A Model of Prison Expenditure and Optimal Punishment

We defined Net Social Gain (NSG) which is a function of probability of capture (p) and length of punishment (f) We identified certain equilibrium and disequilibrium structures by maximizing NSG with respect to p and f separately and hence optimal punishment is determined. The nature of Marginal Social Loss (MSL) and Marginal Social Gain (MSG) curves has been narrated, under equilibrium and disequilibrium states. A relationship between elasticities of Total Social Loss (TSL) and Total Social Gain (TSC) with respect to punishment is established.