Urban and Regional Econ HW question

Suppose that the cost function for a local public good is given by c(n)=(64n -16n2+ 2n3), where n is the number of people who pay for and share the benefits of the public good. a. Using the formula for c(n), derive the formula for the cost per unit of z per capita, or c(n). b. Using the results of (a), compute this per capita cost for n = 1,2,3..,7. What jurisdiction size minimizes unit cost per capita? What is the minimum per capita cost? c. Suppose that all consumers in the economy are identical, and each consumer's demand for z is given by D = 50 - z. Using the results of (b), compute the Dy curve for an optimal-size jurisdiction (this is a jurisdiction of the size found in (b)). This computation is done by adding up as many individual D's as there are people in the optimal jurisdiction. d. Using the unit cost figure from (b), find the optimal level of z in the optimal-size jurisdiction. e. Now suppose that instead of being divided into optimal-size jurisdictions, the population is divided into jurisdictions of size 6. Using the previous results, find the unit cost of z per capita in these jurisdictions. Then find the optimal level of z in each jurisdiction