(eng): We explore possible effects of a Tobin tax on exchange rate dynamics in a heterogeneous agent model. To assess the impact of the Tobin tax in this framework, we extend the model of De Grauwe and Grimaldi (Eur Econ Rev 50(1):1–33, 2006) by including transaction costs and perform numerical simulations. Motivated by the importance of the market microstructure, we choose to model the market as being cleared by a Walrasian auctioneer. This setting could more closely resemble the two-layered structure of foreign exchanges at daily frequency than a price impact function, which is often adopted in similar studies. We find that the Tobin tax can deliver a moderate reduction of return volatility and kurtosis. In addition, simulations indicate that the Tobin tax reduces the degree of mispricing in the time series, which is primarily achieved by eliminating long-lasting deviations from fundamental value.