In this problem, you will compare the level of a public good chosen under majority voting with the socially optimal level under three dif ferent sets of circumstances. Suppose rst that individual i's demand curve for z is given by dilz, where oi is a positive parameter. Instead of being linear, this demand curve is a hyperbola. Suppose further that 2 costs $1 per unit to produce (c = l) and that this cost is shared equally among consumers. Therefore, cost per person is Lin 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 collec- tions of d values for the consumers. The number of consumers is denoted by n and the vector of E! values by A = (:11, d2,...,o.n1,dn). 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, 10,45,12, 7.13.5.8, 11). Using this information, do the following: (a) For each case, compute the preferred 2 level for each voter. Identify the median voter, and indicate the 2 level chosen under majority voting. {b} For each case, compute the DE curve, and nd the socially optimal level of z. (c) For each case, compare the 2 level under majority voting with the socially optimal 2. Explain the difference (if any) between the two 2 values