Suppose that the total benefit to any one person (all people are identical) of a fireworks display is, where g is the dollar amount of fireworks (thus the marginal cost of $1 worth of fireworks is $1). Also suppose that each person in a town pays an equal share of the cost of the display. Does adding more people to the town make each person better off (in terms of net benefits derived from fireworks displays) ? If so, by exactly how much?

Question

Gunner Chang

Business

4 February, 08:25

Suppose that the total benefit to any one person (all people are identical) of a fireworks display is, where g is the dollar amount of fireworks (thus the marginal cost of $1 worth of fireworks is $1). Also suppose that each person in a town pays an equal share of the cost of the display. Does adding more people to the town make each person better off (in terms of net benefits derived from fireworks displays) ? If so, by exactly how much?

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Brylee Petersen · Answer 1

Answer: The answer is provided below

Explanation:

As g is a constant, the addition of more people to the town will decrease per person cost of firework display. Therefore, adding more people to the town will make each person better off.

The net benefit is also equal to the total benefit each person gets (2√g) minus cost of per person of the firework display which is (g/h), where h is the number of people that are in the town.

Net benefits = 2√g - (g/h)

Therefore, as h increases, "g/h" decreases and net benefits will increase.

If we then derivative net benefits with its respect to h, we then get how much the net benefit will change.

∆net benefits/∆h=+g/h²