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Problem 3: Consider a government that must nance a given level of spending G with taxes on either labor income or output. (a) Suppose the government imposes a proportional income tax 1' so that after-tax labor income is (l _, r)wL = (1 1')w(N l), where N is the total time available to the household to allocate between labor and leisure, i is the time devoted to leisure, L is the time devoted to labor, and w is the wage. What is the rst order condition for the household's problem? What is the rst order condition for the rm's problem? Show that the M RS is less than the M PL. What does this mean, compared to the case without labor income taxes? (b) Now suppose the government imposes an output tax t on firms so that after tax revenue is (1 - t) F(K, L), where K is capital and L is labor. Again: What is the first order condition for the household's problem? What is the first order condition for the firm's problem? Show that the MRS is less than the MPL. What does this mean, compared to the case without labor income taxes? (c) The government must decide whether to impose an income tax or an output tax to finance expenditures G. Under both scenarios, after-tax receipts must equal G, i.e. TLw = G and ty = G. Show that the household is indifferent to both revenue-equivalent tax schemes. Hint: First show that if t = (1-a)7, the amount of labor supplied in equilibrium is the same. Then compare the resulting consumption allocation from the budget constraints. Remember that the household owns the firms (and hence receives any profit from pro- ducing output), and that the houshold rents capital to the firms, so that the budget constraint of the household can be expressed as C = wLtrk + = wLtrk +(Y -wL-rk)