Exam 33: Externalities-Part B

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suppose that the cost function of the honey farm is CH(H, A)= H 2/100 - 3A and the cost function of the apple orchard is CA(H, A)= A2/100, 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.

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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

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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 - Y 2 - 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.

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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.

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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.

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