Intermediate Microeconomics Problem Set 3+ An economic agent has the following utility function, U(RC) = C0.5 R0.5 where C is a consumption good and R is leisure. Furthermore, the economic agent has an endowment of $m dollars of nonlabor income, and R hours of time that can be used for either leisure or work such that endowment = (R,C) = 100, 1000). Let the wage rate, w = 10 and the price, p = 1. < 1. Find the bundle (R*, C*) that maximizes utility. Show work. < < 2. The government decides to impose a 5% sales tax on the consumption good. Find the bundle (R*, C*) that maximizes utility after the sales tax is imposed. Show work. + 3. Perform a Slutsky decomposition for the change from (1) to (2). Show the exact size of the substitution effect and income effects in terms of R. Show work. 4. Instead of the sales tax, the government decides to impose a lump-sum tax of a size that generates the same tax revenue as in (2). Find the bundle (R*, C*) that maximizes utility after the lump-sum tax is imposed. 5. Under which case (2) or (4) does the economic agent have higher utility? Show work. 6. Which tax (2) or (4) do you think people would find more fair?