We model a system of interacting agents characterized by a given wealth and a certain criminal propensity, measured by an honesty coefficient. This honesty is related to intrinsic factors, like moral barriers, and extrinsic ones, as the risk of being imprisoned if committing an offense. In the simulation the honesty level of the agents is variable, and a function of the level of punition, on one hand, and on the contact with other agents (learning or contagion effect) on the other hand. The number of crimes per habitant is measured as a function of the probability of being caught. A sharp phase transition is observed as a function of the probability of punishment. That means that once criminality has attained a high level, the probability of retribution must considerably increase in order to come back to a state of low criminality. Also, some precursor signals are observed that indicate possible bursts of crime activity. We also analyze other consequences of criminality as the growth of the economy, the inequality in the wealth distribution (the Gini coefficient) and other relevant quantities under different scenarios of criminal activity and probabilities of apprehension.