Illegal exploitation of wildlife is one of the biggest threats to biodiversity, affecting over 2,000 species. Traditionally, actions to reduce poaching have focussed on increasing the efficacy and capacity of law enforcement. However, recently, non-governmental agencies (NGOs) are heavily investing in alternative interventions to reduce consumer demand for poached wildlife products. But which action is more efficient, policing or demand reduction? Using elephant poaching for ivory as a case study, and a simple open-access harvest model, we show that demand reduction interventions need to reduce ivory price by roughly 29% to be more cost-effective than investing in the police. We use an analytic derivation to show that this threshold is robust to several types of uncertainty but sensitive to specific socio-economic factors. The calculations can provide context for stakeholder engagement so that monitoring of ivory price can better inform decisions for protecting elephants from poaching.