A1: PERFECT SUBSTITUTES... (a) Suppose we have preferences U(X, Y) = min[X, 3Y]. What is the utility at the bundle X = 10 and Y = 10? Create a table then graph/sketch the indifference curve through (10, 10). (b) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain. (c) State the consumer's utility maximization problem and express this in words. Sketch this in a figure and explain.
A1: PERFECT SUBSTITUTES... (a) Suppose we have preferences U(X, Y) = min[X, 3Y]. What is the utility at the bundle X = 10 and Y = 10? Create a table then graph/sketch the indifference curve through (10, 10). (b) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain. (c) State the consumer's utility maximization problem and express this in words. Sketch this in a figure and explain.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![A1: PERFECT SUBSTITUTES..
(a) Suppose we have preferences U(X, Y) = min[X, 3Y]. What is the utility at the bundle X = 10 and
Y = 10? Create a table then graph/sketch the indifference curve through (10, 10).
(b) What do we mean by a composite good? What does this composite good look like with these
preferences? Show and explain.
(c) State the consumer's utility maximization problem and express this in words. Sketch this in a
figure and explain.
(d) Show that demands are: X = 3M/[3Px + Py] and Y = M/[3Px + Py]. Hint: use the composite
good from (b).
(e) Let prices be Px = $5, Py = $3 and income M = $1000. What is optimal X, Y, and utility? Show
your work.
(f) Suppose Px rises to $6 and Py falls to $2 but income stays at $1000. Calculate the Compensating
Variation that ensures the consumer is no worse off nor better off with these price changes.
Show and explain your work.
A2: RISK and INSURANCE...
Consider the following FIRE-INSURANCE PROBLEM where fire partially destroys a $500 house.
EVENT
FIRE
NO FIRE
PROBABILITY OUTCOME INSURANCE PAYOUT
$100
$500
0.02
0.98
$400
0
PREMIUM
??
??
(a) What do we mean when we say an agent is Risk Averse?
(b) Assume utility is U(x) = V(x). Why does this utility function imply the agent is risk-averse? Use a
figure/diagram to explain.
(c) What is the expected payoff and expected utility of having no insurance for this agent?
(d) What do we mean by certainty equivalent? What is the certainty equivalent of no insurance?
(e) What is the maximum the agent will pay for complete insurance that pays out $400 in the case
of fire? Show your work.
(f) Suppose insurance is incomplete and only pays out $300 in case of fire. What is the maximum
the agent will pay for insurance now? Show your work and explain relative to (e). Note: I am
interested in your solution technique more than the answer. So show your thought process.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8a9802b-ded9-4a7b-93c8-71218002814a%2F46348b14-3fc5-4bd5-a0e8-298238466f50%2Fakxas2i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A1: PERFECT SUBSTITUTES..
(a) Suppose we have preferences U(X, Y) = min[X, 3Y]. What is the utility at the bundle X = 10 and
Y = 10? Create a table then graph/sketch the indifference curve through (10, 10).
(b) What do we mean by a composite good? What does this composite good look like with these
preferences? Show and explain.
(c) State the consumer's utility maximization problem and express this in words. Sketch this in a
figure and explain.
(d) Show that demands are: X = 3M/[3Px + Py] and Y = M/[3Px + Py]. Hint: use the composite
good from (b).
(e) Let prices be Px = $5, Py = $3 and income M = $1000. What is optimal X, Y, and utility? Show
your work.
(f) Suppose Px rises to $6 and Py falls to $2 but income stays at $1000. Calculate the Compensating
Variation that ensures the consumer is no worse off nor better off with these price changes.
Show and explain your work.
A2: RISK and INSURANCE...
Consider the following FIRE-INSURANCE PROBLEM where fire partially destroys a $500 house.
EVENT
FIRE
NO FIRE
PROBABILITY OUTCOME INSURANCE PAYOUT
$100
$500
0.02
0.98
$400
0
PREMIUM
??
??
(a) What do we mean when we say an agent is Risk Averse?
(b) Assume utility is U(x) = V(x). Why does this utility function imply the agent is risk-averse? Use a
figure/diagram to explain.
(c) What is the expected payoff and expected utility of having no insurance for this agent?
(d) What do we mean by certainty equivalent? What is the certainty equivalent of no insurance?
(e) What is the maximum the agent will pay for complete insurance that pays out $400 in the case
of fire? Show your work.
(f) Suppose insurance is incomplete and only pays out $300 in case of fire. What is the maximum
the agent will pay for insurance now? Show your work and explain relative to (e). Note: I am
interested in your solution technique more than the answer. So show your thought process.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 9 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
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
![ENGR.ECONOMIC ANALYSIS](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9780190931919/9780190931919_smallCoverImage.gif)
![Principles of Economics (12th Edition)](https://www.bartleby.com/isbn_cover_images/9780134078779/9780134078779_smallCoverImage.gif)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
![Engineering Economy (17th Edition)](https://www.bartleby.com/isbn_cover_images/9780134870069/9780134870069_smallCoverImage.gif)
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
![ENGR.ECONOMIC ANALYSIS](https://compass-isbn-assets.s3.amazonaws.com/isbn_cover_images/9780190931919/9780190931919_smallCoverImage.gif)
![Principles of Economics (12th Edition)](https://www.bartleby.com/isbn_cover_images/9780134078779/9780134078779_smallCoverImage.gif)
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
![Engineering Economy (17th Edition)](https://www.bartleby.com/isbn_cover_images/9780134870069/9780134870069_smallCoverImage.gif)
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)](https://www.bartleby.com/isbn_cover_images/9781305585126/9781305585126_smallCoverImage.gif)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
![Managerial Economics: A Problem Solving Approach](https://www.bartleby.com/isbn_cover_images/9781337106665/9781337106665_smallCoverImage.gif)
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-…](https://www.bartleby.com/isbn_cover_images/9781259290619/9781259290619_smallCoverImage.gif)
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education