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Consider a simple Robinson Crusoe economy with two goods. Robinson is endowed with T = 1 units of time. He uses time t to produce guavas x and time ty to produce oysters y. The remaining time l = T – të – ty is leisure. Robinson's utility is given by U (x, y,l) = x² · y + al, where a > 0 is a parameter that captures the importance of leisure. The production functions have the form 1 z(t-) = VE, y(ty) = /ty. (i) First assume that a = 1. Find the Pareto-efficient allocation for this economy.

Consider a simple Robinson Crusoe economy with two goods. Robinson is endowed with T = 1 units of time. He uses time t to produce guavas x and time ty to produce oysters y. The remaining time l = T – të – ty is leisure. Robinson's utility is given by U (x, y,l) = x² · y + al, where a > 0 is a parameter that captures the importance of leisure. The production functions have the form 1 z(t-) = VE, y(ty) = /ty. (i) First assume that a = 1. Find the Pareto-efficient allocation for this economy.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Consider a simple Robinson Crusoe economy with two goods. Robinson is endowed with T = 1 units of time. He uses time t to produce guavas x and time ty to produce oysters y. The remaining time l = T - ta – ty is leisure. Robinson's utility is given by %3D U (x, y,l) = x² . y +al, where a > 0 is a parameter that captures the importance of leisure. The production functions have the form z(t2) = VEz, y(ty) = Vty. (i) First assume that a = 1. Find the Pareto-efficient allocation for this economy.
Transcribed Image Text:Consider a simple Robinson Crusoe economy with two goods. Robinson is endowed with T = 1 units of time. He uses time t to produce guavas x and time ty to produce oysters y. The remaining time l = T - ta – ty is leisure. Robinson's utility is given by %3D U (x, y,l) = x² . y +al, where a > 0 is a parameter that captures the importance of leisure. The production functions have the form z(t2) = VEz, y(ty) = Vty. (i) First assume that a = 1. Find the Pareto-efficient allocation for this economy.
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