A large factory pumps its waste into a nearby lake. The lake is also used for recreation by 1,000 people. Let X be the amount of waste that the firm pumps into the lake. Let Y, be the number of hours per day that person i spends swimming and boating in the lake, and let C, be the number of dollars that person i spends on consumption goods. If the firm pumps X units of waste into the lake, its profits will be II(X) 1,200X100X² = (a) If there is no restrictions on pumping waste into the lake, how much waste will the firm pumps to maximize its profits? (b) Consumers have identical utility functions given by U(Y, C, X) = C +9Y-Y² - XX₁, and identical incomes. Suppose that there is no charge to consumers for using the lake. If the firm pumps the waste based on (a), how many hours per day will each consumer spend? (e) If the firm decides as in (a) and each consumer decides as in (b), then how much is each consumer willing to pay to the firm to reduce the waste by 1 unit? (d) How much reduction in the profits will be there if the firm reduces the waste by 1 unit? (e) Suppose that one consumer takes a lead and asks everyone to contribute $0.10 for the 1 unit reduction of the waste into the lake. Will he/she succeed to make everyone happy, including the firm? Explain your answer.
A large factory pumps its waste into a nearby lake. The lake is also used for recreation by 1,000 people. Let X be the amount of waste that the firm pumps into the lake. Let Y, be the number of hours per day that person i spends swimming and boating in the lake, and let C, be the number of dollars that person i spends on consumption goods. If the firm pumps X units of waste into the lake, its profits will be II(X) 1,200X100X² = (a) If there is no restrictions on pumping waste into the lake, how much waste will the firm pumps to maximize its profits? (b) Consumers have identical utility functions given by U(Y, C, X) = C +9Y-Y² - XX₁, and identical incomes. Suppose that there is no charge to consumers for using the lake. If the firm pumps the waste based on (a), how many hours per day will each consumer spend? (e) If the firm decides as in (a) and each consumer decides as in (b), then how much is each consumer willing to pay to the firm to reduce the waste by 1 unit? (d) How much reduction in the profits will be there if the firm reduces the waste by 1 unit? (e) Suppose that one consumer takes a lead and asks everyone to contribute $0.10 for the 1 unit reduction of the waste into the lake. Will he/she succeed to make everyone happy, including the firm? Explain your answer.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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please just answer c,d,e
Transcribed Image Text:A large factory pumps its waste into a nearby lake. The lake is also used for recreation by 1,000
people. Let X be the amount of waste that the firm pumps into the lake. Let Y, be the number of
hours per day that person i spends swimming and boating in the lake, and let C, be the number
of dollars that person i spends on consumption goods. If the firm pumps X units of waste into
the lake, its profits will be
II(X) = 1,200X100X².
(a) If there is no restrictions on pumping waste into the lake, how much waste will the firm
pumps to maximize its profits?
(b) Consumers have identical utility functions given by
U(Y₁, C₁, X) = C +9Y-Y² - XY₁,
and identical incomes. Suppose that there is no charge to consumers for using the lake. If
the firm pumps the waste based on (a), how many hours per day will each consumer spend?
(c) If the firm decides as in (a) and each consumer decides as in (b), then how much is each
consumer willing to pay to the firm to reduce the waste by 1 unit?
(d) How much reduction in the profits will be there if the firm reduces the waste by 1 unit?
(e) Suppose that one consumer takes a lead and asks everyone to contribute $0.10 for the 1 unit
reduction of the waste into the lake. Will he/she succeed to make everyone happy, including
the firm? Explain your answer.
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