Question

Willy the Worker has unavoidable personal commitments taking 8 hours per day. He can choose to work or to play (i.e., take leisure, a normal good) in the remaining hours. Being a graduate in Economics, he can charge $100 per hour for his consulting services when he chooses to work. The government's income tax system has a 0% tax rate for daily incomes from $0 to $ $600 per day; above $600 per day, the tax rate is 20%. Willy has a certain Utility Function U(L, I) where L = leisure play time and I = Income. His Marginal Rate of Substitution is known to be derived from this equation: MRSLI = 21/L . [Note that the "price" of Income is $1.] 1.1 (4) Willy thinks he pays enough taxes via the excise taxes on things he buys. So he decides to work the maximum number of hours he can without paying any income taxes. According to our Indifference Theory model, is Willy maximizing his satisfaction with his "no tax" choice, or should he work fewer hours? Explain your answer. [No diagram; use "the logic" of the model only.] At equilibrium, MRSLA = price ratio =PL/P1 = 100/1 = slope of BL = wage rate = 100 At "no tax” point, L = 10 and I = $600, hence MRS = 1200/10 = 120 Since MRS > P ratio, he must reduce MRS by taking more Leisure and working less He should (be at the "no tax" point / work fewer hours than the "no tax" point*)