Exam 35:Externalities-Part A

Firm 1 produces output x with a cost function c₁(x)=x²+ 10.Firm 2 produces output y with a cost function c₂(y,x)= y²+ x.Thus,the more that firm 1 produces,the greater are firm 2's costs.Both firms face competitive product markets.The competitive price of x is $20 and the competitive price of y is $40.No new firms can enter the industry and the old ones must remain.The efficient Pigouvian tax on the x good is

If there are negative externalities in production or consumption,competitive equilibrium is unlikely to be Pareto efficient but positive externalities enhance the efficiency of the market.

Marbella has 101 residents.All wear the same fancy clothes and each has the same utility function,u(m,b,B)= m + 24b - b² - B/50,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?

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

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 (75 +x₂)x₁ -2x²₁ for store 1 and (105 + 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?

Peter's utility is U(c,d,h)= 2c + 9d -d² -6h,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 Peter'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

Peter's utility is U(c,d,h)= 8c+18d -d ² - 6h,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 Peter'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

Millie Bush has written a best-seller.Revenues net of production costs are $300T^1/3A^1/3,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 trade between two people is an example of an externality.

If preferences are quasilinear,then the delineation of property rights has no distributional consequences.

A mountain village owns a common pasture where villagers graze their goats.The cost to a goat owner of owning and caring for a goat is 4 groschens.The pasture gets overgrazed if too many goats share the pasture.The total revenue from all goats on the common pasture is f (g)=48g - 2g²,where g is the number of goats on the pasture.The town council notices that total profit from the pasture is not maximized if villagers are allowed to pasture goats for free.The council decides to allow a goat to use the common pasture only if its owner buys it a goat license.To maximize total profit (of villagers and council),how many groschens per goat should the council charge?

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=25f -f ² - 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 11 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?

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?

Two firms in a grimy Ohio town produce the same product in a competitive industry.Each has an old factory using an old technology.It still pays to operate these factories but it would not pay to expand them.The only variable factor used by either firm is labor.Each firm pollutes the other and thus reduces the output of the other firm.The production functions of firms A and B respectively are Q a = L .5 a (2/3)Q b and Q b =L .5 b (1/3)Q a,where L .5 a and L .5 b are the square roots respectively of the amount of labor used by firms A and B.The wage rate of labor is $1 and the price of the firms output is $12. a.If the two firms each maximize profits independently,what is their total output and how much quasi-rents do their factories earn? b.If someone buys them both and maximizes joint profits,how much quasi-rent is earned in total?

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 -2C ² and the profits of the jeweler will be (24 + C )J - 2J ².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

Suppose that in Horsehead,Massachusetts,the cost of operating a lobster boat is $4,000 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(28x -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.

Charlie's utility is U(c,d,h)= 4c + 10d - d ² - 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

Suppose that in Horsehead,Massachusetts,the cost of operating a lobster boat is $4,000 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(28x-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 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)= H ²/100 = 2A and the cost function of the apple orchard is C_A(H,A)=A²/100,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.