Suppose that optimal deterrence of a particular crime requires setting the expected punishment equal to $2,000. Assume that the probability of apprehension is fixed at .2.

a. Suppose an offender has wealth of $5,000 and incurs a cost of $1,000 per month spent in prison. What combination of a fine and prison term achieves optimal deterrence at the lowest cost?

b. What combination of a fine and prison term is optimal for an offender with wealth of $7,000? (Assume he also incurs cost of $1,000 per month spent in prison.)

c. Suppose considerations of fairness dictate that the prison term of offenders who commit the same crime must be the same. What fine and prison term must be imposed on the two offenders to maintain optimal deterrence? Explain the sense in which this policy reflects a trade-off between fairness and efficiency.