Question

Suppose that N people live on a street and that the cost of providing an extra streetlight is $1000, regardless of the number of streetlights already provided. Also, each person n’s willingness to pay for an extra streetlight is given by MBN = $1000 − 100x, where x is the number of streetlights provided.

(i) If N = 1, what is the Pareto efficient number of streetlights?

(ii) If N = 100, what is the Pareto efficient number of streetlights?

(iii) Why does the Pareto efficient number of streetlights rise with N?

Answer 1

1.) if we equate MC to MBN ; MC = MBN

1000 = 1000- 100X

X= 0. That is no. Of street lights provided is zero because there is only one individual and the cost of providing street light exceeds the individual willingness to pay for street light. Thus individual will be better off without the street light.

2) if N = 100

Total MBN of 100 people = 100*(1000-100X)

MC = MBN

1000 = 100000 - 10000X

10000X = 100000 - 1000

X = 99000/10000 = 9.9

Thus no. of street lights provided when N = 100 is 9.9.

3) Since street light is the public good. No individual want to pay total cost of providing an extra street light. As the no of people increases from 1 to 100, summing up all individuals willigness to pay result in 9.9 no of street light.