IT IS SUGGESTED THAT A MARKET PRICING SYSTEM WILL PERMIT, UP TO A CERTAIN OUTPUT LEVEL, A SOLUTION OF THE PROBLEM OF ALLOCATING CONTRACTOR'S POLICE SERVICES AMONG METROPOLITAN POLITICAL AREAS. HOWEVER, WHEN LOW LEVELS OF CRIMINAL ACTIVITY ARE ACHIEVED THROUGH ADDITIONAL POLICE INPUTS, THE MARKETS MECHANISM WILL HAVE A TENDENCY TO BREAK DOWN BECAUSE THE MARGINAL INCREASES OF POLICE SERVICES WILL NOT BE ABLE TO ELICIT THE EXPECTED DECREASES IN CRIME. A MODEL DEALING WITH ALLOCATIONS OF CENTRALIZED SERVICES AMONG TWO POLITICAL UNITS IS PRESENTED IN WHICH THE CONTRACTOR'S OUTPUT, A COUNTY SHERIFF'S OFFICE, IS QUANTIFIED IN TERMS OF PROBABILITY FOR A RESIDENT OF A GIVEN POLITICAL AREA TO BECOME A VICTIM OF CRIME DURING SOME FIXED PERIOD OF TIME. THUS, RELATIVELY GREATER OUTPUTS WILL BE REFLECTED IN FALLING PROBABILITIES OF BECOMING A CRIME VICTIM. IT IS ASSUMED THAT ONE AREA (C) IS CLOSER TO THE CONTRACTOR'S OPERATIONAL BASE WHILE THE OTHER AREA (F) IS FARTHER AWAY AND CONSEQUENTLY MORE EXPENSIVE TO SERVICE. IT IS ALSO ASSUMED THAT FACTORS CONDUCIVE TO CRIME ARE IDENTICAL AND THAT ALL CRIMINAL ACTS ARE EQUALLY DETRIMENTAL AND SERVICE BENEFITS ACCRUE ONLY TO THOSE AREA RESIDENTS WHO ARE SERVICE RECIPIENTS. FINALLY, IT IS ASSUMED THAT CRIME PREVENTION COSTS BECOME INCREASINGLY HIGHER AS HIGHER LEVELS OF PROTECTION ARE SUPPLIED. GIVEN THIS SITUATION, THE MARGINAL COST CURVE FOR AREA F WILL BE HIGHER AT EVERY OUTPUT LEVEL THAN FOR AREA C. MINIMIZATION OF CRIMES TAKES PLACE WHEN THE MARGINAL CRIME PREVENTION COSTS ARE EQUAL IN BOTH AREAS. HOWEVER, WHEN THE MARGINAL COST IS EQUAL, THE CRIME RATE IN F WILL BE MUCH GREATER THAN IN C. A TRANSFER OF INPUT FROM C TO F WOULD THUS RESULT IN AN INCREASE IN CRIME IN C THAT WOULD BE GREATER THAN THE DECREASE OF CRIME IN F. THUS ALLOCATIONS AIMED AT IMPROVING THE SITUATION IN ONE AREA CAN ONLY DO SO AT THE EXPENSE OF THE OTHER AREA. MOREOVER, A POINT WILL BE REACHED WHERE ADDITIONAL INCREASE IN POLICE SERVICES WILL NOT BE ABLE TO ELICIT ADDITIONAL DECREASES IN CRIME. THIS INDICATES THAT IN AREAS C AND F CONTRACTUAL PROVISION OF POLICE SERVICES IS AN UNATTAINABLE GOAL IF COST-BENEFIT RELATIONSHIPS ARE TO BE PRESENTED. AN ANCILLIARY CONCLUSION OF THE BREAKDOWN OF THE SYSTEM IS THAT EFFORTS OTHER THAN THOSE OF THE POLICE ARE NEEDED TO PREVENT CRIMINALITY. NOTES AND REFERENCES ARE PROVIDED.