## Wednesday, October 28, 2015

### Excel Homework Due 11/3 at 11 PM

This homework is on the simplest possible version of the principal-agent model.  It is this model that produces pay for performance as a feature.  It is important to understand this base model before we delve into various realistic ways of complicating the model.  (Mostly we will talk about that but I might do some additional modeling in class after going over the basic model.)  There is a video I'd like you to watch first.  It should give you the background you need to do the homework.

Video
Excel File

1. I figured out the previous cells except last two cells which are F126 and B128. Could you tell me how to solve those two questions?

2. My goal is to help you think it through, not to tell you how to get the answer. If you respond by saying what you have tried already, then I can respond with a suggestion on how to modify the approach.

Also, realistically, while you probably want to get this done tonight, I might not respond till the morning. It is Saturday night and I'm about to move into relax mode till the morning.

1. I have no clue how to do F126. For cell B128, I think it would be similar to B96. I replaced all the P(0) in the solution of B128 into P(e) and use the answer I got from this change minus e. It turns out incorrect. Then I have no clue. I do know how those two scenario changed would affect the way to apply the formula, I need more hints.

3. Let's focus on just F126. I suggest you write down the equation for expected utility in the high effort case and equate that to the outside option. In the video, that expected utility is given around the 1:50 mark. What you said above has a simple arithmetic mistake in it that you should spot if you write out the equation.

1. And if you get that one, I'd think you can get B128 as well.

4. For F126 i have tried using the same formula as for cell G94 but also with adding and subtracting e. I have also written out the high effort expected utility function and manipulated it algebraically but can't seem to figure it out.

Also, if WL=WH then the equation would simplify to 1u(w)-e=û+e. i tried solving for W this way and still am wrong. How else should i look at the equation?

1. I figured it out. I added e to the utility before solving for the certainty point.

2. Mazel Tov! A little patience goes a long way.

5. How do you find the certainty point? It seems like we don't have all the necessary variables, or I'm looking at the wrong equation?

1. At certainty, wL = wH. Call that common payment w. Your goal is to find out the value of w. You are given some information about u(w) as it pertains to an outside option. That is the information to use to determine w.

2. I don't see u(w)

3. Have you watched the video? This is all explained there.

6. Yea I watched it, but still confused. I just need the equation for the certainty point.

7. For the low effort case, the answer is given in the video at the 3:50 mark.

8. To solve for u^-1 you need y though, and we're not given y

1. In the low effort case, y is ubar.

2. Is u, u bar in the high effort case?

3. I STRONGLY ENCOURAGE YOU to take about 15 minutes and do some algebra with pencil and paper so you can see what the question is asking. These questions are not hard and you will only understand them by doing it this way. The algebra in question is discussed in the video. You need to reproduce that algebra for the homework questions.

4. I plugged in exactly what the equation said from the video using cell references and it's not working