Snowplowing in Minneapolis (Public Economics Problem)

Problem IV. Snowplowing in Minneapolis (40 points) Minneapolis residents obtain util- ity from consuming the private good, c, and from total snowplowing service, G, in the city, u(c. G) = coGl-a. There are N residents living in Minneapolis. Price of the private good is normalized to 1. Individuals are identical and each has income of I. Suppose that snowplowing is provided privately and G = _ _, ga, where g; is the amount of snowplowing service purchased by person i at price p. 1. Find the private optimal level of snowplowing service, G*. (5 pts) 2. Find the social optimal level of snowplowing service, G. (5 pts) 3. Show that the private provision results in underprovision. (5 pts)