Government using tax to cover for spending without increasing inflation

Question

If, at full employment, the government wants to increase its spending by 100 billion without increasing inflation in the short run, it must do which of the following?

1. Raise tax by more than 100 billion
2. Raise tax by 100 billion.
3. Raise tax by less than 100 billion.

Official solution: 1. Reason: If the government does not want to increase inflation, it must increase taxes so that the policies are completely offset. Remember, changes in government spending have a direct effect, whereas changes in taxes have an indirect effect. Changes in taxes affect aggregate demand by changing incomes and, thus, consumer spending. However, people don’t spend all of their income (they do save some portion of it). Thus, the actual change in consumption is equal to the marginal propensity to consumer (MPC) times the change in taxes. So, in order for no inflation to occur, the government is going to have to raise taxes by more than the $100 billion (which is the amount that they increased government spending by).

My thought: I think 2. is correct because the saving mentioned in the reasons should are also counted in aggregate demand as they become investment money and will also increase demand with money multiplier.

Answer 1

Well, there are administrative costs to raising taxes, so those costs need to be covered by something more than the taxes desired for spending.

But I think you're right, these days any of that "saving" is going into the economy by buying assets like stocks or bonds. However, the deadweight losses caused by taxation fundamentally create pressure that increases costs and therefore prices. But this would be a one-time effect and wouldn't change the long run rate of inflation.