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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

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

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Assume Jane, who lives in a farm next to a refinery, has the following utility function: \[ u_j(x_j, e) = \ln(x_j) \] where \( x_j \) 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: \[ x_j = 100 + (0.01 \times e^2) \] In other words, in a year where sulfur dioxide levels are low year round, she can get as many as 1432 lbs. of food from her farm (\( e = 365 \)). However, in a year where sulfur dioxide levels are low for only 100 days (\( e = 100 \)), she can only get 200 lbs. of food from her farm. **(New)** Jane learns that scrubbers, a filter-like technology that reduces sulfur dioxide from refinery emissions, can be purchased in the market for $100 a piece. Each scrubber increases the number of days with low sulfur dioxide by 50. Currently, the days with low sulfur dioxide are 100. Assume that she can sell her farm produce in the market at $1 per lb and can pay for the scrubber technology after the arrival of her crop production. If she could buy one of these scrubbers and convince the refinery to use them, what would her consumption be after paying for the scrubber? - 325 - 250 - 275 - 225 - 175
Transcribed Image Text:Assume Jane, who lives in a farm next to a refinery, has the following utility function: \[ u_j(x_j, e) = \ln(x_j) \] where \( x_j \) 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: \[ x_j = 100 + (0.01 \times e^2) \] In other words, in a year where sulfur dioxide levels are low year round, she can get as many as 1432 lbs. of food from her farm (\( e = 365 \)). However, in a year where sulfur dioxide levels are low for only 100 days (\( e = 100 \)), she can only get 200 lbs. of food from her farm. **(New)** Jane learns that scrubbers, a filter-like technology that reduces sulfur dioxide from refinery emissions, can be purchased in the market for $100 a piece. Each scrubber increases the number of days with low sulfur dioxide by 50. Currently, the days with low sulfur dioxide are 100. Assume that she can sell her farm produce in the market at $1 per lb and can pay for the scrubber technology after the arrival of her crop production. If she could buy one of these scrubbers and convince the refinery to use them, what would her consumption be after paying for the scrubber? - 325 - 250 - 275 - 225 - 175
**Problem Context:** Peter, Sara, and James live by the river and have preferences for water quality (designated as \( w \)) and live trees (\( t \)). Peter and Sara live upstream and have trees on their land. James lives downstream and does not have trees on his land. However, James benefits from Peter’s and Sara’s trees because each tree that stands upstream improves the water quality of the river downstream. James appreciates the benefits of live trees for water quality and feels sad when trees are cut down for timber. Key Definitions: - Water quality downstream: \( W \) - Trees on Peter’s property: \( t_p \) - Trees on Sara’s property: \( t_s \) **Question:** Choose the best option that describes James' preferences for water and trees. **Options:** 1. \( u_j = 100w + t_p + t_s \quad \text{where } w = 100 \) 2. \( u_j = 100w + t_p + t_s \quad \text{where } w = 100 + t_p + t_s \) 3. \( u_j = 100w + t_p + t_s \quad \text{where } w = 100 + t_p \) 4. \( u_j = 100w \quad \text{where } w = 100 + t_p + t_s \) 5. \( u_j = 100w + t_p \quad \text{where } w = 100 + t_p + t_s \)
Transcribed Image Text:**Problem Context:** Peter, Sara, and James live by the river and have preferences for water quality (designated as \( w \)) and live trees (\( t \)). Peter and Sara live upstream and have trees on their land. James lives downstream and does not have trees on his land. However, James benefits from Peter’s and Sara’s trees because each tree that stands upstream improves the water quality of the river downstream. James appreciates the benefits of live trees for water quality and feels sad when trees are cut down for timber. Key Definitions: - Water quality downstream: \( W \) - Trees on Peter’s property: \( t_p \) - Trees on Sara’s property: \( t_s \) **Question:** Choose the best option that describes James' preferences for water and trees. **Options:** 1. \( u_j = 100w + t_p + t_s \quad \text{where } w = 100 \) 2. \( u_j = 100w + t_p + t_s \quad \text{where } w = 100 + t_p + t_s \) 3. \( u_j = 100w + t_p + t_s \quad \text{where } w = 100 + t_p \) 4. \( u_j = 100w \quad \text{where } w = 100 + t_p + t_s \) 5. \( u_j = 100w + t_p \quad \text{where } w = 100 + t_p + t_s \)
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