Fig. 1.

Scaling relations of per capita wage (measured in thousands of inflation-adjusted Swedish kronor) and cities’ male labor force ($N$). (A) Cross-sectional scaling for 73 Swedish LMAs in 1990 (red: $\beta =0.027\pm 0.007$ [95% confidence interval], $R^2=0.465$) and 2012 (blue: $\beta =0.039\pm 0.008$, $R^2=0.605$). Gray lines indicate proportional relations ($\beta =0$); the colored lines show estimates of $\beta$ from a linearized model (Eq. 1 in Materials and Methods). (B) Scaling trajectories of individual LMAs. The average longitudinal $\beta$ is $0.819\pm 0.032$ ($R^2=0.900$; Eq. 2). (C) Model fit ($R^2$) of 73 individual regressions is highest for big cities and decreases for LMAs with fewer than 10,000 male workers. C, Inset plots LMA-specific $\beta$ against population sizes and the horizontal line indicates the average scaling parameter $\beta =0.819$. For the 3 biggest LMAs, Stockholm, Gothenburg, and Malmö, longitudinal $\beta$ varies between $0.695\pm 0.070$ and $0.760\pm 0.097$.