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(100 marks) Consider a simple 2-person economy with Alice and Bob. Alice's utility function is u(x,y) = xy, where x(y) is the quantity Alice consumes of good X(Y), and parameters a and are both positive numbers. Bob's utility function is uB(x, y) = xBya, where x(y) is the quantity Bob consumes of good X(Y). It is assumed that a + B = 1. To produce each of goods X and Y, one type of resources (denoted as R) is required and the production functions of X and Y are the same, described by x= f(Rx) = max{0, Ry 0.1} and y = f(Ry) = max{0, Ry 0.1}, where x(y) is the quantity produced of consumption goods X(Y) when Ry(Ry) units of the resources are used to produce the consumption good. The endowment of R is one unit for the whole economy. Find all the top-level Pareto optimal solutions (XA, YA, XB,YB). Textbooks Yew-Kwang Ng (2004), Welfare Economics: Towards a More Complete Analysis, Palgrave Macmillan (100 marks) Consider a simple 2-person economy with Alice and Bob. Alice's utility function is u(x,y) = xy, where x(y) is the quantity Alice consumes of good X(Y), and parameters a and are both positive numbers. Bob's utility function is uB(x, y) = xBya, where x(y) is the quantity Bob consumes of good X(Y). It is assumed that a + B = 1. To produce each of goods X and Y, one type of resources (denoted as R) is required and the production functions of X and Y are the same, described by x= f(Rx) = max{0, Ry 0.1} and y = f(Ry) = max{0, Ry 0.1}, where x(y) is the quantity produced of consumption goods X(Y) when Ry(Ry) units of the resources are used to produce the consumption good. The endowment of R is one unit for the whole economy. Find all the top-level Pareto optimal solutions (XA, YA, XB,YB). Textbooks Yew-Kwang Ng (2004), Welfare Economics: Towards a More Complete Analysis, Palgrave Macmillan