Exam 33: Externalities

A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spend C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (30 + J)C - 2C² and the profits of the jeweler will be (24 + C)J - 2J². The clothing store gets to choose its amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend. The amount spent by the clothing store will be

Marbella has 101 residents. All wear the same fancy clothes and each has the same utility function, u(m, b, B) = m + 14b - b² - , where m is the amount of macaroni (in kilograms) that he or she eats per day, b is the number of hours that he or she spends on the beach per day, and B is the total number of person-hours spent per day on the beach by other residents of Marbella. Each has an income of $10 per day and macaroni costs $1 per kilogram. The city council is considering a law that would limit the amount of time that any person can spend on the beach. How many hours per day should they allow in order to maximize the utility of a typical Marbellite?

A Pigouvian tax on pollution is designed to collect enough revenue to pay for pollution detection by the government.

An airport is located next to a housing development. Where X is the number of planes that land per day and Y is the number of houses in the housing development, profits of the airport are 28X - X² and profits of the developer are 20Y - Y² - XY. Let H₁ be the number of houses built if a single profit-maximizing company owns the airport and the housing development. Let H₂ be the number of houses built if the airport and the housing development are operated independently and the airport has to pay the developer the total "damages" XY done by the planes to the profits of the developer.

A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spend C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (36 + J)C - 2C² and the profits of the jeweler will be (30 + C)J - 2J². The clothing store gets to choose its amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend. The amount spent by the clothing store will be

Millie Bush has written a best-seller. Revenues net of production costs are $ , where T is the number of publicity trips Millie takes and A is the number of ads for the book that appear. Millie has to pay for all of her own publicity trips, which cost $100 each. Her publisher pays for the advertising, which costs $100 per ad. Revenues from the book are split equally between Millie and her publisher. Let T₁ be the number of trips that Millie would choose to make in a Nash equilibrium where she chooses the number of trips and the publisher chooses the amount of advertising. Let T₂ be the number of trips that Millie should make if trips and advertising are determined so as to maximize total profits net of trip and ad costs.

A small coffee company roasts coffee beans in its shop. The unroasted beans cost the company $2 per pound. The marginal cost of roasting coffee beans is $ per pound when q pounds are roasted. The smell of roasting beans imposes costs on the company's neighbors. The total amount that neighbors would be willing to pay to have the shop stop roasting altogether is 5q², where q is the number of pounds being roasted. The company sells its output in a competitive market at $4.50 per pound. What is the socially efficient amount of coffee for the company to roast?

An airport is located next to a housing development. Where X is the number of planes that land per day and Y is the number of houses in the housing development, profits of the airport are 36X - X² and profits of the developer are 42Y - Y² - XY. Let H₁ be the number of houses built if a single profit-maximizing company owns the airport and the housing development. Let H₂ be the number of houses built if the airport and the housing development are operated independently and the airport has to pay the developer the total "damages" XY done by the planes to the profits of the developer.

Mobil Oil Corporation recently bought the right to emit an additional 900 pounds of noxious gas vapors per day at its Torrance, California, refinery. This suggests that allowing pollution rights to be marketed is likely to lead to more pollution than there would be if there were no restrictions on polluting.

Mike's utility function is U(c, d, h) = 4c + 14d - d² - 6h, where d is the number of hours per day that he spends driving around, h is the average number of hours per day spent driving around by other citizens of his town, and c is the amount of money he has to spend on other things than gasoline and auto repairs. There are 1,001 identical citizens in Mike's home town. Mike's expenses for gasoline and auto repairs amount to $.50 per hour for the time he spends driving. If Mike believes that his amount of driving won't affect the amount that others drive, how many hours per day will he choose to drive?

An apiary is located next to an apple orchard. The apiary produces honey and the apple orchard produces apples. The cost function of the apiary is C_H(H, A) = - 1A and the cost function of the apple orchard is C_A(H, A) = , where H and A are the number of units of honey and apples produced respectively. The price of honey is $5 and the price of apples is $6 per unit. Let A₁ be the output of apples if the firms operate independently, and let A₂ be the output of apples if the firms are operated by a single owner so as to maximize total profit.

Charlie's utility is U(c, d, h) = 4c + 10d - d² - 4h, where d is the number of hours per day that he spends driving around, h is the number of hours per day spent driving around by other people in his home town, and c is the amount of money he has left to spend on other stuff besides gasoline and auto repairs. Gas and auto repairs cost $.50 per hour of driving. All the people in Charlie's home town have the same tastes. If each citizen believes that his own driving will not affect the amount of driving done by others, they will all drive D₁ hours per day. If they are all drive the same amount, they would all be best off if each drove D₂ hours per day, where

The 130 campers at Bear Creek Campground love their own campfires but hate the smoke from their neighbors' campfires. Each camper's utility function is U = 17f - f² - s, where f is the number of hours her own campfire burns per day and where s is the amount of smoke in the air. It happens that s is 7 times the average amount of hours that campers use their fires. The campground authority could make all campers better off by limiting the number of hours of campfire per day for everyone. How many hours of campfire per day should the authority allow each camper in order to make the typical camper as well off as possible?

Two stores are located side by side. They attract customers to each other and to themselves by advertising. The profit functions of the two stores are (45 + x₂)x₁ - 2x²₁ for store 1 and (90 + x₁)x₂ - 2x²₂ for store 2, where x₁ and x₂ are total advertising expenditures by stores 1 and 2 respectively. If each store sets its advertising expenditures independently (as in Nash equilibrium), how much would store 1 spend on advertising?

A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spend C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (18 + J)C - 2C² and the profits of the jeweler will be (24 + C)J - 2J². The clothing store gets to choose its amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend. The amount spent by the clothing store will be

An apiary is located next to an apple orchard. The apiary produces honey and the apple orchard produces apples. The cost function of the apiary is C_H(H, A) = - 2A and the cost function of the apple orchard is C_A(H, A) = , where H and A are the number of units of honey and apples produced respectively. The price of honey is $1 and the price of apples is $3 per unit. Let A₁ be the output of apples if the firms operate independently, and let A₂ be the output of apples if the firms are operated by a single owner so as to maximize total profit.

A trade between two people is an example of an externality.

The only known way to eliminate externalities is through taxes or subsidies.

Mike's utility function is U(c, d, h) = 8c + 12d - d² - 6h, where d is the number of hours per day that he spends driving around, h is the average number of hours per day spent driving around by other citizens of his town, and c is the amount of money he has to spend on other things than gasoline and auto repairs. There are 1,001 identical citizens in Mike's home town. Mike's expenses for gasoline and auto repairs amount to $.50 per hour for the time he spends driving. If Mike believes that his amount of driving won't affect the amount that others drive, how many hours per day will he choose to drive?

The 130 campers at Bear Creek Campground love their own campfires but hate the smoke from their neighbors' campfires. Each camper's utility function is U = 22f - f² - s, where f is the number of hours her own campfire burns per day and where s is the amount of smoke in the air. It happens that s is 10 times the average amount of hours that campers use their fires. The campground authority could make all campers better off by limiting the number of hours of campfire per day for everyone. How many hours of campfire per day should the authority allow each camper in order to make the typical camper as well off as possible?