A Lucas island model to analyse labour movement choice between cities based on personal characteristics

The labour movement has been a key factor for cities' development and caused regional inequality between cities. Although empirical studies have been conducted to investigate it, little theoretical evidence has been provided to find out the underlying mechanism. This paper describes and derives a Lucas-Prescott style island model to study the location choices of the heterogeneous agents by utilising endogenous technology growth, which in turn influences personal human capital growth. It leads to the U-shape curve of the inequality of wage income with the technology of these islands but not in terms of total income. In the extended two-goods model, the magnitude of the implications is increased by the impact of non-tradable goods price. Together with empirical research using the US census data, this paper finds that skilled labours with less endowed wealth tend to live in large cities for its high salary. On the other hand, those less-skilled but with more endowed wealth tend to live in cities with better environment, which drives up the price level of non-tradable goods in these cities. This explains the population concentration in the super cities and the high housing price-wage ratio in some beautiful cities, which provides theoretical basement for further empirical studies about labour movement in other cities