Adverse Selection: Solving a basic problem

Описание: After reportedly experiencing some technical difficulties when watching this video on my website, I'm uploading it to YouTube.
Note:
· At min. 5:15, my statement "we only have to compensate for any outside opportunity" could be misleading: of course, the principal also needs to compensate the agent for the effort she wants him to exert - but the way I defined the utility function of the agents, in some sense it is true that the principal only needs to make sure that those utilities, after accounting for the cost of the action, are at least equal to any outside opportunity they might have (in fact, "at least equal to the best outside opportunity" would be more accurate, since this way you are also considering the hypothetical case in which there are several outside opportunities that provide different utilities).
· At min. 17:10, I said that "we are gonna check back that our solution indeed satisfies this constraint", but... I forgot to do it (as you probably have realized). So I do it now: by the definition we have of WI, the left-hand side is equal to 0; then the right-hand side is equal to 5/18 - 2*(1/4) which is equal to -4/18, and thus, indeed, 0 ≥ -4/18.
· At min. 39:05, just to clarify, it would be more accurate to say that if the principal observes the low outcome and in case she requested the high outcome instead, the salary will not only be "low", but in fact negative: because the action is now observable thanks to the investment in technology, the principal and the agent will make a contract that establishes the effort level to be exerted (e.g. the high effort), and agree on a liquidated damages clause that establishes the amount to be paid by the agent in case of breach (in view of the expected loss that it'd cause). Regarding the high effort, the principal will just have to pay a salary that is enough to compensate for the cost of the effort and for the best outside opportunity the agent has (so no "extra" payment needed to induce him to choose the agreed level of effort). My apologies for the loss of clarity towards the end of the video.