Consider an economy with two goods - X and Y - and two agents - Ann...

 

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Consider an economy with two goods - X and Y - and two agents - Ann and Bob. Ann and Bob wish to trade with one another in order to maximize their individual utilities. We will consider how their trading decisions depend on the initial endowments of X and Y and on their utility functions. Suppose Ann is endowed with one unit of X and half a unit of Y i.e. e Ann (1, 1/2 ) and Bob is endowed with 1 unit of X and 1.5 units of Y i.e. e Bob (1, 3/2 ). Additionally, suppose their utility functions are given by: U Ann (X, Y) = XY U Bob (X, Y) = Y + 2X %3D (a) With Ann on the "lower part", draw an Edgeworth box indicating the endowment and preferences of this problem. (b) Find the set of Pareto Optimal Allocations in this economy mathematically. (c) Represent those in your Edgeworth box, how is this set of points called? Consider an economy with two goods - X and Y - and two agents - Ann and Bob. Ann and Bob wish to trade with one another in order to maximize their individual utilities. We will consider how their trading decisions depend on the initial endowments of X and Y and on their utility functions. Suppose Ann is endowed with one unit of X and half a unit of Y i.e. e Ann (1, 1/2 ) and Bob is endowed with 1 unit of X and 1.5 units of Y i.e. e Bob (1, 3/2 ). Additionally, suppose their utility functions are given by: U Ann (X, Y) = XY U Bob (X, Y) = Y + 2X %3D (a) With Ann on the "lower part", draw an Edgeworth box indicating the endowment and preferences of this problem. (b) Find the set of Pareto Optimal Allocations in this economy mathematically. (c) Represent those in your Edgeworth box, how is this set of points called?