Below is a Zipf’s law graph for the largest cities in California 2-(a) Xavier Ga

Question

Below is a Zipf’s law graph for the largest cities in California

2-(a) Xavier Gabaix has shown that one way to obtain Zipf’s law is through Gibrat’s law.
What is the basic idea behind Gibrat’s Law?
2-(b) If Gibrat’s Law holds, then how do we explain how we obtain some very large cities
like Los Angeles?
2-(c) If Gibrat’s Law holds, does Los Angeles, which is currently the largest city in California, have a higher probability of being the largest city in California 100 years from now than any other city?

Explanation / Answer

2-(a) The law of proportionate effect states that the proportional change in the size of a firm is independent of its absolute size. The idea behind this theory is the way the population is distributed across geographical area, while continuously changing, is not at random. Therefore, it implies that the logarithms of the variables will be distributed following the normal distribution.

2-(b) It is generally agreed that economic factors are the principal determinant of the dynamics of city population. There is, in fact, a direct connection between economic activity and population mobility. Understanding fully the general economic activity involves understanding population mobility and economic driving forces. When high-technological growth is evident there is a possibility of an exodus to the area where it occurs thereby showing signs of higher-than-average population growth and increased economic activity. If we can confirm the agglomeration and residential mobility of population that are connected to economic activity. we can obtain some very large cities like Los Angeles.

2-(c) As mentioned earlier, the growth rate of a city does not depend on the size of the city. City growth rae is proprtionate, larger cities do not grow faster or slower than smaller cities. If we take the current growth as per census, greater Los Angeles will surpass Greater NY by 2040. It is aiming to become the largest city in the US and the LA metro is expected to outgrow New York's by 2050. Now the question is whether NYc fall to LA?

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