estion 5 A utility function is given by u(x₁, x2)=-4x+80x18x+100x2-x1x2. Suppose that prices are p₁ = 5, and p2 = 1. Income is I. 1. Specify the Lagrangean using all three constraints. 2. Use the Lagrangean determine the range of values of income / for which the different constraints may bind. Note: these preferences are not monotone. As a consequence, the budget constraint itself may not bind.

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
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Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.11P
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Question 5 A utility function is given by u(x, x2) = -4x + 80x - 8x3 + 100.x2 – x142.
Suppose that prices are pi = 5, and p2 = 1. Income is I.
1. Specify the Lagrangean using all three constraints.
2. Use the Lagrangean determine the range of values of income / for which the
different constraints may bind. Note: these preferences are not monotone. As
a consequence, the budget constraint itself may not bind.
Transcribed Image Text:Question 5 A utility function is given by u(x, x2) = -4x + 80x - 8x3 + 100.x2 – x142. Suppose that prices are pi = 5, and p2 = 1. Income is I. 1. Specify the Lagrangean using all three constraints. 2. Use the Lagrangean determine the range of values of income / for which the different constraints may bind. Note: these preferences are not monotone. As a consequence, the budget constraint itself may not bind.
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