a) Show that the utility function is strictly increasing in x1 and x2. b) For a given level of utility U, derive the marginal rate of substitution between good 1 and good 2. c) Find the optimal choice of x1 and x2 when the consumer maximizes his/her utility.

a) Show that the utility function is strictly increasing in x1 and x2. b) For a given level of utility U, derive the marginal rate of substitution between good 1 and good 2. c) Find the optimal choice of x1 and x2 when the consumer maximizes his/her utility.

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section: Chapter Questions

Problem 4SQP

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Consider a consumer with the following utility function:
U(x1, x2)=(x1+4) (x2 + 6) for x1, x2 20
with the accompanying budget constraint:
p1x1 +p2x2=Y where p1, p2, Y>0
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a) Show that the utility function is strictly increasing in x1 and x2.
For a given level of utility U, derive the marginal rate of substitution between good 1 and good 2.
Find the optimal choice of x1 and x2 when the consumer maximizes his/her utility.
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