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3. Consider a representative consumer who has preferences over an

Question : 3. Consider a representative consumer who has preferences over an : 2542

3. Consider a representative consumer who has preferences over an aggregate consumption good c and leisure l. Her preferences are described by the utility function:U(c,l) = ln(c) + ln(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 worker’s after-tax wage is (1t)w. The consumer also has dividend income of . (Note that there is no lump-sum tax here.)(a) Set up the consumer’s utility maximization problem.(b) Analyze what would happen to consumption and leisure if the tax rate t increased: (a) show the eect of an increase in t on a graph. (b) Explain the economic intuitions for your results

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