THE AUTHORS FORMULATE AND DISCUSS A SIMULTANEOUS-EQUATIONS MODEL THAT LINKS EXPENDITURES ON POLICE TO MEASURED CRIME RATES. IT IS ARGUED THAT SEVERAL FACTORS DETERMINE THE SIGN OF THIS RELATIONSHIP, AND A SIMPLE NUMERICAL EXAMPLE IS PRESENTED TO ILLUSTRATE A SITUATION IN WHICH AN INCREASE IN POLICE IS FOLLOWED BY AN INCREASE IN THE REPORTED CRIME RATE. THE RESULTS OF ESTIMATING THE MODEL ARE THEN DISCUSSED. THESE RESULTS SHOW THE ANOMALOUS SITUATION OF INCREASED POLICE PROTECTION CAUSING INCREASED MEASURED CRIME. THE CONCLUDING SECTION OF THIS ANALYSIS SUMMARIZES THESE RESULTS AND PROVIDES AN EXPLANATION FOR THE PARADOX FOUND IN THE ESTIMATION MODEL. (AUTHOR ABSTRACT)