There is massive variation in rates of violence across time and space. These rates are positively associated with economic deprivation and inequality. They also tend to display a degree of local persistence, or ‘enduring neighbourhood effects’. Here, we identify a single mechanism that can produce all three observations. We formalize it in a mathematical model, which specifies how individual-level processes generate the population-level patterns. Our model assumes that agents try to keep their level of resources above a ‘desperation threshold’, to reflect the intuitive notion that one of people's priorities is to always meet their basic needs. As shown in previous work, being below the threshold makes risky actions, such as property crime, beneficial. We simulate populations with heterogeneous levels of resources. When deprivation or inequality is high, there are more desperate individuals, hence a higher risk of exploitation. It then becomes advantageous to use violence, to send a ‘toughness signal’ to exploiters. For intermediate levels of poverty, the system is bistable and we observe hysteresis : populations can be violent because they were deprived or unequal in the past, even after conditions improve. We discuss implications of our findings for policy and interventions aimed at reducing violence.