Zipf's law for cities: Is Zipf exponent correlated with level of freedom?

This master thesis contains three independent papers on the Zip's law for cities. In the first essay I summarize accumulated knowledge and use examples from the Czech Republic to show problems of the empirical research. The main findings of this essay are: City size distribution in the Czech Republic can be better described by a log-normal distribution than by a Pareto distribution; Pareto exponents are sensitive to sample selection. The second essay is the largest empirical cross-country study on Zipf's law for cites. The mean value for 157 countries is 0.919. The comparison with the study by Soo (2005) showed a decreasing tendency of the Pareto exponent, since for the same countries, the average exponent decreased from 1.11 to 1.02. One possible explanation of this trend is the process of urbanization. The last essay looks at the topic from a different angle. I have developed an agent based model to describe the process of suburbanization and cities merging and its impact on the size of the Pareto exponent. I have shown that when cities merge, the exponent starts to fall down from a steady state.