Suppose a prosecutor expects to convict a defendant with probability .5, and that the sentence on conviction is ten years in prison. Assume the prosecutor values prison time at $1,000 per year (its value as a deterrent of crime), and incurs a cost of trial equal to $2,000.
(a) What is the minimum prison sentence the prosecutor will offer as part of a plea bargain if her objective is to maximize the expected value of the sentence imposed, less the cost of trial (if any)?
(b) Suppose the defendant believes his chances of being convicted are .30, his cost of prison time is $5,000 per year, and his cost of a trial is $1,000. Will he accept the plea bargain in (a)?