Aaron sells costume jewelry at a kiosk in Conestoga Mall and earns a flat hourly wage. Betty owns the kiosk and wants to redesign a wage schedule that will induce Aaron to work hard. If Aaron engages with the shoppers in the mall and works hard to sell them jewelry, the kiosk makes a high daily profit of $1000 with probability 0.8 and a low daily profit of $500 with probability 0.2. However, left to his own devices, Aaron prefers to surf the web and text his friends most of the day, in which case the kiosk’s daily profit is $500 with probability 0.8 and
$1000 with probability 0.2. For Aaron to be motivated to work hard, he needs to receive a daily wage of $150 (this is Aaron's cost of effort).
1. Suppose Betty could observe whether Aaron works hard. Would she be willing to pay him $150?
2. Now let's assume Betty can't observe whether Aaron works hard. Suppose Betty decides to offer a bonus to Aaron that is tied to the kiosk's profit. Only if the kiosk earns $1000 does Aaron receive the bonus. If Aaron is risk-neutral, how much does the bonus need to be to make Aaron indifferent between working hard and slacking?