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Suppose the government introduces a simultaneous tax and subsidy on a consumption good, which is produced under perfect competition. If the tax and the subsidy are equal, then there will be no distortion, but also no tax revenue.

Similarly, a policy combining taxes and subsidies on a good can only raise revenue if it reduces the equilibrium amount of the good, i.e. if it introduces distortion. In other words, there is no possibility to raise tax revenue through taxes and subsidies on consumption (no lump sum taxes) without distorting the market.

What were the (first) papers to analyze this problem? Could someone provide a reference for such a result? I would prefer an academic paper with such an analysis to lecture slides. As a bonus, any exception to this line of argument would also be interesting.

I remember reading somewhere that combining taxes and subsidies used to be a real policy proposal in order to have taxation without distortion until a paper came along showing that such a policy cannot raise revenue. Unfortunately, I can't remember where I read that.

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