Padma is the founder/owner of a startup, and wants to hire Amba to manage the company on her behalf. Padma estimates that Amba's effort a will affect the company's gross profits (i.e. gross of Amba's compensation), which will equal $100 with probability a, and $0 with probability (1 - a). The realized profits ($100 or $0) are observable and contractible. Moreover, Padma estimates that the dollar value of Amba's personal cost of exerting effort can be expressed as c(a) = 50a 2 . Finally, both Padma and Amba are risk-neutral and maximize their expected payoffs; and Amba's next best job opportunity is a volunteering job that would pay her $0. a) What is the first-best level of effort for Amba, i.e. the level of effort that maximizes Padma and Amba's expected total surplus? What is the first-best expected total surplus generated? b) Assume that Amba's effort is NOT observable to Padma, but that Amba's is NOT wealth- constrained. Suppose that Padma "sells the firm" to Amba, by offering her a share s 1 = 1 of the company's future gross profits, in exchange for a fixed fee F 1 paid by Amba to Padma. i. How much effort does Amba