1. Each A,- chooses effort level ei. At the same time, P chooses E1 and E2. 2. Each player's attempt (to generate an idea) either succeeds or fails. 3. For each project, P chooses which idea (if both are successful) to implement 4. Payoffs are realized. We'll go through the problem set-by-step. a) Write down Ai's expected utility as a function of e,- and Bi. Calculate Ai's choice of e,- as a function of 13,-. b) Write down P's expected utility as a function of his and the agents' effort choices. Write down the rst-order conditions that specify P's choice of E1 and E2. c) Work out the equilibrium levels of the agents' effort choices el and e2, and the Principal's effort choices, E1 and E2. (You'll have to solve a system of four simultaneous equations, each of which correspond to one of the rst-order conditions. Hint: once you have the four equations, it may be convenient to nd a way to solve for E1 rst.)