How to Pay Mark? $(30\%)$

Consider this situation. Julie is the owner of an airport shuttle. The shuttle transports passengers between Bowling Green and the Nashville Airport. Most customers pay with cash because there is a big discount. Since she is old and spends most of the time in Florida, she hired Mark, as the only employee and driver. Julie is far away from Bowling Green, therefore she has to believe Mark unless there is an unambiguously clear evidence against Mark$$s claim$/$report$.$

Each period, Mark reports and turns in the revenue. Then, the payment to Mark is determined and sent to Mark. Assume that Mark is rational $($in economics, rational is synonymous with selfish$)$ and he will always cheat on Julie if doing so is beneficial to him. Julie is trying to find the best method in avoiding potential cheating by Mark. Cheating means pocketing $($stealing$)$ revenue, not working hard, or reporting incorrect information about Mark$$s work.

Julie is considering the following five possible compensation methods:

I$)$ Pay Mark a flat salary $($e$.$g$.,$ $$3,500$ each month$)$

II$)$ Pay Mark an amount equal to reported revenue less fixed amount

$($e$.$g$.,$ pay X$,$ where X $=$ reported revenue less $$3,000$; if X is negative, negative pay occurs

meaning Mark pays Julie the absolute value of X$)$

III$)$ Pay Mark a certain percent of sales $($e$.$g$.,30\%$ of reported fares from passengers$)$

IV$)$ Pay Mark on an hourly basis $($e$.$g$.,$ $$25$ per hour $*$ Reported work hours$)$

V$)$ Pay Mark based on the mileage $($e$.$g$.,$ $$0\mathrm{.}30$ for each mile added in the mileage gauge$)$

VI$)$ Pay Mark based on his efforts $($how hard he works$)$