Pareto distribution and exponential distribution are related by the generalized Pareto distribution, which has been proposed to describe the income structure of the total population. The underlying mechanism for driving the Pareto distribution has been known as the Matthew effect of income accumulation. Today, the Pareto distribution has been observed universally in the richest class (1%~3% of populations); however, this distribution could dominate a larger proportion of populations when the investigation dated back to Renaissance Europe, Hungarian medieval society, and ancient Egypt. By contrast, the underlying mechanism for driving exponential income distribution is due to the equal opportunity of market competition, which radically differs from the Matthew effect. Here, we empirically find that, during the last 40 years, the income structures of different market-economy countries uniformly exhibit a two-class pattern, in which the great majority of populations obeys an exponential distribution and only the remaining (richest) part follows a Pareto distribution. In particular, we empirically show how the income structure in China evolved to an exponential distribution after the market-oriented economic reformation. The finding of a larger proportion of populations evolving to an exponential income distribution may reveal a potential trend of human civilization towards equal opportunity.