An employer (principal) hires a worker (agent) of productivity to produce an output Xi = θi et. The worker is either high productivity θt = θH, or low productivity θi= θL, where prior type probabilities are P(θi = θH) = π; P(θi = θL). It may be convenient to use this shorthand: (θL/θH)^2 = y. The worker's outside option is normalized to 0, and his cost of effort is c(et) = ei^2/2. The employer offers a take-it-or-leave-it contract to the worker that specifies wages (w.) given type reports and related outputs. The employer only observes output directly, not effort or type. All parties are risk neutral, so the agent's realized) objective function is Wi = - ei^2/2,
and the principal's (realized) objective function is θiei - Wi. a. This type of problem is called a "false moral hazard" because the principal does not observe effort, but it is an adverse selection problem. What is an adverse selection problem, and why is this principally an adverse selection issue?