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The Tobin tax is a solution proposed by many economists for limiting the speculation in foreign exchange and stock markets and for making these markets stabler. In this paper we present a study on the effects of a transaction tax on one and on two related markets, using an artificial financial market based on heterogeneous agents. The microstructure of the market is composed of four kinds of traders: random traders, fundamentalists, momentum traders and contrarians, and the resources allocated to them are limited. In each market it is possible to levy a transaction tax. In the case of two markets, each trader can choose in which market to trade, and an attraction function is defined that drives their choice based on perceived profitability. We performed extensive simulations and found that the tax actually increases volatility and decreases trading volumes. These findings are discussed in the paper.