Consider a society that has two individuals, Carrie and Diana, who each have the following individual demand curve for streetlights (a public good): Q = 100 – 5P. The marginal cost of each streetlight is $10.

a) Find the socially optimal level of streetlights in this society.

b) Without any intervention, what is the likely market equilibrium outcome in terms of the number of streetlights? What is the difference (in terms of the number of streetlights) between what the market would provide and the socially optimal level?

c) Now, consider a situation where Diana’s income increases suddenly and so her demand for streetlights changes to: Q = 140 – 5P. Carrie’s demand curve remains the same as in the initial situation. Find the socially optimal level of streetlights after Diana’s demand increases.

d) Find the likely market equilibrium number of streetlights after Diana’s demand increases. What is the difference between your answer for parts c and d (i.e. what is the difference between the number of streetlights that is socially optimal and the number that is provided by the market)?

e) When Diana’s demand increases, does the market outcome get closer to or further away from the optimal outcome?