In: Economics
All potential criminals are alike. Each has a benefit B of committing a crime, where B = $10,000. The cost, to the criminal, of being punished is T =$1,000 for each year spent in prison. The probability of a criminal being caught and punished is p. Let S represent the number of years spent in prison (i.e., the sentence). Suppose there are 100 potential criminals. Each chooses whether to commit this crime which has a social harm cost of $100,000. Suppose criminals are caught with a 15% probability. The cost of prison is $5,000 per prisoner, per year.
(a) Write down the condition for a rational criminal to commit a crime. What is the optimal choice of sentence, S? What is the total social cost associated with this choice? [5 marks]
(b) Now suppose that there are an additional 50 criminals who are irrational and therefore, always commit crimes. How does your answer to part (a) change? [5 marks]
(c) Now suppose you can choose from one of the following two police forces:(i) Catches criminals with probability 0.25 and costs $500,000.(ii) Catches criminals with probability 0.15 and costs $250,000.The social cost of crime is: prison costs plus social harm plus police costs less the benefit to the criminal. In a world with 100 rational criminals and 50 irrational criminals, which of these police forces would you choose, and what level of sentence S would you choose. Justify for your answer. [10 marks]