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# ps3a - Urban Economics Problem Set#3 due Tuesday Apr 5 in...

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Urban Economics Problem Set #3 due Tuesday, Apr 5, in class (1) The third largest city of a country has a population of 2.5 million. Using the rank- size rule, what is the population of the 10 th largest city? Answer: The rank-size rule states that N i =C/R i , where N=population and R=rank of the i th city. C is a constant, i.e., the population of the largest city. If the third largest city has a population of 2.5m, the largest one has 7.5m. Thus, the 10 th largest city has a population of 0.75m. (2) Assume an urban cluster’s income (I) is given by the function I=4N, where N denotes the cluster’s population in million. The cluster’s diseconomies of aggregation (C) are given by C=0.5N 2 . (a) Calculate the city’s utility maximizing population. (b) At this population, how large is the resulting utility? (c) Calculate the resulting utility if the population were on million higher and one million lower than the optimum. Answer: (a) if I=4N MI=4 if C=0.5 N2 MC=N MI=MC N=4 (b) at N=4 I=16 and C=8 U=I-C=8 (c) at N=5 I=20 and C=12.5

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ps3a - Urban Economics Problem Set#3 due Tuesday Apr 5 in...

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