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3. Consider a representative consumer who has preferences over an aggregate consumption good e and leisure. Her preferences are described by the uility function: U(c,l) In(e) +In(l) The consumer has a time endowment of h hours which can be used to work at the market or enjoyed as leisure. The real wage rate is w per hour. The worker pays a proportional wage tax of rate t, so the workers after-tax wage is (1 t). The consumer also has dividend income of π. (Note that there is no lump-sum tax here.) (a) Set up the consumers utility maximization problem (b) Analyze what would happen to consumption and leisure if the tax rate t increased: (a) show the effect of an increase in t on a graph. (b) Explain the economic intuitions for your results
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