Wednesday, October 19, 2016

Excel Homework Due October 26 at 11 PM

This one you should find interesting.  It is on insurance under private information.  A person could be a low risk (low probability of loss) or a high risk (high probability of loss) but there are no distinguishing features that lets the insurance company know which type an individual is.  The individuals know which type they are, but if low risk types get better rates then both types have incentive to claim they are low risk.  The market must somehow address this incentive problem.

Note:  In years past students have had a hard time understanding when a pooling equilibrium will occur and when a separating equilibrium will prevail instead.  I plan to cover that in class after the homework is due.

1. I'm having trouble calculating the expected utility without insurance. I'm currently using the equation E(U) = (1-P) * U(W) + P * U(W-L)
Is there a different equation that I should be using? Thank you.

2. Its the right equation but note that there are two different risk types. For low risks, what you called P is qL and its value is in cell D25. For high risks, it is qH and the value is in cell D27.

There is possibly some joke here about minding your Ps and Qs but if that seems too obscure know that I switched the symbol for the loss probability here because when you get to the pooling probability later in the exercise, it is helpful to think of that as P (pooling starts with P) and it is function of the individual type loss probabilities.

Sorry if that's what caused the confusion.

1. I've been using cell references and the formula I mentioned above (with qL) and I'm still getting an incorrect answer. Any tips?

2. Normally, I wouldn't share the exact formula but you might looks at this and see if what you are writing is the same thing or not.

=(1-D25)*D20^D23+D25*(D20-D21)^D23

3. Professor Arvan,

I have trouble with the same question, the one asking for the expected utility without insurance. I used the same equation with Susan and I calculated the pooled probability for loss (P= b*qL+(1-b)*qH)

I used cell reference and my answer is exactly the same with the utility calculated in the previous blank. I'm not sure where am I doing wrong?

Thank you!

1. If you are referring to the question where the answer goes into cell B85, there it is using qL as the probability of loss, not the pooled probability.

2. I don't understand why is it just using qL? Why are we ignoring the high risk types?

3. I get it... It's in the same part with the previous questions. Thank you!

4. I am completely missing on how to graph the first question- the fair insurance line for a low risk type. Not sure if someone can break it down in to a simpler manner, but I guess I'm not sure what answer they're looking for

1. Premium = prabability of loss * coverage, which is Pi = P*I, and since the graph is y-axis for coverage and x-axis for premium, it should be written as I = Pi/P = (1/P)*Pi, and there you get the slope

5. If you've got any last minute questions for this evening, get them in before 6PM. Or I will respond in the morning.

6. i am having a lot of trouble with finding the certainty equivalent. i have tried multiple formulas that revolve around p*e(x)+((1-p)*(x-e(x)) and nothing seems to work. is there anything that I'm missing here?

1. Let me point out that you did this type of calculation in the previous homework. So if you got it right there, you should be able to get it right this time as well.

7. I am confused on how to find the risk premium (entered in cell B94), I'm not exactly sure what the question is asking for. I considered the formula pi=F + vI
but could not figure out how to apply it here.

8. Hmmm - this is still just like the previous homework. If you've computed the certainty equivalent and also the expected value of the gamble, the risk premium is the difference between the expected value and the certainty equivalent.

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