D3=20z These formulas give the height of each consumer's demand curve at a given level of z. Note that each demand curve cuts the horizontal axis, eventually becoming negative. For the problem to work out right, you must use this feature of the curves in deriving Dz. In other words, don't assume that the curves become horizontal once they hit the axis. a) The height of the D2 curve at a given 2 is just the sum of the heights of the individual demands at that z. Using this fact, compute the expression that gives the height up to the D; curve at each z. b) The cost of park land per acre, denoted c, is 9 (like the demand intercepts, you can think of this cost as measured in thousands of dollars). Given the cost of park land, compute the socially optimal number of acres of park land in the city. c) Compute the level of social surplus at the optimal z. Remember that this is just the area of a surplus triangle. d) Suppose there are two other communities, each with 3 consumers, just like the given community. Compute total social surplus in the three communities, assuming each chooses the same amount of park acres as the first community. e) Now suppose the population is reorganized into 3 homogeneous communities. The first has 3 type-1 consumers (i.e., high demanders). The second has 3 type-2 consumers (medium demanders), and the third has 3 type-3 consumers (low demanders). Repeat parts (a), (b), and (c) for each community, finding the D 2 curve, the optimal number of park acres, and social surplus in each community. f) Compute total social surplus by summing the social surplus results from part (e) across communities. How does the answer compare to social surplus from part (d)? Based on your answer, are homogeneous communities superior to the original mixed communities? 3. Suppose that the cost function for a particular public good is given by C(z,n) = (40n 12H 2 + n3)z In this case, the unit cost of z is 40n - 12n 2 + n3, 3 function of n. a) Using the above formula for the unit cost of z, derive the formula for the unit cost of 2 per capita. This is just the unit cost of z divided by n. b) The best community size is where the unit cost of z on a per capita basis is as small as nnccihln TTm'na H113 rncnlfc Inc nnrf {z r'nmnnfn thin nnr nnnifn nncf Fnr n =