3. In the linear incentive model, w(x) 2 xxx | . The cost function of the salesperson (agent) is c(e,s) = 0.5(e s)2, where e is the effort put into working for the principal and s is the quality of his mobile phone. The agent also values his mobile phone outside work; he attaches utility 11(5) 2 s in non-work related activities to a mobile phone of quality 5. The cost of buying a mobile phone with quality 5 is p(s) = 52. The agent has a mean-variance utility function with risk aversion coefficient r = 2. Output from work is x = e | (9, where 6 is normally distributed with mean 0 and variance 1. (a) Suppose there is no incentive problem because effort level 6 is observ- able. What is the first-best level of effort level 6 and quality level 5 chosen by the agent? (b) Suppose the principal observes neither 6 nor 5. What is the optimal choice of oz in this case? Does the agent buy a higher or lower quality mobile phone in this case compared to case (a)? Why? (c) The principal can provide a small subsidy to the salesperson toward buying his mobile phone, so that the salesperson pays p(s) 65 for a phone with quality 5 (the principal pays the amount (35). Suppose the principal keeps the contract (0:, 3) the same as in case (b). Is it a good idea for the principal to introduce a small subsidy? Why? (d) If the principal can adjust the contract (0?, ) while providing the sub- sidy, would it be a good idea to provide a small subsidy? Why? [A verbal answer is sufficient for this part.]