d) g) 1,2,3,...,8,9,10. What community size minimizes unit cost per capita? Multiply your unit cost per capita by the relevant n to get total unit cost in the optimalsize community (i.e., the c value for use with the D 2 curve below). Suppose that all consumers in the economy are identical, and each consumer's demand for z is given by D = 20 - 2. Using the results of part (b), compute the D2 curve for an optimal-size community (this is a community of the size found in part (b)). This is done by adding up as many individual D's as there are people in the optimal community. Using the unit cost figure from part (b), find the optimal level of z in the optimalsize community. Also, compute social surplus in the optimal-size community. Suppose the economy contains 18 people. How many optimalsize communities can be created out of this population? Using the results of part (d), what is total social surplus in the economy? Now suppose that instead of being divided into optimal-size communities, the population is divided into 2 communities of size 9. Using the previous results, find the unit cost of z per capita in these communities. Then find the optimal level of z in each community, as well as social surplus in each community. Compute social surplus in the whole economy when there are two 9person communities. Compare you answer to that from part (e). How big is the loss from non- optimal community sizes? 4. Suppose that the cost function for a particular public good is given by C(z,n) = (8n - n2 + .05n3)z In this case, the unit cost of 2 per capita is 8 - n + .05n 2. 3) Compute unit cost per capita for n = 1,2,...,10,11,12. At what value of n is this cost minimized? Compute c (the total cost per unit of z) for n = 5 and n = 10. As before, this is done simply by multiplying your unit cost per capita values by the relevant n. Suppose the economy contains 5 high demanders and 5 low demanders. The demand curves for z are given by D1 = 6 - z and D 2 = 20 z for the low and high demanders, respectively. Suppose the economy is organized into two homogeneous communities each with population 5, one for the low demanders and one for the high demanders. b) P'l Using the results of part (a), compute the sociallyoptimal 2 level in the lowdemand community. Also compute the level of social surplus in that community at the optimum. Dnnnnf nnrf (l' Fnr H113 hiUl-Lrlnmnn r'nmmnnihr Arlrl H113 cnrinl cnrnlnc lnvnlc 'Frnm