Suppose 20 people each have the demand Q=20-P for streetlights, and 5 people have the demand Q=18-2P for streetlights. The cost of building each streetlight is $10. If it is impossible to purchase a fractional number of streetlights, how many streetlights are socially optimal?

Q = 435/22.5 = 19 streetlights

Explanation:

Since the streetlights is apublic good

Obtaining the market demand curve by adding them vertically

P = 20*20Q - 20*Q

P = 5 * ( - 5*Q/2

hence

P = 445 - 22.5Q

Socially optimal number of street lights

MB20 + MB5 = MC

400 - 20Q + 45 - 2.5Q = 10

22.5Q = 435

Q = 435/22.5 = 19 streetlights