Question

Suppose that the total benefit to any one person (all people are identical) of a fireworks display is 2 root g , 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?

Answer 1

As g being constant ,more addition of people in the town will reduce per person cost of firework display. And net benefit is EQUAL to total benefit a person gets(2√g) minus the cost of per person of firework display which (g/h) ,h is number of people in the town.

Net benefits =2√g-g/h

So as h increase the term 'g/h' gets lower and net benefits increase.

If we derivative net benefits with respect to h ,we will get how much net benefit would change from increasing the number of people.

∆net benefits/∆h=+g/(h^2)