Assume Jane, who lives in a farm next to a refinery, has the following utility function: u/(x,e)=In(x)) where x; is Jane's food consumption from her farm in lb. and e is the number of days in a year with low levels of Sulfur Dioxide (emitted by the refinery) in the air. When it rains, sulfur dioxide into sulfuric acid resulting in "acid rain". Acid rain damages Jane's crops. Hence the production function of food in her farm is given by 100: (0.01 21
Assume Jane, who lives in a farm next to a refinery, has the following utility function: u/(x,e)=In(x)) where x; is Jane's food consumption from her farm in lb. and e is the number of days in a year with low levels of Sulfur Dioxide (emitted by the refinery) in the air. When it rains, sulfur dioxide into sulfuric acid resulting in "acid rain". Acid rain damages Jane's crops. Hence the production function of food in her farm is given by 100: (0.01 21
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Please help
![**Jane's Preferences for Air Quality**
**Utility Function:**
Assume Jane lives on a farm next to a refinery and has the following utility function:
\[ u_i(x_i, e) = \ln(x_i) \]
where \( x_i \) is Jane's food consumption from her farm in pounds, and \( e \) is the number of days in a year with low levels of sulfur dioxide (emitted by the refinery) in the air. When it rains, sulfur dioxide turns into sulfuric acid, resulting in "acid rain," which damages Jane's crops. Therefore, her farm's food production function is given by:
\[ x_i = 100 + (0.01 \times e^2) \]
In other words, in a year where sulfur dioxide levels are low year-round, she can get as much as 1432 pounds of food from her farm (\( e = 365 \)). However, in a year with low sulfur dioxide levels for only 100 days (\( e = 100 \)), she can only get 200 pounds of food.
**Options Describing Jane's Preferences:**
1. **Strong Anthropocentric:** Jane is concerned about air quality only to the extent that it is an input for something she does care about: food.
2. **Biocentric:** Because Jane's crops are living organisms that suffer from air pollution.
3. **Altruistic:** Clean air benefits everyone's utility, which increases Jane's preference for reducing pollution.
4. **Biocentric and Paternalistic:** Jane derives utility not only from healthier trees and cleaner air, but also from its positive impact on neighbors' crop consumption.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F676198b1-cb35-454f-b21c-01c3265d0f1a%2Fc4aee639-3058-4bbd-a4dd-f6fe0d01e0ec%2Fpjwkbhd_processed.png&w=3840&q=75)
Transcribed Image Text:**Jane's Preferences for Air Quality**
**Utility Function:**
Assume Jane lives on a farm next to a refinery and has the following utility function:
\[ u_i(x_i, e) = \ln(x_i) \]
where \( x_i \) is Jane's food consumption from her farm in pounds, and \( e \) is the number of days in a year with low levels of sulfur dioxide (emitted by the refinery) in the air. When it rains, sulfur dioxide turns into sulfuric acid, resulting in "acid rain," which damages Jane's crops. Therefore, her farm's food production function is given by:
\[ x_i = 100 + (0.01 \times e^2) \]
In other words, in a year where sulfur dioxide levels are low year-round, she can get as much as 1432 pounds of food from her farm (\( e = 365 \)). However, in a year with low sulfur dioxide levels for only 100 days (\( e = 100 \)), she can only get 200 pounds of food.
**Options Describing Jane's Preferences:**
1. **Strong Anthropocentric:** Jane is concerned about air quality only to the extent that it is an input for something she does care about: food.
2. **Biocentric:** Because Jane's crops are living organisms that suffer from air pollution.
3. **Altruistic:** Clean air benefits everyone's utility, which increases Jane's preference for reducing pollution.
4. **Biocentric and Paternalistic:** Jane derives utility not only from healthier trees and cleaner air, but also from its positive impact on neighbors' crop consumption.
![### Utility Calculation and Environmental Impact on Agriculture
#### Scenario Overview
Jane, a farmer living near a refinery, experiences fluctuations in her utility based on sulfur dioxide levels emitted by the refinery. Sulfur dioxide combines with water to create acid rain, adversely affecting her crop yield.
#### Utility Function
Jane's utility is determined by the function:
\[ u_j(x_j, e) = \ln(x_j) \]
Where:
- \( x_j \) is the food consumption from her farm (in lbs).
- \( e \) is the number of days with low sulfur dioxide levels.
#### Production Function
The production of food on Jane’s farm is given by:
\[ x_j = 100 + (0.01 \times e^2) \]
Key Points:
- In an optimal year with 365 low sulfur dioxide days, Jane yields 1432 lbs of food.
- With only 100 low sulfur dioxide days, the yield significantly drops to 200 lbs.
#### Problem Statement
Calculate Jane's utility for 10, 20, 100, 200, and 300 days with low sulfur dioxide levels.
#### Utility Calculation Options
1. **Option A:**
- 10 days = 4.12
- 20 days = 4.94
- 100 days = 5.92
- 200 days = 6.01
- 300 days = 6.91
2. **Option B:**
- 10 days = 4.62
- 20 days = 4.64
- 100 days = 5.30
- 200 days = 6.21
- 300 days = 6.91
3. **Option C:**
- 10 days = 3.62
- 20 days = 3.64
- 100 days = 5.650
- 200 days = 6.21
- 300 days = 6.91
4. **Option D:**
- 10 days = 4.11
- 20 days = 4.38
- 100 days = 5.64
- 200 days = 6.28
- 300 days = 7.12
5. **Option E:**
- 10 days = 4.62](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F676198b1-cb35-454f-b21c-01c3265d0f1a%2Fc4aee639-3058-4bbd-a4dd-f6fe0d01e0ec%2Fa178mc_processed.png&w=3840&q=75)
Transcribed Image Text:### Utility Calculation and Environmental Impact on Agriculture
#### Scenario Overview
Jane, a farmer living near a refinery, experiences fluctuations in her utility based on sulfur dioxide levels emitted by the refinery. Sulfur dioxide combines with water to create acid rain, adversely affecting her crop yield.
#### Utility Function
Jane's utility is determined by the function:
\[ u_j(x_j, e) = \ln(x_j) \]
Where:
- \( x_j \) is the food consumption from her farm (in lbs).
- \( e \) is the number of days with low sulfur dioxide levels.
#### Production Function
The production of food on Jane’s farm is given by:
\[ x_j = 100 + (0.01 \times e^2) \]
Key Points:
- In an optimal year with 365 low sulfur dioxide days, Jane yields 1432 lbs of food.
- With only 100 low sulfur dioxide days, the yield significantly drops to 200 lbs.
#### Problem Statement
Calculate Jane's utility for 10, 20, 100, 200, and 300 days with low sulfur dioxide levels.
#### Utility Calculation Options
1. **Option A:**
- 10 days = 4.12
- 20 days = 4.94
- 100 days = 5.92
- 200 days = 6.01
- 300 days = 6.91
2. **Option B:**
- 10 days = 4.62
- 20 days = 4.64
- 100 days = 5.30
- 200 days = 6.21
- 300 days = 6.91
3. **Option C:**
- 10 days = 3.62
- 20 days = 3.64
- 100 days = 5.650
- 200 days = 6.21
- 300 days = 6.91
4. **Option D:**
- 10 days = 4.11
- 20 days = 4.38
- 100 days = 5.64
- 200 days = 6.28
- 300 days = 7.12
5. **Option E:**
- 10 days = 4.62
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 4 steps
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