QUESTION 1 (a) Consider an economy with two goods x and y, and 2 individuals A and B with preferences (b o' represented by the utility functions: UA(XA:}\"A)Z'\\JXAYA UE(XEJYB):\\'XEYB where x; and y; represent the consumption of goods x and y by each individual i = A, B. The initial endowment of the goods is that A has 2 units of x and 8 units of y while B has 8 units of x and 2 units of good y. (i) Show formally how the two goods must be allocated among the two individuals at any a]location in this economy. Draw the corresponding contract curve in the Edgeworth box. (2 points) (ii) Assume B gets to choose a new allocation to maximize her utility subject to the constraint that A's utility is no lower than at the endowment point. Find the corresponding Pareto efficient allocation. What is the magnitude of the increase in B'S utility when moving from the endowment point to this Pareto efficient allocation? Provide a graphical illustration. (3 points) The utility possibilities frontier for the two consumers (A and B) can be represented by the equation U, =10-U, , where Ua and Ug stand for the utilities of A and B respectively. (i) What are the optimal levels of Ua and Ug according to the Rawlsian criterion? (1 point) (i) What are the optimal levels of U and Ug according to thriterion? Provide a brief explanation of the nature of the utilitarian solution in this case. (2 points) (iii)Provide a graphical representation in the (U, ,Ug)-space. (2 points) QUESTION 2 (a) Provide the step by step formal derivation of the expression for the DWL of commodity taxes when supply is perfectly (elastic Explain in detail the factors that determine the magnitude of the DWL. (4 points) (b) Consider an individual with income I who consumes two goods x and y, with prices px and Py respectively. If the individual has Cobb-Douglas preferences, then the indirect utility function and the expenditure function are given by: V ( P x , Py , I ) =- 0.51 and E(P., P,,U )=2U PxPy P xPy where U stands for a given level of utility. (i) Assume that initially 1=8, px =1, and py =4. Use the information provided to compute the compensating variation (CV) and the equivalent variation (EV) for an increase in Px from 1 to 4. (2 points) (ii) The ordinary and compensated demands for good x are given respectively by x ( Px, Py , I ) = 0.51 and x" (Px) P , U) = UP. Px P x If the increase in px is due to a per unit tax of $3 compute the EBEV and EBcv were EB stands for excess burden (or deadweight loss]. (2 points) (iii)Provide a graphical representation for (i) and (ii) in the compensated demand space. Make sure to include all relevant labels. (2 points)