3. A consumer is faced with a utility functionu(x, y) = 4x² + 3xy + y²And his budget constraint is given by ln( xy) = 5.a) Find the optimal values of x and yb)Find the value of the shadow pricec) Interpret the value of lambda. Does it make economic sense?d)Other than completeness, monotonicity and transitivity, discuss the other three axioms ofconsumer preferences.e) Using practical examples discuss the duality principle as it relates to both the firm andhouseholds.

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3. A consumer is faced with a utility function u(x, y) = 4x² + 3xy + y² And his budget constraint is given by ln(xy) = 5. a) Find the optimal values of x and y b) Find the value of the shadow price Interpret the value of lambda. Does it make economic sense?

3. A consumer is faced with a utility function u(x, y) = 4x² + 3xy + y² And his budget constraint is given by ln(xy) = 5. a) Find the optimal values of x and y b) Find the value of the shadow price Interpret the value of lambda. Does it make economic sense?

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter10: Consumer Choice Theory

Section: Chapter Questions

Problem 6P

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Question

3. A consumer is faced with a utility function
u(x, y) = 4x² + 3xy + y²
And his budget constraint is given by ln( xy) = 5.
a) Find the optimal values of x and y
b)
Find the value of the shadow price
c) Interpret the value of lambda. Does it make economic sense?
d)
Other than completeness, monotonicity and transitivity, discuss the other three axioms of
consumer preferences.
e) Using practical examples discuss the duality principle as it relates to both the firm and
households.

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