i) You are selling your house, and your estate agent has a contract that pays her 3% of the sale price. The state agent knows how much your house is worth, but you do not. All you know is that the value of your ouse is uniformly distributed between $200,000 and $300,000. You come up with idea of offering her a higher commission rate to make her work harder. Specifically, you are considering offering her a 5% commission rate. If you do, she will work harder and the value ofyour house goes up by 4%. (As an example, if your house would sell for $200,000 under the old contract, it will sell for $208,000 under the new one). The cost to her of working harder is $5,000. If you offer her this deal, she may say no. If she says no, she stays on the old deal of 3% Should you offer her the new 5% contract? How much more or less do you make from it? (15) (ii) You are designing a compensation plan for a hairdressing service that does peoples' hair in their homes. You have the list of clients and you assign a hairdresser to the client. For simplicity, assume that there is jus one client. The client pays $300 to have her hair cut by your hairdresser through your firm. The hai has a market wage of $120 to cut her hair rdresser The problem that you are worried about is that the client also needs to have her hair cut again in two months and is again willing to pay $300 if done through your service. However, the hairdresser might directly contract with the client to have her hair cut, thereby eliminating you from the transaction. Assume that the client is willing to pay $220 to have her hair cut in that way If the hairdresser tries to do this, assume that you only catch her 1/3 of the time- say because the client finds it unethical and turns the hairdresser in. If that happens, you fire her and she gets her market wage of $120 instead of whatever you promise to pay her. The other 2/3 of the time, if she makes this offer to the client, she gets to cut you out of the transaction and she gets paid the $220 Assume that there is no discounting here, so that money two months from now is worth the same as money today. Also assume that there is no further interaction between the hairdresser, the client, and you after two months. You have a choice here- you can either offer some sort of efficiency wage that will stop her from trying to cut you out, or you can choose not to offer such a wage, and to let her do so. This is a bit like the following: you can either employ her for the long term - by offering the efficiency wage- or you can be like a referral service that benefits one time, but lets the client go to the hairdresser afterwards. What is the optimal compensation policy here? Should you offer a compensation package to deter her from cutting you out, or are you better off allowing her to do so? (20)