  The highly detailed international trade data among all countries in the world
during 1971-2000 shows that the kinds of export goods and the logarithmic GDP
(gross domestic production) of a country has an S-shaped relationship. This
indicates all countries can be divided into three stages accordingly. First,
the poor countries always export very few kinds of products as we expect.
Second, once the economic size (GDP) of a country is beyond a threshold, its
export diversity may increase dramatically. However, this is not the case for
rich countries because a ceiling on the export diversity is observed when their
GDPs are higher than another threshold. This pattern is very stable for
different years although the concrete parameters of the fitting sigmoid
functions may change with time. In addition, we also discussed other
relationships such as import diversity with respect to logarithmic GDP,
diversity of exporters with respect to the number of export goods etc., all of
these relationships show S-shaped or power law patterns. Although this paper
does not explain the origin of the S-shaped curve, it may provide a basic
empirical fact and insights for economic diversity.
