We develop a model of rational bubbles based on the assumptions of unknown market liquidity and limited liability of traders. In a bubble, the price of an asset rises dynamically above its steady-state value, justified by rational expectations about future price developments. The larger the expected future price increase, the more likely it is that the bubble will burst because market liquidity becomes exhausted. Depending on the interactions between uncertainty about market liquidity, fundamental riskiness of the asset, the compensation scheme of the fund manager, and the risk-free interest rate, we give a condition for whether rational bubbles are possible. Based on this analysis, we discuss several widely-discussed policy measures with respect to their effectiveness in preventing bubbles. A reduction of manager bonuses or a Tobin tax can create or eliminate the possibility of bubbles, depending on their implementation. Monetary policy and long-term compensation schemes can prevent bubbles.