2. All potential criminals are alike. Each has benefit B =$10,000 of committing a crime. The...

2. All potential criminals are alike. Each has benefit B =$10,000 of committing a crime. The cost to the criminal of being punished is T =$1,000 for each year spent in prison. Let p = 0.15 be the probability that a criminal is caught and punished. If a potential criminal decides not to commit a crime, they receive a wage w = $6, 000 with no probability of punishment.

(a) What condition dictates when it is profitable for a potential criminal to commit a crime? Justify this condition. [5 marks]

(b) Suppose there are 100 potential criminals each of whom makes a “rational” choice of whether or not to commit a crime. Each crime that is committed causes social harm equal to $100,000. It costs society $5,000 per year to imprison a criminal, and $500,000 per year for the police force. Total social cost = prison costs + cost of harm + police costs - benefit to criminals. What is the optimal prison sentence, S ∗ What are total social costs given this optimal sentence? [5 marks]

(c) Suppose society has the option of giving a wage subsidy to workers. Show how this changes the condition you found in part (a)? [2 marks]

(d) What wage subsidy is necessary to deter crime? What is the optimal combination of wage subsidy and sanction choice? Justify your answer

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