Problem 2 Suppose that John's preferences over meat (M) and vegetables (V) are represented by the following utility function U(M,V) = a ln(M) + (1 − a) ln(V) where 0 < a < 1. ¹No claim of realism is made for the numbers in this example. 1 (a) Write down the Lagrangian for John's optimization problem. (Recall that John max- imizes utility given an income, I, and prices pm and py for the goods.) (b) Solve for John's optimal consumption bundle (M*, V*) (as a function of income and prices) using the Lagrangian method. 200 and faces prices PM = 1 and pv = 2. What is the value of John's optimal consumption bundle? What happens if John's income doubles to I = 400? (c) Suppose a = . Suppose also that John has income I =
Problem 2 Suppose that John's preferences over meat (M) and vegetables (V) are represented by the following utility function U(M,V) = a ln(M) + (1 − a) ln(V) where 0 < a < 1. ¹No claim of realism is made for the numbers in this example. 1 (a) Write down the Lagrangian for John's optimization problem. (Recall that John max- imizes utility given an income, I, and prices pm and py for the goods.) (b) Solve for John's optimal consumption bundle (M*, V*) (as a function of income and prices) using the Lagrangian method. 200 and faces prices PM = 1 and pv = 2. What is the value of John's optimal consumption bundle? What happens if John's income doubles to I = 400? (c) Suppose a = . Suppose also that John has income I =
Micro Economics For Today
10th Edition
ISBN:9781337613064
Author:Tucker, Irvin B.
Publisher:Tucker, Irvin B.
Chapter6: Consumer Choice Theory
Section: Chapter Questions
Problem 3SQP
Related questions
Question
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 5 steps with 13 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you