Question

Three families live at the end of a road outside town. They must pay to install street-
lights. Streetlights are a public good for these households|that is if one household buys a a
streetlight, all households will get access to the streetlight. Assume family 1 has an inverse
demand for streetlights of p = 100 -Q, family 2 has an inverse demand for streetlights of
p = 200 -Q, and family 3 has an inverse demand for streetlights of p = 300 - Q. Assume
the supply of streetlights is horizontal at the marginal cost of $200.

4.1 Assuming the families act independently, find the quantity of
streetlights each family will demand. What will be the total
amount of streetlights provided?
4.2 Now find the socially optimal quantity of streetlights for these
three families.
4.3 Please draw this market, including all three demand curves,
the supply curve, and the social demand curve. Indicate the
social optimum.
4.4 What is one way that the households could achieve the socially
optimal quantity of streetlights?
4.5 Explain how this problem illustrates the problem of public
goods and free riding.

Answer 1