The best jurisdiction size

Suppose that the cost function for a particular public good is given by c(n)z = (40n — 12n2 + (a) Using this formula, derive the formula for the cost per unit of z per capita, or c(n)/n. (b) The best jurisdiction size is where c(n)/n is as small as possible. Using the results of (a), compute this per capita cost for n = 1, 2, 3, • • 10. What jurisdiction size minimizes unit cost per capita? What is the resulting level of the unit cost? (c) Suppose that all consumers in the economy are identical, and each consumer's demand for z is given by D = 20 — z. Using the results of (b), compute the DE curve for an optimal-size jurisdiction (this is a b jurisdiction of the size found in (b)). This computation is done by                                                                                                

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