Answer to Question #124659 in Economics for Prince Wonsongmah

Question

Suppose that 10 people live on a street and that each of them is willing to pay $2 for
each extra streetlight, regardless of the number of streetlights provided. If the cost of
providing x streetlights is given by 2 C(x)  x , what is the Pareto efficient number of
streetlights to provide?

Answer 1

The price of the public good is

$$p=C^/(x)=2x$$

$$2x=2$$

$$x=1$$

Since the condition of the problem does not say that the usefulness of this agreement for different consumers is different, or there is some differentiation between the utility of benefits for different consumers, it is necessary to install one additional lamp.