题目
Dashboard Microeconomic Analysis (ECON4020) 2025-26
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Question textIn an exchange economy, there are two people, A and B, and two goods, [math: x1]x_1 and [math: x2]x_2. Their respective utility functions and endowments are [math: uA(x1A,x2A)=min{2x1A,3x2A}]u^A(x_1^A,x_2^A) = \min\{2 x_1^A, 3 x_2^A\}[math: uB(x1B,x2B)=x1B⋅x2B]u^B(x_1^B,x_2^B) = x_1^B \cdot x_2^B[math: ωA=(6,10)andωB=(5,1)]\omega^A = (6, 10) \quad\text{and}\quad \omega^B = (5, 1) The minimum and maximum possible amounts of [math: x2A]x_2^A on the contract curve are (enter up to two decimal places if necessary): Minimum [math: x2A]x_2^A = Answer 1 Question 2[input] Maximum [math: x2A]x_2^A = Answer 2 Question 2[input] --- The minimum and maximum possible amounts of [math: x1A]x_1^A on the contract curve are (enter up to two decimal places if necessary): Minimum [math: x1A]x_1^A = Answer 3 Question 2[input] Maximum [math: x1A]x_1^A = Answer 4 Question 2[input]

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思路分析
Question restatement: In an exchange economy with two goods x1 and x2, two agents A and B, and utility functions uA(x1A,x2A) = min{2x1A, 3x2A} and uB(x1B,x2B) = x1B·x2B. Endowments are ωA = (6,10) and ωB = (5,1). We are asked for the minimum and maximum possible amounts of x2A on the contract curve, and the minimum and maximum possible amounts of x1A on the contract curve. The answers to fill are: Min x2A = 0, Max x2A = 7.33, Min x1A = 0, Max x1A = 11.
Step-by-step analysis of each option and reasoning for the contract curve:
1) Minimum x2A = 0. Why could x2A be zero on the contract curve?
- If A has no units of good 2, then x2A = 0. Since total resources are 11 of good 2, B would hold all of good 2 (x2B = 11). For Pareto efficiency (contract curve), the marginal rates of substitution (MRS) between A and B must be aligned or one party must be at a corner where their MRS is not finite. In this setup, it is possible to allocate all......Login to view full explanation登录即可查看完整答案
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