- a) Suppose that income from legitimate employment for former prison inmates is a function of the number of years that the individual served in prison. Assume the function is income = 12 In(years in prison), where ln() is the natural log function, such that income from legitimate employment is decreasing in the number of years that the individual served in prison (i.e., legitimate employment yields less income for individuals that have been in prison longer). Suppose that in addition to legitimate employment, former prison inmates also have the option of illegitimate employment, which involves stealing loot. Assume that the amount of loot is valued at $20 and that the cost to plan and steal the loot is $3. Also, assume that there is a 25% chance of being caught while stealing the loot and that if caught, the individual goes back to prison, which carries a cost of $7. What is the expected value of income from illegitimate employment? What is the minimum number of years that the former prison inmate would have to have served in prison, for it to be more profitable to pursue illegitimate employment? b) (Continued from above, New information) Suppose that the size of the police force increases, such that the chance of being caught while stealing the loot is 30%. What is the new expected value of income from illegitimate employment? What is the new minimum number of years that the former prison inmate would have to have served in prison, for it to be more profitable to pursue illegitimate employment?