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A consumer has preferences described by utility function u(x1,x2)=In(1+x1)+x2. Suppose p1=1, p2=3, and her income is 10. The government can tax good 1 at rate t, such that the price the consumer faces will become (1+t)p1. Find a tax rate t such that after the introduction of the tax the consumer decreases her consumption of good 1 by 50%.

A consumer has preferences described by utility function u(x1,x2)=In(1+x1)+x2. Suppose p1=1, p2=3, and her income is 10. The government can tax good 1 at rate t, such that the price the consumer faces will become (1+t)p1. Find a tax rate t such that after the introduction of the tax the consumer decreases her consumption of good 1 by 50%.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A consumer has preferences described by utility function u(x1,x2)=In(1+x1)+x2. Suppose p1=1, p2=3, and her income is 10. The government can tax good 1 at rate t, such that the price the consumer faces will become (1+t)p1. Find a tax rate t such that after the introduction of the tax the consumer decreases her consumption of good 1 by 50%.
Transcribed Image Text:A consumer has preferences described by utility function u(x1,x2)=In(1+x1)+x2. Suppose p1=1, p2=3, and her income is 10. The government can tax good 1 at rate t, such that the price the consumer faces will become (1+t)p1. Find a tax rate t such that after the introduction of the tax the consumer decreases her consumption of good 1 by 50%.
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