The paper presents a simple model to study the effects of rumours on markets. Agents in our economy communicate with their local neighbours which gives rise to the possible spread of a rumour. As the rumour affects beliefs of the agents the evolution of the rumour has a direct impact on market outcomes. Our results show that if the rumour dies out long-run equilibrium prices correspond to pre-rumour values. However, if the rumour stays present it produces a price run-up for the good that is positively targeted by the rumour. Price run-ups related to rumours have been observed in empirical studies by Rose [Rose, A.M., 1951. Rumor in the stock market. Public Opinion Quarterly 15, 461–486], Pound and Zeckhauser [Pound, J., Zeckhauser, R., 1990. Clearly heard on the street: the effect of takeover rumors on stock prices. Journal of Business 63, 291–308] and Zivney et al. [Zivney, T., Bertin, W.J., Torabzadeh, K.M., 1996. Overreaction to take-over speculation. Quarterly Review of Economics and Finance 36, 89–115]. The present model provides an analytical foundation for this finding.