If you could show the work, so I can understand how to get the answer

4. Suppose that the cost function for a particular public good is given by C(zn) = (Un -m' + 0in')= In this case, the unit cost of _ per capita is 8 - n + 0in'. 2) 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 :) 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 S low demanders. The demand curves for _ are given by D. = 6 - z and D. = 20 - z for the low and high demanders, respectively. Suppose the economy is organized into two homogeneous com mities each with population 5, one for the low demanders and one for the high demanders b) Using the results of port (2). compute the socially-optimal _ level in the low-demand community. Also compute the level of social surplus in that community at the optimum. c) Repeat part (b) for the high-demand community. Add the social surplus levels from both communities to get overall social surplus in the homogeneous case Now suppose the economy is organized into one wired community of population 10, containing 5 low demanders and 5 high demanders d) Using the results of part (2). compute the socially-optimal I level in the mixed community. Also compute the level of social surplus in the mixed community, which gives the overall surplus level since this is only community. Comparing your answers to parts (c) and (d), decide whether the mixed or homogeneous arrangement is superior. Given an intuitive explanation for your conclusion Now suppose that the demand rives for the low demanders, with D, = 10 - z giving the demand curve. Repeat part (b) using this new demand curve. Using your result along with part (c). recompute overall social surplus in the homogeneous case. [) Using the movumptions of part (f). compute the socially-optimal z level in the mixed community of size 10. and compute social surplus. Comparing your answers to parts (f) and (). decide whether the mixed or homogeneous arrangement is superior. Give a thorough intuitive explanation of why different conclusions are reached in parts () and (h)