The basic question posed by Kuznets through his simple numerical model was:
what happens to national inequality as urbanization proceeds and the share of
urban population goes from 0% to 100%? This can be answered by using the
GE(0) measure of inequality. Differentiating equation (13.2) with respect to the
share of urban population x gives
dL/dx =(L1 − L2)+[(k −1)/(x(k −1)+1)]−log(k) (13.5)
We assume that k>1, so that sector 1 is the sector with the highermean income.
With this specification we come close to the natural specification, with sector
1 being the urban sector and x increasing with development. The mathematical
expression for the turning point x∗ can be obtained by setting dL/dx = 0, and is
given by
x∗ =1/[log(k)−(L1 − L2)]−1/(k −1) (13.6)