“…In the form of f(density) , previous studies focused on the positive elasticity coefficient (see Table 1), considering density as equivalent to the population size of the unit area, and then, according to the logic of the optimum city size (Henderson, 1974; Mills, 1967; Mills and Ferranti, 1971), the optimum urban population density exists and can be reached at the balancing point of the economic effect and crowding effect. On the economic effect side, density affects productivity in several ways originating from the input-output relationship, externalities and beneficial specialisation (Ciccone and Hall, 1996; Fang et al, 2013; Libertun de Duren and Guerrero Compeán, 2016). For the same urban land area, a higher population density means higher population size, and the density economic effect contains three classical sources of agglomeration economies (Krugman, 1991; Marshall, 1890).…”