In this under majority voting with the socially optimal level under three dif fe

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In this under majority voting with the socially optimal level under three dif ferent sets of circumstances. Suppose first that individual i's demand curve for z is given by o,/z, where o, is a positive parameter. Instead of being linear, this demand curve is a hyperbola. Suppose further that z costs $1 per unit to produce (c-1) and that this cost is shared equally among consumers. Therefore, cost per person is 1/n per unit of z. 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 values for the consumers. The number of consumers is denoted by n and the vector of values by A-(, 2, . . . , " 1, .) problem, you will compare the level of a public good chosen Case 1:-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) Using this information, do the following: (a) For each case, compute the preferred z level for each voter. Identify the median voter, and indicate the z level chosen under majority voting (b) For each case, compute the Dz curve, and find the socially optimal level of z. (c) For each case, compare the z level under majority voting with the socially optimal z. Explain the difference (if any) between the two z values.

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