predicted anything of empirical note! All their predictions come to nought.
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