Consider a pure exchange economy in which two consumers (a and b) trade their initial endow-...

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Consider a pure exchange economy in which two consumers (a and b) trade their initial endow- ment of two goods (good 1 and 2) in a competitive market. Consumer a's endowment is given by wa = (25,75) and b's endowment is wb = (75,125). The two consumers' preferences are repre- sented by u²(x,x) = aln x² + (1 - a) In x2 and u²³ (x²₁x²) = x² + x ²₂, where a € (0,1) is a constant. (a) If the total endowment of good 2 is evenly allocated to the two consumers, determine the allocation of good 1 for Pareto efficiency. (b) Compute the excess demand function for each good, and show that Walras' law holds. (c) Compute the Walrasian equilibrium price. (d) Characterize the core of this economy, and label the allocation inside the core that is obtained as a competitive equilibrium. Consider a pure exchange economy in which two consumers (a and b) trade their initial endow- ment of two goods (good 1 and 2) in a competitive market. Consumer a's endowment is given by wa = (25,75) and b's endowment is wb = (75,125). The two consumers' preferences are repre- sented by u²(x,x) = aln x² + (1 - a) In x2 and u²³ (x²₁x²) = x² + x ²₂, where a € (0,1) is a constant. (a) If the total endowment of good 2 is evenly allocated to the two consumers, determine the allocation of good 1 for Pareto efficiency. (b) Compute the excess demand function for each good, and show that Walras' law holds. (c) Compute the Walrasian equilibrium price. (d) Characterize the core of this economy, and label the allocation inside the core that is obtained as a competitive equilibrium.