In terms of the initial impact on national income, a tax increase which aims to increase tax revenue at the current level of national income by $x is less damaging than a spending cut of $x?
Answer: True
The answer is True.
The question is only seeking an understanding of the initial drain on the spending stream rather than the fully exhausted multiplied contraction of national income that will result. It is clear that the tax increase increase will have two effects: (a) some initial demand drain; and (b) it reduces 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 impact on demand motivated by an decrease 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 cut
A cut in government spending (say of $1000) is what we call an exogenous withdrawal from the aggregate spending stream and this directly reduces aggregate demand by that amount. So it might be the cancellation of a long-standing order for $1000 worth of gadget X. The firm that produces gadget X thus reduces production of the good or service by the fall in orders ($1000) (if they deem the drop in sales to be permanent) and as a result incomes of the productive factors working for and/or used by the firm fall by $1000. So the initial fall in aggregate demand is $1000.
This initial fall in national output and income would then induce a further fall in consumption by 64 cents in the dollar so in Period 2, aggregate demand would decline by $640. Output and income fall further by the same amount to meet this drop in spending. In Period 3, aggregate demand falls by 0.8 x 0.8 x $640 and so on. The induced spending decrease gets smaller and smaller because some of each round of income drop is taxed away, some goes to a decline in imports and some manifests as a decline in saving.
Tax-increase induced contraction
The contraction coming from a tax-cut does not directly impact on the spending stream in the same way as the cut in government spending.
First, imagine the government worked out a tax rise cut that would reduce its initial budget deficit by the same amount as would have been the case if it had cut government spending (so in our example, $1000).
In other words, disposable income at each level of GDP falls initially by $1000. What happens next?
Some of the decline in disposable income manifests as lost saving (20 cents in each dollar that disposable income falls in the example being used). So the lost consumption is equal to the marginal propensity to consume out of disposable income times the drop in disposable income (which if the MPC is less than 1 will be lower than the $1000).
In this case the reduction in aggregate demand is $800 rather than $1000 in the case of the cut in government spending.
What happens next depends on the parameters of the macroeconomic system. The multiplied fall in national income may be higher or lower depending on these parameters. But it will never be the case that an initial budget equivalent tax rise will be more damaging to national income than a cut in government spending.
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! I am also ignoring the empirically-questionable mainstream claims that tax increases erode work incentives which force workers to supply less labour.
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