Three years ago Maricopa County implemented a policy to tackle the problem of pa

Question

Three years ago Maricopa County implemented a policy to tackle the problem of particulate matter in the air. The project/policy consisted in paving and compacting some of the roads the dairy industry uses for feeding the cattle and transporting the milk in the West part of Maricopa. At the beginning of the project the abatement level was estimated to be in 10 units (micrograms per cubic meter). After 3 years of project implementation, the abatement levels rose to 20 units. The Maricopa Environmental Service Department estimates that

MSB = 120 – 2.5A

whereas

TSB = 120A – 1.25A².

Find the incremental benefit using either one of the functions (from 10 units to 20 units). Express your results in million dollars.

Explanation / Answer

We will use the TSB (Total Social Benefit) to answer this question

TSB (Total Social Benefit) = 120A -1.25A2

At A = 10, TSB(10) = 120*10 -1.25*102 = 1200 - 125 = $ 1075 million

At A = 20, TSB(20) = 120*20 -1.25*202 = 2400 - 500 = $ 1900 million

Hence the incremental benefit = TSB(20) - TSB(10) = $1900 - $1075 = $825 million

Answer = incremental benefit = $825 million

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