The Picketty inequality in the Nash-Bargained social contract

As a proxy for a Pareto-efficient market economy, we adopt the two-party Nash Bargaining model featuring a qualitative bias in the treatment of the contributions of the parties. The Piketty inequality here is the share in total welfare accruing to the richer party over total welfare attained at agreement point. We show that this inequality can never exceed the inequality in initial contributions if the qualitative bias is zero. The rising Piketty inequality requires that the qualitative bias exceed a positive threshold. The Piketty trajectory emerges if the qualitative bias oscillates around the threshold due to changing social and economic environment.