1. (20 pts) Consider a team Of six employees who are working on a shared project. The project consists Of several separated parts and at the end of each week each employee will receive a reward based on the number of parts that she has completed during the week as well as the number of parts completed by whole team. Let us assume E,- is the number of c0mpleted parts for employee 2' e {1, 2,3, 4, 5, 6} at the end of one week and R,- = (log(E.)1)/3 + 25 (1/3) 233:, E,- for j 6 {1,2, - - - ,6} is the amount Of reward received by i. There are two Options for each employee: (i) COOperate with others and maximize the team reward (ii) do not COOperate and individually decide what to do (a) If each employee chooses the second Option, what is the equilibrium amount for E. What is the amount Of reward received by each em- ployee? What kind of externality you can observe in this situation? Explain. (Spts) (b) Is the answer you found in part a Pareto-efcient? Why?(5pts) (c) If they choose the rst Option and try tO maximize the total reward for the team, what is the new level of E and R for each employee? Does any one has an incentive to deviate from the agreement? Ex- plain. (7pts)