1. Constrained Consumer Choice: Mitzie loves green tea and cappuccinos, where G and C denote cups of green tea and cappuccinos that Mitzie consumes. Mitzie has a modest weekly budget, Y=$42, from providing care to her beloved Uncle Morty. The price of a cup of green tea (PG) is $1 and the price of a cup of cappuccino (Pc) is $3. Mitzie has preferences that can be described by the quasilinear utility function: U(G, C) = 2G + C. Use this information to answer the following questions. a. Set up Mitzie's constrained utility maximization problem. Be sure to identify what she is maximizing and what is her constraint. b. Suppose that G is on the x-axis and C is on the Y-axis. What is Mitzie's marginal rate of substitution (MRS) and her marginal rate of transformation (MRT)? Illustrate (without precisely computing) in a graph with a budget constraint and indifference curve the choice of G and C that maximizes Mitzie's utility. c. Following up on part b., calculate numerical values for Mitzie's optimal consumption of G and C using the budget constraint and the fact that at the optimal bundle MRS = MRT. d. Now let's grind out the solution to Mitzie's optimal choice of G and C using the substitution method. Using her budget constraint, write an equatic for the cups of cappuccinos Mitzie buys in terms of her cups of green tea. Given this write Mitzie's utility purely as a function of the cups of green tea she chooses to consume and do this symbolically. e. Using your set-up from part (d), find the cups of green tea and cappuccinos Mitzie will chose to purchase. First do this symbolically and then plug in numbers for income for prices. f. How much utility does Mitzie get from consuming her utility maximizing bundle of goods?
1. Constrained Consumer Choice: Mitzie loves green tea and cappuccinos, where G and C denote cups of green tea and cappuccinos that Mitzie consumes. Mitzie has a modest weekly budget, Y=$42, from providing care to her beloved Uncle Morty. The price of a cup of green tea (PG) is $1 and the price of a cup of cappuccino (Pc) is $3. Mitzie has preferences that can be described by the quasilinear utility function: U(G, C) = 2G + C. Use this information to answer the following questions. a. Set up Mitzie's constrained utility maximization problem. Be sure to identify what she is maximizing and what is her constraint. b. Suppose that G is on the x-axis and C is on the Y-axis. What is Mitzie's marginal rate of substitution (MRS) and her marginal rate of transformation (MRT)? Illustrate (without precisely computing) in a graph with a budget constraint and indifference curve the choice of G and C that maximizes Mitzie's utility. c. Following up on part b., calculate numerical values for Mitzie's optimal consumption of G and C using the budget constraint and the fact that at the optimal bundle MRS = MRT. d. Now let's grind out the solution to Mitzie's optimal choice of G and C using the substitution method. Using her budget constraint, write an equatic for the cups of cappuccinos Mitzie buys in terms of her cups of green tea. Given this write Mitzie's utility purely as a function of the cups of green tea she chooses to consume and do this symbolically. e. Using your set-up from part (d), find the cups of green tea and cappuccinos Mitzie will chose to purchase. First do this symbolically and then plug in numbers for income for prices. f. How much utility does Mitzie get from consuming her utility maximizing bundle of goods?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
100%
d-f please!
![1. **Constrained Consumer Choice**: Mitzie loves green tea and cappuccinos, where G and C denote cups of green tea and cappuccinos that Mitzie consumes. Mitzie has a modest weekly budget, \( Y = \$42 \), from providing care to her beloved Uncle Morty. The price of a cup of green tea (\( P_G \)) is $1, and the price of a cup of cappuccino (\( P_C \)) is $3. Mitzie has preferences that can be described by the quasilinear utility function:
\[
U(G, C) = 2G^{\frac{1}{2}} + C
\]
Use this information to answer the following questions.
a. Set up Mitzie’s constrained utility maximization problem. Be sure to identify what she is maximizing and what is her constraint.
b. Suppose that G is on the x-axis and C is on the y-axis. What is Mitzie’s marginal rate of substitution (MRS) and her marginal rate of transformation (MRT)? Illustrate (without precisely computing) in a graph with a budget constraint and indifference curve the choice of G and C that maximizes Mitzie’s utility.
c. Following up on part b., calculate numerical values for Mitzie’s optimal consumption of G and C using the budget constraint and the fact that at the optimal bundle MRS = MRT.
d. Now let’s grind out the solution to Mitzie’s optimal choice of G and C using the substitution method. Using her budget constraint, write an equation for the cups of cappuccinos Mitzie buys in terms of her cups of green tea. Given this, write Mitzie’s utility purely as a function of the cups of green tea she chooses to consume and do this symbolically.
e. Using your set-up from part (d), find the cups of green tea and cappuccinos Mitzie will choose to purchase. First, do this symbolically and then plug in numbers for income for prices.
f. How much utility does Mitzie get from consuming her utility maximizing bundle of goods?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad5f8718-b822-43a6-888a-6d9b997f8030%2F61fda8f7-1da9-4d58-a31f-840089c1d65a%2Fqzahg8p_processed.png&w=3840&q=75)
Transcribed Image Text:1. **Constrained Consumer Choice**: Mitzie loves green tea and cappuccinos, where G and C denote cups of green tea and cappuccinos that Mitzie consumes. Mitzie has a modest weekly budget, \( Y = \$42 \), from providing care to her beloved Uncle Morty. The price of a cup of green tea (\( P_G \)) is $1, and the price of a cup of cappuccino (\( P_C \)) is $3. Mitzie has preferences that can be described by the quasilinear utility function:
\[
U(G, C) = 2G^{\frac{1}{2}} + C
\]
Use this information to answer the following questions.
a. Set up Mitzie’s constrained utility maximization problem. Be sure to identify what she is maximizing and what is her constraint.
b. Suppose that G is on the x-axis and C is on the y-axis. What is Mitzie’s marginal rate of substitution (MRS) and her marginal rate of transformation (MRT)? Illustrate (without precisely computing) in a graph with a budget constraint and indifference curve the choice of G and C that maximizes Mitzie’s utility.
c. Following up on part b., calculate numerical values for Mitzie’s optimal consumption of G and C using the budget constraint and the fact that at the optimal bundle MRS = MRT.
d. Now let’s grind out the solution to Mitzie’s optimal choice of G and C using the substitution method. Using her budget constraint, write an equation for the cups of cappuccinos Mitzie buys in terms of her cups of green tea. Given this, write Mitzie’s utility purely as a function of the cups of green tea she chooses to consume and do this symbolically.
e. Using your set-up from part (d), find the cups of green tea and cappuccinos Mitzie will choose to purchase. First, do this symbolically and then plug in numbers for income for prices.
f. How much utility does Mitzie get from consuming her utility maximizing bundle of goods?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 8 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
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education