Problem 1 (Snowplowing in Minneapolis) - 35 points. Minneapolis residents obtain utility from consuming the private good, c, and from total snow- plowing service, G, in the city, u(c,G) = MG-. 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 = [N18i, 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, G*. 2. (5 points) Find the social optimal level of snowplowing services, G. 3. (5 points) Show that the private provision results in underprovision. 4. (10 points) Now suppose that snowplowing is publicly provided. Design a financing system that leads to the social optimum. That is, describe how snowplowing service is financed and show that the equilibrium subject to this financing matches the social optimum. 5. (10 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 of snowplowing provided publicly and take it as exogenous