1. Dividing the dollar Suppose there are two people in the economy: A, B The economy is purely an exchange economy (no production). Utility in the economy is derived from income y. Social weflare is: S (UA(y), UB (y)) and YA + YB = 100 A.) Suppose utility is linear in $$, so that UA (YA) = YA, UB (YB) = YB What allocation (YA, YB) maximizes a utilitarian social welfare function? What allocation (YA,YB) maximizes a Rawlsian Social Welfare Function? B.) Suppose now that utility is concave in $$, so that u(YA) = YA and B (YB) = YB What allocation (YA, YB) maximizes a utilitarian social welfare function? What allocation (YA, YB) maximizes a Rawlsian Social Welfare Function? C.) Suppose now that utility is u(YA) = 2A and (YB) = YB What allocation (YA,YB) maximizes a utilitarian social welfare function? What allocation (YA,YB) maximizes a Rawlsian Social Welfare Function? 2. Consumption and Subsidy Consider Rob has utility over two goods: x and c and we can represent his utility as: u(x, c) = aln(x) + (1 a)ln(c) Suppose he has income (y), and y = 12, the price of x is px = 2 and the price of c: pc == 1 A) Maximize Rob's utility and solve for his demand for x and c in terms of a, then calculate when a = 0.75 B) Now suppose the government subsidizes consumption of good x with a 50% proportional subsidy. Solve for Rob's demand for x and c under the subsidy C) Graph utility maximizing choice from part A) and then from part B) (put c on the vertical axis) D) Calculate the income and substitution effects on Rob's consumption of x resulting from part B) 3. Empirical Effects of Minimum Wage Increase A famous older study of the minimum wage used data from two states Pennsylvania (PA) and New Jersey (NJ), and a large minimum wage hike in New Jersey (NJ) (which didn't apply to PA) to examine the impact of minimum wage increases on full-time equivalent (FTE) employment in fast food establishments in each state. Below are the authors average FTE employment before the minimum wage hike and after for NJ and PA. Year 1991 (before) 1992 (after) NJ PA 20.43 23.30 21.03 21.15 A) Propose a time-series estimator for the impact of the minimum wage hike: - Provide the symbolic formula for the estimator as well as the numerical estimate. Provide a brief description of the estimator. Discuss the key assumption required for the estimator to be valid (no bias) Discuss a scenario under which each assumption would be violated (bias). B) Propose a cross-sectional estimator for the impact of the minimum wage hike: - Provide the symbolic formula for the estimator as well as the numerical estimate. Provide a brief description of the estimator. Discuss the key assumption required for the estimator to be valid (no bias) Discuss a scenario under which each assumption would be violated (bias). C) Propose a difference-in-differences estimator for the impact of the minimum wage hike: Provide the symbolic formula for the estimator as well as the numerical estimate. Provide a brief description of the estimator. Discuss the key assumption required for the estimator to be valid (no bias) Discuss a scenario under which each assumption would be violated (bias).