Assume an urban cluster's income (I) is given by the function I=4N-0.05N2, where N denotes the cluster's population in million. The cluster's diseconomies of aggregation (C) are given by C=0.5N2.
(a) Calculate the city's utility maximizing population.
(b) At this population, how large is the resulting utility, how large is the cost?
(c) Calculate the resulting utility if the population were on million higher and one million lower than the optimum.