Exam 33: A: Externalities

Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $6,000 per month. Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the bay is $1,000(18x - x²). If there are no restrictions on entry and new boats come into the bay until there is no profit to be made by a new entrant, then the number of boats who enter will be X₁. If the number of boats that operate in the bay is regulated to maximize total profits, the number of boats in the bay will be X₂.

A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spends C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (18 + J)C - C² 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

In Problem 2, suppose that the cost function of the honey farm 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 $2 and the price of apples is $4 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 profit-maximizing single owner.

A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spends C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (18 + J)C - C² and the profits of the jeweler will be (36 + 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 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 20X - X² and profits of the developer are 28Y - 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 developer's profits.

Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $5,000 per month. Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the bay is $1,000(21x - x²). If there are no restrictions on entry and new boats come into the bay until there is no profit to be made by a new entrant, then the number of boats who enter will be X₁. If the number of boats that operate in the bay is regulated to maximize total profits, the number of boats in the bay will be X₂.

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 22X - 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 developer's profits.

Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $6,000 per month. Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the bay is $1,000(18x - x²). If there are no restrictions on entry and new boats come into the bay until there is no profit to be made by a new entrant, then the number of boats who enter will be X₁. If the number of boats that operate in the bay is regulated to maximize total profits, the number of boats in the bay will be X₂.

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 22X - X² and profits of the developer are 26Y - 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 developer's profits.

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 22X - X² and profits of the developer are 32Y - 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 developer's profits.

In Problem 3, suppose Harry, a typical citizen, has the utility function U(m, d, h) = m + 7d² - d² - 2h, 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 people in his home town, and m is the amount of money he has left to spend on other stuff besides gasoline and auto repairs. Gas and auto repairs cost $1 per hour of driving. If each citizen believes that their own driving will not affect the amount of driving done by others, they will all drive D₁ hours per day. If all citizens drive to maximize the utility of a typical citizen, they will all drive D₂ hours per day, where

In Problem 2, suppose that the cost function of the honey farm is C_H(H, A) = - 3A 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 $2 and the price of apples is $7 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 profit-maximizing single owner.

A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spends C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (24 + J)C - C² and the profits of the jeweler will be (66 + 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

In Problem 2, suppose that the cost function of the honey farm is C_H(H, A) = - 3A 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 $7 and the price of apples is $5 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 profit-maximizing single owner.

Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $2,000 per month. Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the bay is $1,000(10x - x²). If there are no restrictions on entry and new boats come into the bay until there is no profit to be made by a new entrant, then the number of boats who enter will be X₁. If the number of boats that operate in the bay is regulated to maximize total profits, the number of boats in the bay will be X₂.

Suppose that in Horsehead, Massachusetts, the cost of operating a lobster boat is $2,000 per month. Suppose that if x lobster boats operate in the bay, the total monthly revenue from lobster boats in the bay is $1,000(26x - x²). If there are no restrictions on entry and new boats come into the bay until there is no profit to be made by a new entrant, then the number of boats who enter will be X₁. If the number of boats that operate in the bay is regulated to maximize total profits, the number of boats in the bay will be X₂.

In Problem 2, suppose that the cost function of the honey farm 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 $5 and the price of apples is $4 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 profit-maximizing single owner.

In Problem 3, suppose Wilfred, a typical citizen, has the utility function U(m, d, h) = m + 13d² - d² - 4h, 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 people in his home town, and m is the amount of money he has left to spend on other stuff besides gasoline and auto repairs. Gas and auto repairs cost $1 per hour of driving. If each citizen believes that their own driving will not affect the amount of driving done by others, they will all drive D₁ hours per day. If all citizens drive to maximize the utility of a typical citizen, they will all drive D₂ hours per day, where

In Problem 3, suppose Sam, a typical citizen, has the utility function U(m, d, h) = m + 13d² - 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 people in his home town, and m is the amount of money he has left to spend on other stuff besides gasoline and auto repairs. Gas and auto repairs cost $1 per hour of driving. If each citizen believes that their own driving will not affect the amount of driving done by others, they will all drive D₁ hours per day. If all citizens drive to maximize the utility of a typical citizen, they will all drive D₂ hours per day, where

In Problem 3, suppose Lawrence, a typical citizen, has the utility function U(m, d, h) = m + 7d² - d² - 4h, 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 people in his home town, and m is the amount of money he has left to spend on other stuff besides gasoline and auto repairs. Gas and auto repairs cost $1 per hour of driving. If each citizen believes that their own driving will not affect the amount of driving done by others, they will all drive D₁ hours per day. If all citizens drive to maximize the utility of a typical citizen, they will all drive D₂ hours per day, where