Consider the utility function U = 2 In x₁ + In x2, where the x₁ are consumption goods.1. Set up the budget-constrained utility-maximization problem, and derive the Marshalliandemand functions.2. Suppose prices are p₁ = 3 and p₂ = 1, and income m = 100. Use your answer from #1to calculate the specific numerical solutions. Calculate the specific utility value for yoursolution.3. Use your answers to #1 to derive the indirect utility function.4.Use Roy's Identity to derive the Marshallian demand functions from the indirect utilityfunction found in #3.5.Set up the expenditure-minimization function, which is the dual version of the primalconsumer maximization problem you set up in #1, and derive the Hicksian demandfunctions.6. Use the same prices and calculated utility value in #2 to calculate the specific numericalsolutions to #5.7. Use your answer to #5 to derive the expenditure function.8. Use Hotelling's Lemma to derive the Hicksian demand functions from the expenditurefunction.9. Use Slutsky's Equation to show the connection between Marshallian and Hicksiandemand functions.10. Suppose the price of good 2 increases to P2 = 2. Calculate the compensating variationassociated with this price change.11. Now calculate the Equivalent Variation associated with that same price change.

Utility is a concept in economics that measures the satisfaction, well-being, or happiness a person…

Consider the utility function U = 2 In x₁ + In x₂, where the x, are consumption goods. 1. Set up the budget-constrained utility-maximization problem, and derive the Marshallian demand functions. 2. Suppose prices are p₁ = 3 and p₂ = 1, and income m= 100. Use your answer from #1 to calculate the specific numerical solutions. Calculate the specific utility value for your solution. 3. Use your answers to #1 to derive the indirect utility function. stions from the indirect utility

Consider the utility function U = 2 In x₁ + In x₂, where the x, are consumption goods. 1. Set up the budget-constrained utility-maximization problem, and derive the Marshallian demand functions. 2. Suppose prices are p₁ = 3 and p₂ = 1, and income m= 100. Use your answer from #1 to calculate the specific numerical solutions. Calculate the specific utility value for your solution. 3. Use your answers to #1 to derive the indirect utility function. stions from the indirect utility

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter6: Consumer Choice And Demand

Section: Chapter Questions

Problem 2QFR

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Question

Consider the utility function U = 2 In x₁ + In x2, where the x₁ are consumption goods.
1. Set up the budget-constrained utility-maximization problem, and derive the Marshallian
demand functions.
2. Suppose prices are p₁ = 3 and p₂ = 1, and income m = 100. Use your answer from #1
to calculate the specific numerical solutions. Calculate the specific utility value for your
solution.
3. Use your answers to #1 to derive the indirect utility function.
4.
Use Roy's Identity to derive the Marshallian demand functions from the indirect utility
function found in #3.
5.
Set up the expenditure-minimization function, which is the dual version of the primal
consumer maximization problem you set up in #1, and derive the Hicksian demand
functions.
6. Use the same prices and calculated utility value in #2 to calculate the specific numerical
solutions to #5.
7. Use your answer to #5 to derive the expenditure function.
8. Use Hotelling's Lemma to derive the Hicksian demand functions from the expenditure
function.
9. Use Slutsky's Equation to show the connection between Marshallian and Hicksian
demand functions.
10. Suppose the price of good 2 increases to P2 = 2. Calculate the compensating variation
associated with this price change.
11. Now calculate the Equivalent Variation associated with that same price change.

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