please just answer c,d,e A large factory pumps its waste into a nearby lake. The lake is also used for recreation by 1,000people. Let X be the amount of waste that the firm pumps into the lake. Let Y, be the number ofhours per day that person i spends swimming and boating in the lake, and let C, be the numberof dollars that person i spends on consumption goods. If the firm pumps X units of waste intothe lake, its profits will beII(X) = 1,200X100X².(a) If there is no restrictions on pumping waste into the lake, how much waste will the firmpumps to maximize its profits?(b) Consumers have identical utility functions given byU(Y₁, C₁, X) = C +9Y-Y² - XY₁,and identical incomes. Suppose that there is no charge to consumers for using the lake. Ifthe 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 eachconsumer 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 unitreduction of the waste into the lake. Will he/she succeed to make everyone happy, includingthe firm? Explain your answer.

This economics question revolves around a large factory that pumps its waste into a nearby lake,…

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.

8th Edition

ISBN:9781337091992

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter7: Consumers, Producers, And The Efficiency Of Markets

Section: Chapter Questions

Problem 8PA