Answered: (a) If there is no restrictions on…

(a) If there is no restrictions on pumping waste into the lake, how much waste will the firm pumps to maximize its profits? (b) check photo for part B please

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter6: Demand Relationships Among Goods

Section: Chapter Questions

Problem 6.4P

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Question

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 Yi be the number of hours per day that person i spends swimming and boating in the lake, and let Ci 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;

Π(X) = 1, 200X − 100X^2.

(a) If there is no restrictions on pumping waste into the lake, how much waste will the firm
pumps to maximize its profits?
(b) check photo for part B please

(b) Consumers have identical utility functions given by
U(Y₁, C₁, X) = C₁ +9Y-Y²-XY₁₁
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?

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Step 3: Solve for (b)

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Let me know if you are able to answer these as the next part

(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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Could you show the work for getting X = 6 and Y = (9-X)/2

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