Assume the utility functions for two cities are identical and are given by U=1.6N --- 0.13*N2, where N denotes the city’s population in million.
(a) What is each city’s utility maximizing population?
(b) If each city had a population of 9 million people, how would these cities change their size? Assuming that the total population of 18 million cannot be changed, would there be a smaller and a larger city? Would there be three or more cities? Or would there be no change at all. Explain.