but lauper would never he beat a in Problem f.4 (used payment) P The plaintif prefer Au beat , in Problem 4.2 (proportional payment), of Problem 5 Randal Graves works at RST Video, a video rental store. He's there for & hours, bit may the work hard for all 8 hours. Let e be the number of hours he works hard. The video store's gross profit is s, = 1000 + Gle + 4, where ? is a random variable with E() = 0 and Var(e) - 1/2. Its pet profit is * = r - s, where s is the salary it pays Randal. Randal has expected utility piven by Eu = E() - {Var(s) - c(e), where c(e) = $ is his cost of effort. Problem 5.1 (First Best) Suppose the video store owner can videotape Randal's performance. The owner offers a contract saying he is paid s' if Randal works hard for at least e' hours. What e" and s' will the owner's "first best" contract? Consider the "second best" case where the firm cannot monitor Randal's choice of c. Suppose the firm offers a linear contract of the form s(*,) = a+ bag. Problem 5.2 Given an arbitrary contract s(s,) = a + ly, what effort e will Randal choose to marimice his expected utility? Problem 5.3 Write down Randal's participation constraint (meaning, for what a will he be willing to accept the contract s (*,) = a + b, P Problem 5.4 Solve for the video store owner's second-by form the problem to one of chans