Bearbeite Exam 2018 (AI) und vergleiche deine Lösungen. Aus dem Kurs Microeconometrics an der Technische Universität Berlin (TU Berlin).
Consider a two-consumer, two-good economy where the goods are represented by X and Y. Consumer A has a utility function of UA(x, y) = 3x + y^2. Consumer B has a utility function of UB(x, y) = 2xy.
Initially, Consumer A owns 10 units of good X and 5 units of good Y, while Consumer B owns 5 units of good X and 15 units of good Y. What is the initial endowment point for this economy in terms of X and Y?
Calculate the marginal rate of substitution (MRS) for both consumers. What is the interpretation of the MRS? Is this endowment Pareto efficient? Explain.
Suppose both consumers are willing to trade at a price ratio of 2:1 (that is, 2 units of Y for one unit of X). How many units of X and Y would each consumer end up consuming in equilibrium? What would be their final utility levels? Explain your reasoning.