This papers studies the impact of a ﬁnancial transactions tax on the trading volume and asset price volatility in a model with heterogeneous beliefs. To model heterogeneous beliefs we follow Kurz (1994, 1997) and restrict the class of beliefs to the subset of rational beliefs. We study a tax on bond and asset purchases. The simulated model shows that the introduction of a transaction tax results in a lower trading volume and therefore in less liquid ﬁnancial markets. Because of the decreased liquidity the volatility of the stock market increases. We also study the welfare effects of a ﬁnancial transaction tax and the simulation results also show that there is only a small change in welfare.