4. Two agents, agent 1 and agent 2, can exert effort to produce a joint output according to the following technology: X = 2(e1 + ez), where X is the joint output, and e, and ez denote the effort exerted by agent 1 and agent 2, respectively. Each agent's cost of effort (in terms of unit of output) is given by the following function: C(ei) = 2(e)?, i = 1,2. Denoting with wi paid to agent i (i.e., the compensation of agent i) according to the different contracts considered below, the utility of agenti is given by: U(wi, ei) = Wi-2(e;), i = 1,2. a) Find the first-best levels of effort of the two agents and the corresponding output. [20%] b) Suppose that the agents sign a contract which prescribes equal sharing of the joint output, and then simultaneously choose their respective effort levels. Find the equilibrium levels of effort, compare them to the first-best levels. [20%] c) Explain clearly in words why the equal sharing contract fails in achieving the agents supplying the first best level of effort. (10%)