Consider a consumer with utility function u(x1, x2) = a_1x_1^( 2) + a_2x_2^( 2) where a1 > 0 and a2 > 0. Assume that p1, p2 > 0. (a) Show that the utility function represents strongly monotone preferences (b) Draw indifference curves passing through points (1, 2), (3, 3) and (0, 3). What properties of the preference relation can you derive from these indifference curves? (c) State the expenditure minimization problem and derive the Hicksian demand. Does the EMP problem have a unique solution at every price vector p >> 0? (d) Derive expenditure function e(p, u). Verify that it is homogeneous of degree 1 in p and increasing in u. (e) Using expenditure function and Hicksian demand, calculate Walrasian demand and indirect utility
Consider a consumer with utility function u(x1, x2) = a_1x_1^( 2) + a_2x_2^( 2) where a1 > 0 and a2 > 0. Assume that p1, p2 > 0. (a) Show that the utility function represents strongly monotone preferences (b) Draw indifference curves passing through points (1, 2), (3, 3) and (0, 3). What properties of the preference relation can you derive from these indifference curves? (c) State the expenditure minimization problem and derive the Hicksian demand. Does the EMP problem have a unique solution at every price vector p >> 0? (d) Derive expenditure function e(p, u). Verify that it is homogeneous of degree 1 in p and increasing in u. (e) Using expenditure function and Hicksian demand, calculate Walrasian demand and indirect utility
Chapter6: Consumer Choice Theory
Section6.A: Indifference Curve Analysis
Problem 11SQ
Related questions
Question
Transcribed Image Text:Consider a consumer with utility function u(x1, x2) = a 1x_1^( 2) + a_2x_2^( 2) where a1 > 0 and a2 > 0.
Assume that p1, p2 > 0. (a) Show that the utility function represents strongly monotone preferences (b)
Draw indifference curves passing through points (1, 2), (3, 3) and (0, 3). What properties of the
preference relation can you derive from these indifference curves? (c) State the expenditure
minimization problem and derive the Hicksian demand. Does the EMP problem have a unique solution
at every price vector p >> 0? (d) Derive expenditure function e(p, u). Verify that it is homogeneous of
degree 1 in p and increasing in u. (e) Using expenditure function and Hicksian demand, calculate
Walrasian demand and indirect utility
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 1 images
Recommended textbooks for you
Economics (MindTap Course List)
Economics
ISBN:
9781337617383
Author:
Roger A. Arnold
Publisher:
Cengage Learning
Economics (MindTap Course List)
Economics
ISBN:
9781337617383
Author:
Roger A. Arnold
Publisher:
Cengage Learning
