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If your are in a first-year macro economics course then...
1) yes government purchases can increase total income.
2) cutting taxes could achieve the same result,
3) But the tax cut would need to be larger because the tax multiplier is one less than the government multiplier.

If you are in a second year or higher, then then answer becomes murkier. Government purchases with out a tax increase can only occur by government borrowing or by printing more money. A tax cut, in addition to increasing spending, may change the labor supply.

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