One-period production economy

One-period production economy Consider the case of a consumer who lives only for one period. Answer the following questions. For all these questions assume that her felicity function is given by the function u(c, l) = ? ln c + (1 ? ?) ln l, where c stands for consumption, l for leisure and ? denotes how she values consumption relative to leisure. For instance, if ? = 1 then shes does not care about leisure. In addition, she earns a wage w per hour worked. 1. Assme that her only source of income is her labor income. Derive algebraic expressions for the optimal leisure and consumption 2. Assume now that she receives a lump-sum subsidy S . What is the e?ect of this susbsidy on her optimal hours-worked and consumption? 3. Assume now that she receives the same lump-sum subsidy S but in addition she pays a lump-sum tax T of the same amount. Determine what happens with her optimal leisure and consumption 4. Assume that she pays a labor income tax t for every dollar earned. Determine what happens with her optimal decisions on leisure and consumption 5. Assume that she pays a labor income tax t for every dollar earned. Suppose in addition that the proceedings of this tax are rebated to her as a lump-sum subsidy S . Determine what happens with her optimal decisions on leisure and consumption 6. Assume that she pays a consumption tax ? for every dollar consumed. Compare this case with a situation in which she pays a labor income tax t and argue that there is an equivalence between a consumption tax and this labor income tax. What is the consumption tax the government has to set in order to have the same e?ect on the consumer’s behavior of a labor income tax of t = 30%? 7. Assume now that the government provides a non-working insurance b. That is, per every hour she spent in leisure activities the government commits to pay her b. What happens with her optimal consumption and leisure? 8. Assume that the government levies a tax on savings. Discuss how does her behavior change as a result of this policy 9. Consider two separate cases depending on who bears a labor income tax. In the ?rst case, the consumer pays this tax. Call it tc . In the second case, the ?rm pays this tax. Call it tf . Show that there exits an equivalence between tc and tf . Does it matter who pays the tax?. Provide an intuitive answer. Hint: Be careful when writing down the ?rms’s pro?t function to account for this tax 10. Suppose that suddenly there is a change in her preferences regarding her love for leisure. That is, assume that there is an increase in ?. Discuss what happens with her optimal decision on consumption and leisure 2

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