Understanding how shirking decreases team output

Valerie sells bottled water from a small stand by the beach. On the last day of summer vacation, many people are on the beach, and Valerie realizes that she can make a lot more money this day if she hires someone to walk up and down the beach selling water. She finds a college student named Shen and makes him the following offer: They'll each sell water all day and split their earnings (revenue minus the cost of water) equally at the end of the day. Valerie knows that if they both work hard, Shen will earn $90 on the beach and Valerie will earn $180 at her stand, so they will each take home half of their total revenue:$90+$180=$135

$90+$1802=$135. If Shen shirks, he'll generate only $50 in earnings. Valerie does not know that Shen estimates his personal cost (or disutility) of working hard as opposed to shirking at $25.

Once out of Valerie's sight, Shen faces a dilemma: work hard (put in full effort) or shirk (put in low effort).

In terms of Shen's total utility, it is better for him to work hard/shirk.

Taking into account the loss in utility that working hard brings to Shen, Valerie and Shen together are/aren't better off if Shen works hard instead of shirking.

Valerie knows Shen will shirk if unsupervised. She considers hiring her good friend Carrie to keep an eye on Shen. The most Valerie should be willing to pay Carrie to supervise Shen, assuming supervision is sufficient to encourage Shen to work hard, is$20, $15, 25, 45? .

It turns out that Valerie's friend Carrie is unavilable that day, so Valerie cannot find a reliable person to watch Shen. Which of the following arrangements will ensure that Shen works hard without making Valerie any worse off than she is when Shen shirks?

a)Pay Shen $70, regardless of how many bottles of water he sells

b)Make Shen promise to work hard

c)Allow Shen to keep 73% of the revenue from the bottles of water he sells instead of 50%

d)Allow Shen to keep 70% of the revenue from the bottles of water he sells instead of 50%