Snowplowing in Minneapolis (Public Economics Question)

Need help with the first 3 parts please

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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) 4. Design a system of public provision and show that it leads to social optimum. In other words describe how snowplowing public service is financed and show that the equilibrium subject to the snowplowing finance matches the social optimum. (10 pts) 5. Now suppose individuals have different incomes, I, # Ij. Would the public provision you designed still match the social optimum? Explain. (5 pts) 6. Now suppose that snowplowing is provided privately and publicly simultaneously. Show that public provision crowds out the private provision. (Hint: Let H denote the amount of snowplowing provided publicly and take it as erogenous.) (10 pts)