Consider an economy with 2 goods and 2 agents. The Örst agent has the utility function, u (x1; x2) = ln x1 + 2 ln x2, and the other one has u (y1; y2) = 2 ln y1 + ln y2. The aggregate endowments of the 2 goods are given by (50; 100). Suppose there is a social planner who cares about agents equally. (a) Set up the plannerís problem b) Calculate the first-best outcome (i.e., the social plannerís solution).
Consider an economy with 2 goods and 2 agents. The Örst agent has the utility function, u (x1; x2) = ln x1 + 2 ln x2, and the other one has u (y1; y2) = 2 ln y1 + ln y2. The aggregate endowments of the 2 goods are given by (50; 100). Suppose there is a social planner who cares about agents equally. (a) Set up the plannerís problem b) Calculate the first-best outcome (i.e., the social plannerís solution).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Consider an economy with 2 goods and 2 agents. The Örst agent has the utility
function, u (x1; x2) = ln x1 + 2 ln x2, and the other one has u (y1; y2) = 2 ln y1 + ln y2.
The aggregate endowments of the 2 goods are given by (50; 100). Suppose there is a
social planner who cares about agents equally.
(a) Set up the plannerís problem
b) Calculate the first-best outcome (i.e., the social plannerís solution).
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