Distributions of region size and GDP and their relation

We first analyze the distribution of metropolitan (city) size, the distribution of metropolitan (city) GDP and the relation of both distributions. It is found that (1) the tails of distributions of size and GDP both obey Pareto Law with the Pareto exponent 1; (2) compared with Pareto exponent in GDP, Pareto exponent in size is bigger. Then an agent model is built to study the underlying formation mechanism of distributions of region size and GDP. Our model presents the mechanism how economic factors flow between regions to reproduce the tail behavior and the difference between the Pareto exponents of size and those of GDP. At last, the simulated results agree with the real empirical well.