Zipf's law for cities and beyond -: The case of Denmark

Zipf's law for cities is one of the most conspicuous and robust empirical facts in the social sciences. It says that for most countries, the size distribution of cities must fit the power lan : the number of cities with populations greater than S is inversely proportional to S. The present paper answers three questions related to Zipf's law: (1) does the Danish case refute Zipf's law for cities?, (2) what are the implications of Zipf's law for models of local growth?, and (3) do we have a Zipf's law for firms? Based on empirical data on the 61 largess Danish cities for year 2000, the answer (1) is NO-the Danish case is not the exception which refutes Zipf's law. The consideration of (2) then leads to an empirical test of(S). The question of the existence of Zipf's law for firms is tested on a sample of 14,541 Danish production companies (the total population for 1997 with 10 employees or more). Based on the empirical evidence, the answer to (3) is YES in the sense that the growth pattern of Danish production companies follows a clean rank-size distribution consistent with Zipf's law.