Recall the principal-agent model of Stringer Bell (the principal) and the street-level drug dealers (the agent) from class. Stringer Bell wants his dealers to expend high effort in drug dealing to ensure a successful drug deal. If the drug deal is successful, Stringer Bell earns $400,000. He earns $0 if the drug deal is unsuccessful. The dealers can expend high or low effort in drug dealing. The probability a drug deal is successful is 40% if the dealers put in low effort and 80% if they put in high effort. Exhibiting effort in drug dealing is costly however. If the dealers puts in low effort, he gets $100,000 of disutility (as in the lecture notes). Recently, a drug dealer hunter named Omar has arrived in the neighbourhood. He makes putting high effort into drug dealing even more costly than the example from the lecture notes. Specifically, if the dealers put in high effort with Omar around, they get $175,000 of disutility since they will be dealing in the streets where Omar can hunt them. If the dealers do not work at all, they get a payoff of 0. Throughout assume dealers exhibit high effort if indifferent between exhibiting high and low effort. Also assume that drug dealers will work if they are indifferent between working and not working. 4.1 Derive the full information wage contract where Stringer Bell can perfectly observe the dealers' effort level. Compute the expected profits of Stringer Bell under this contract. 4.2 Suppose Stringer Bell cannot observe how much effort the dealers are exerting. Further suppose Stringer Bell offers a wage scheme consisting of a base salary s, and a bonus b. The base salary is paid no matter the outcome of the drug deal, while the bonus is paid only if the drug deal is successful. Derive the profit-maximizing values of s and b that Stringer Bell should offer the dealers to induce high effort. Compute the expected profits of Stringer Bell under this contract. In no more than two sentences, provide intuition as to why the contract you derived here differs from that found in the lecture notes. 4.3 Continue to assume Stringer Bell does not observe drug dealer effort, but now does not care about inducing high effort and only wants to induce low effort. What is the profit-maximizing wage contract? Compute the expected profits of Stringer Bell under this contract. 4.4 Would Stringer Bell prefer to offer the high-effort inducing wage contract from 4.2 or the low-effort inducing wage contract from 4.3? Recall the principal-agent model of Stringer Bell (the principal) and the street-level drug dealers (the agent) from class. Stringer Bell wants his dealers to expend high effort in drug dealing to ensure a successful drug deal. If the drug deal is successful, Stringer Bell earns $400,000. He earns $0 if the drug deal is unsuccessful. The dealers can expend high or low effort in drug dealing. The probability a drug deal is successful is 40% if the dealers put in low effort and 80% if they put in high effort. Exhibiting effort in drug dealing is costly however. If the dealers puts in low effort, he gets $100,000 of disutility (as in the lecture notes). Recently, a drug dealer hunter named Omar has arrived in the neighbourhood. He makes putting high effort into drug dealing even more costly than the example from the lecture notes. Specifically, if the dealers put in high effort with Omar around, they get $175,000 of disutility since they will be dealing in the streets where Omar can hunt them. If the dealers do not work at all, they get a payoff of 0. Throughout assume dealers exhibit high effort if indifferent between exhibiting high and low effort. Also assume that drug dealers will work if they are indifferent between working and not working. 4.1 Derive the full information wage contract where Stringer Bell can perfectly observe the dealers' effort level. Compute the expected profits of Stringer Bell under this contract. 4.2 Suppose Stringer Bell cannot observe how much effort the dealers are exerting. Further suppose Stringer Bell offers a wage scheme consisting of a base salary s, and a bonus b. The base salary is paid no matter the outcome of the drug deal, while the bonus is paid only if the drug deal is successful. Derive the profit-maximizing values of s and b that Stringer Bell should offer the dealers to induce high effort. Compute the expected profits of Stringer Bell under this contract. In no more than two sentences, provide intuition as to why the contract you derived here differs from that found in the lecture notes. 4.3 Continue to assume Stringer Bell does not observe drug dealer effort, but now does not care about inducing high effort and only wants to induce low effort. What is the profit-maximizing wage contract? Compute the expected profits of Stringer Bell under this contract. 4.4 Would Stringer Bell prefer to offer the high-effort inducing wage contract from 4.2 or the low-effort inducing wage contract from 4.3