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601-2goodsleisure

# 601-2goodsleisure - E 601 1 More on taxation So we know...

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E frqrplfv 601 1 More on taxation So we know from earlier notes that: (1) in a two-good (or n -good) world where both goods can be taxed the budget constraint is (1 + t 1 ) p 1 x 1 + (1 + t 2 ) p 2 x 2 = wealth and setting t 1 = t 2 = t is equivalent to a tax on wealth, t w , where 1 t w 1 / (1 + t ) , which is a lump-sum tax; (2) in a two-good world where one of the goods is leisure which can’t be taxed, a consumption tax (1 + t ) pc = w ( T l ) is equivalent to an earnings tax pc = (1 t ) w ( T l ) and either one of them will cause deadweight loss. We also know that the dead- weight loss works solely o ff the substitution e ff ect – no substitution e ff ect, no dead- weight loss. What is the optimal tax structure in a three-good world, where leisure is one of the goods? The budget constraint could be written as (1 + t 1 ) p 1 x 1 + (1 + t 2 ) p 2 x 2 = (1 t ) w ( T l ) But, as we noted above, this system would be duplicated by 1 + t 1 1 t p 1 x 1 + 1 + t 2 1 t p 2 x 2 = w ( T l ) or (1 + t 1 ) p 1 x 1 + (1 + t 2 ) p 2 x 2 = w ( T l ) So the question becomes when should t 1 > t 2 ? Rewriting the budget constraint as

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E frqrplfv 601 2 wl + (1 + t 1 ) p 1 x 1 + (1 + t 2 ) p 2 x 2 = wT it is clear that the only barrier to a fi rst-best outcome is the government’s inabil- ity to tax leisure. It follows that the answer to the question must revolve around which of goods 1 or 2 is “more complementary” with leisure, and from (2) above, complementarity should be measured with utility held constant. Changing leisure or
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