4. From Exercise 8.1 in Brueckner's \"Lectures on Urban Economics\" (see page 264) (copied below for your convenience with additional discussion) In this problem, you will compare the level of a public good, 2, chosen under majority voting with the socially optimal level under three different sets of circumstances. Suppose first that individual i's demand curve for z is given by p = oci/z, where cc,- is a positive parameter, p is cost of the public good to the individual (i.e. the price, hence it is called p). Note that instead of this demand curve being linear, this demand curve is instead a hyperbola. Suppose further that 2 costs $1 per unit to produce (so c = 1) and that this cost is shared equally among consumers. Therefore, cost per person is 1 per unit of 2. Then consider the three sets of circumstances listed below. Each situation has a different number of consumers in the economy and different collections of a values for the consumers. The number of consumers in denoted by n and the vector of (1 values by A = (0'1: 0:2: I och1! OCH)- Case 1: n = 7, A = (4, 2, 12, 4, 5, 13, 8) Case 2: n = 5, A = (10, 6, 11, 14, 8) Case 3: n = 9, A = (6, 9, 10, 4.5, 12,7, 13.5, 8, 11)