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Two firms, a and b, each currently dump 50 tons of chemicals into the local river. The government has decided to reduce the pollution and from now on will require a pollution permit for each ton of pollution dumped into the river. It costs firm a $100 for each ton of pollution that it eliminates before it reaches the river, and it costs firm b $50 for each ton of pollution that it eliminates before it reaches the river. The government gives each firm 20 pollution permits. Government officials are not sure whether to allow the firms to buy or sell the pollution permits to each other. What is the total cost of reducing pollution if firms are not allowed to buy and sell pollution permits from each other? what is the total cost of reducing pollution if the firms are allowed to buy and sell permits from each other?.

Respuesta :

ayune

Total cost of reducing pollution if the pollution permit trading is not allowed is $4,500. This cost is reduced to $3,500 if the pollution permit trading is allowed.

Using unitary method, total cost can be calculated as:

total cost = cost per unit x number of units.

In the given problem,

data of Firm A

chemical waste = 50 tons

cost of eliminate pollutant = $100 per ton

pollution permit from government = 20 tons

total cost of reducing pollution of firm A = (50 - 20) x $100

                                                                   = 30 x $100 = $3,000

data of Firm B

chemical waste = 50 tons

cost of eliminate pollutant = $50 per ton

pollution permit from government = 20 tons

total cost of reducing pollution of firm B = (50 - 20) x $50

                                                                   = 30 x $50 = $1,500

Hence, total cost of firm A and firm B if they don't sell/buy pollution permit to each other = $3,000 + $1,500 = $4,500

If the firms are allowed in trading the pollution permit, then firm A will buy the pollution permit of firm B.

Hence, the costs are:

total cost of reducing pollution of firm A = (50 - 40) x $100

                                                                   = 10 x $100 = $1,000

total cost of reducing pollution of firm B = 50 x $50 = $2,500

Hence, total cost of firm A and firm B if pollution permit trading is allowed = $1,000 + $2,500 = $3,500

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