The following figure shows that a tax on clothing can reduce the price of food. Suppose that after the tax on clothing consumption is imposed, another tax is levied on the consumption of food. For example, the consumption of both commodities would be subject to a tax of five percent. Describe the conclusions of your analysis assuming the same tax is present in both the clothing and the food markets. Further assume that the tax revenue is returned in equal lump-sum transfers to all citizens.
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This problem, I'm guessing, assumes a two-good world (food and clothing) where changes to taxation affect one, the other, or both. In theory, two countervailing taxes should be offsetting, especially if (as shown in the diagrams) the elasticity of the demand and supply are exactly the same for both goods.
Of course, this is a common fallacy ...
This solution looks at the effects of counter-vailing taxes, and how they can impact consumption.