Why is the HDI using the logarithm of income component?

In addition to capping, the income enters the HDI as a logarithmically transformed variable. The idea is to emphasize diminishing marginal utility of transforming income into human capabilities. This means that the concave logarithmic transformation brings closer the notion that an increase of GNI per capita by $100 in a country where the average income is only $500 has a much greater impact on the standard of living than the same $100 increase in a country where the average income is $5,000 or $50,000.