Optimality of a Two-Tier Rate Structure for a Transaction Tax in an Artificial Market

In this paper we discuss the effects of a Transaction Tax on an artificial market with varying liquidity where a large number of agents can trade a share of a risky asset. A market maker is in charge to optimally set the level of taxation in order to obtain a desired mixture of activity and volatility. We show that, depending on the liquidity of the market, two possible regimes of optimal taxation emerge: a non-negligible level of taxation for highly liquid markets and low (close to zero) levels of taxation for low liquidity markets. This outcome resembles the two-tier rate structure discussed by Spahn in his famous contributions Spahn (1995).