Suppоse thаt а crime hаs a sоcial cоst of $10,000 each time it is committed. Every time an offender is caught, he or she is tried, convicted, and imprisoned. The cost of trying and punishing each offender who gets caught is $75,000. A city is considering hiring additional police dedicated to detecting this crime. The change would increase the fraction of offenders who get caught from 20% to 30%. Suppose this increase in detection would result in a decrease in the number of crimes committed from 1,000 a year to 800 a year. From an efficiency point of view, what is the most the city should be willing to pay to hire additional police?