Exam 35:Externalities-Part A

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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 CH(H,A)=H 2/100-1A 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 $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.

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A

Two stores are located side by side and attract customers to each other and to themselves by advertising.Where x1 and x2 are the advertising expenditures of stores 1 and 2,the profits of the firms are (48 + x2)x1 - 2(x1)2 for store 1 and (54 + x1)x2 -2(x2)2 for store 2.Knowing these functions,one investor buys both stores.In order to maximize his total profits,how much should he spend on advertising for store 1?

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C

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 - 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 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?

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D

The efficient amount of air pollution is in general independent of whether polluters or pollutees pay to reduce pollution.

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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 - 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 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?

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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 )-2C 2 and the profits of the jeweler will be (30 + 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

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Marbella has 101 residents.All wear the same fancy clothes and each has the same utility function,u(m,b,B)=m + 14b - 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?

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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?

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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 $(150 -10q + q2)/100 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?

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

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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 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 $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 single owner so as to maximize total profit.

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Mike's utility function is U(c,d,h)=4c +14d - d 2 - 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?

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If your consumption of toothpaste produces positive externalities for your neighbors (which you ignore),then you are consuming less toothpaste than is Pareto optimal.

(True/False)
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Marbella has 101 residents.All wear the same fancy clothes and each has the same utility function,u(m,b,B)= m + 14b - 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?

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The "tragedy of the commons" refers to the tendency for common property to be overused.

(True/False)
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The only known way to eliminate externalities is through taxes or subsidies.

(True/False)
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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 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.

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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 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.

(Multiple Choice)
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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 -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

(Multiple Choice)
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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 (75 + 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?

(Multiple Choice)
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