My friend Ray V. asked how this chart can be improved:
Let's try to read this chart. The Economist is always the best at writing headlines, and this one is simple and to the point: the rich get richer. This is about inequality but not just inequality - the growth in inequality over time.
Each country has four dots, divided into two pairs. From the legend, we learn that the line represents the gap between the rich and the poor. But what is rich and what is poor? Looking at the sub-header, we learn that the population is divided by domicile, and the per-capita GDP of the poorest and richest regions are drawn. This is a indirect metric, and may or may not be good, depending on how many regions a country is divided into, the dispersion of incomes within each region, the distribution of population between regions, and so on.
Now, looking at the axis labels, it's pretty clear that the data depicted are not in dollars (or currency), despite the reference to GDP in the sub-header. The numbers represent indices, relative to the national average GDP per head. For many of the countries, the poorest region produces about half of the per-capita GDP as the richest region.
Back to the orginal question. A growing inequality would be represented by a longer line below a shorter line within each country. That is true in some of these countries. The exceptions are Sweden, Japan, South Korea.
It doesn't jump out that the key task requires comparing the lengths of the two lines. Another issue is the outdated convention of breaking up a line (Britian) when the line is of extreme length - particularly unwise given that the length of the line encodes the key metric in the chart.
Further, it has low data-ink ratio a la Tufte. The gridlines, reference lines, and data lines weave together in a complex pattern creating 59 intersections in a chart that contains only 40 numbers.
I decided to compute a simpler metric - the ratio of rich to poor. For example, in the UK, the richest area produces about 20 times as much GDP per capita as the poorest one in 2015. That is easier to understand than an index to the average region.
I had fun making the following chart, although many standard forms like the Bumps chart (i.e. slopegraph) or paired columns and so on also work.
This chart is influenced by Ed Tufte, who spent a good number of pages in his first book advocating stripping even the standard column chart to its bare essence. The chart also acknowledges the power of design to draw attention.