Narcotic drugs are hazardous to health and promote violence in the society. In this paper, we discuss two alternatives to reduce the consumption of narcotics: a forbidden market and an open market. Whether a forbidden market for narcotics can efficiently reduce the consumption of narcotics depends on the price elasticity of demand for narcotics. Previous researches do not reach consistent results for the price elasticity of demand for addictive products. However, a forbidden market will almost surely result in more violence. We argue that if the price elasticity of demand for narcotics is low, the open market approach will do a better job not only in reducing the consumption of narcotic drugs, but also in reducing the violente activities in our society.