3. |Lionsider a two-consumer (Ms. A and Mr. B). two-commodity {m1 and is} pure exchange economy. Consumer A's preferences are represented by the utility function: more) = met. a}. Consumer B's preferences are represented by the utility function: Haiti's?) = may. If} where x; denotes the quantity of commodity j E {1, 2} consumed by consumer is Lat, H}. The total quantities available in the economy of commodity 3:1, denoted by El. and of commodity 1:2. denoted by :32. are identical. That is $1 = :32 = E :5 i]. Further, assume that the endowment allocation is such that A owns are of commodity m1. and {3 EH4 of commodity \"2. {i} [4 marks] Find the offer sums of both Ms. A and Mr. E. {ii} {3 marl-rs] Find the set of Walrasian equilibrium prices and allocations in this economy. {iii} [5 marl-rs] Find the set of Pareto efficient allocations. Are the Walrasian equilibrium allocationtsi you found in {ii} above Pareto efficient? Explain your answer. |L'ionsider now the economy described above where the endowments of the two consumers are modified in the following way. The total quantities available in the economy of commodity 11, denoted by 5:1, is twice the total quantity available in the economy of commodity I2, denoted by Q. That is i1 = 2&2 2: I]. Further, assume that the endowment allocation is such that A owns 5:133 of commodity m1, and {3 sh's of commodity m2- {iy} [4 marks] What are the offer writes of his. A and Mr. B in this new economy? {to [3 marks] What is the set of Walrasian equilibrium prices and allocations? {iii} [4 marks] Find the set of Pareto efficient allocations. Are the Walrasian equilibrium allocationts} you found in {yi} aboye Pareto efficient? Explain your answer. 5. Ben's swim coach estimates that his time, t, in the 100-yard butterfly at a big upcoming meet as a function of the number of yards he swims per week, y, is t=47+9005y Based on this production function, his coach also estimates that if Ben swims 15,000 yards per week, his time will be 51.25 seconds, and he will finish tenth place. If he swims 30,000 yards per week, his time will be 49.01 seconds, and he will come in third. If he swims 45,000 yards per week, his time will be 47.95 seconds, and he will win the meet. Use calculus to determine Ben's marginal productivity of time given the number of yards he practices. Is there diminishing marginal productivity of practice yards? Ben's marginal productivity of swim time given y practice yards (MP ,) is MP y = increasing Ben's marginal producitivity of practice yards is decreasing constant In terms of Ben's place in the big meet, what is his marginal productivity of the number of yards he practices? Is there diminishing marginal productivity of practice yards? Ben's marginal productivity of increasing practice yards from 15,000 yards to 30,000 yards is swim meet places, and his marginal productivity of increasing practice yards from 30,000 yards to 45,000 yards is |swim meet places. (Enter numeric responses using integers.) decreasing Ben's marginal productivity of practice yards is increasing constantKuhn-Tucker Conditions Note: You can use this equation solver to solve any single-variable equations after you set them up. The focus of these problems is not on algebraic manipulations, but on the concepts and the procedure involved. Problem KTCl. Use the Kuhn-Tucker conditions to find maximum for the following: F(x, y) = 2x y , subject to constraints (v) 18x + 3y
