Problem 1 {Snowplowing in Minneapolis} - 35 points. Minneapolis residents obtain utility from consuming the private good, e, and from total snow- plowing service, (3, in the city, u{e,G) = city'1. There are N residents living in Minneapolis. Price of the private good is normalized to 1. individuals are identical and each has income of 1'. Suppose that snowplowing is provided privately and G = Eli] 31': where g; is the amount of snowplowing service purchased by person i at price p. 1. (5 points) Find the private optimal level of snowplowing services, (3*. 2. (5 points) Find the social optimal level of snowplowing services, if". 3. (5 points) Show that the private provision results in underprovision. 4. (1f) points} Now suppose that snowplowing is publicly provided. Design a nancing system that leads to the social optimum. That is, describe how snowplowing service is nanced and show that the equilibrium subject to this nancing matches the social optimum. 5. {if} points) Finally, suppose that snowplowing is provided privately and publicly simulta- neously. Show that public provision crowds out the private provision. Hint: Let H denote the amount ofsuowpiowiug provided publicly and take it as exogenous