Question 4: Suppose Billy is endowed with non-labor income of $100, and 40 hours to allocate between leisure and work. Assume he can earn $8 an hour in the labor market. As in class, assume the price of the composite consumption good C is $1 per unit. Suppose Billy's utility function is u(R,C) = R%C, where MUg = 2RC and MU = R2. (a) Draw a graph of Billy's budget constraint and endowment bundle (make sure to label all axes, intercepts, bundles, slopes, etc.). (b) Solve for Billy's optimal bundle (R*, C*). PUBPOL 2000 Question 4: (cont.) (c) Policy #1: Suppose the government levies a $60 lump-sum tax on Billy (regardless of how many hours Billy works, the government collects $60 from him poor Billy Gilmour!). Portray the effect of this tax policy on your graph of Billy's budget constraint? After the lump-sum tax, will Billy choose a bundle such that he works more or less? Interpret your result in terms of income and substitution effects (as in class). Note: You can answer without finding the new bundle, but you may resolve if it helps. (d) Policy #2: Now suppose that, instead of a lump-tax, the government levies a tax of t = $2 (per hour) on hourly wages. Draw a new graph with Billy's original budget (from part a) and then with this new tax policy imposed (make sure to label all axes, intercepts, bundles, slopes, etc.). Solve for Billy's new optimal bundle under this tax policy. Will he choose to work more or less as a result of the tax? Interpret your result in terms of income and substitution effects