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

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.2P
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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 xy 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) = 100+ (0.01 x e²)
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/(x,e)=In(x)) where xy 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) = 100+ (0.01 x e²) 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
Given the information below, choose the best option that describes James' preferences for water
and trees.
Peter, Sara and James live by the river and have preferences for water quality (w) and
live trees (t). Peter and Sara live upstream and have trees in their land. James lives
downstream and does not have trees in his land. James, however, benefits from Peter
and Sara's trees because each tree that stands upstream improves the water quality of
the river downstream. Besides the positive effect on the water he drinks, James also
likes the idea of live trees and gets really sad every time he sees trees turned into timber
carried down the stream. Define water quality downstream as W. Define trees in Peter
and Sara's property as tp and ts, respectively.
O Uj 100w + tp + ts
100w + tp + ts
100w+tp + ts
100w where w= 100+ tp + ts
O
U j
O U j
Please use the following information for the remainder of the questions.
U j
O U j
=
=
=
=
=
where w =
where w
where w
100w+tp where w
=
100
=
100+ tp + ts
100 + tp
100 + tp + ts
Transcribed Image Text:Given the information below, choose the best option that describes James' preferences for water and trees. Peter, Sara and James live by the river and have preferences for water quality (w) and live trees (t). Peter and Sara live upstream and have trees in their land. James lives downstream and does not have trees in his land. James, however, benefits from Peter and Sara's trees because each tree that stands upstream improves the water quality of the river downstream. Besides the positive effect on the water he drinks, James also likes the idea of live trees and gets really sad every time he sees trees turned into timber carried down the stream. Define water quality downstream as W. Define trees in Peter and Sara's property as tp and ts, respectively. O Uj 100w + tp + ts 100w + tp + ts 100w+tp + ts 100w where w= 100+ tp + ts O U j O U j Please use the following information for the remainder of the questions. U j O U j = = = = = where w = where w where w 100w+tp where w = 100 = 100+ tp + ts 100 + tp 100 + tp + ts
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