This is the homework on insurance under asymmetric information. Note that the economics here is harder (I tried to keep the math as simple as I could). If you have questions on the mechanics for producing an answer in Excel, please post those as comments to this post. If however, you have questions about the underlying economics, note that I plan to lecture on this in class the following day, to explain both the modeling and the consequences of the model.
Hello, I am having trouble getting started with the first question. Based on the lecture slides it seems as though v represents the slope from the insurance pricing equation. And the question says that v= probability of loss in the fair insurance model. So is the answer not supposed to be = to the prob of loss for low risk type, D25?
ReplyDeleteIn the graph, the premium is on the horizontal axis while the coverage is on the vertical axis. Normally we think of the premium as a function of the coverage, but here it is asking for the inverse, where the coverage is a function of the premium.
DeleteProfessor,
ReplyDeletethere is a typo in cell O137 where alpha should be equal to 0.00005 instead of 0.005.
Just let you know since I got incorrect answers when I used cell reference to cell O137.
Thanks for letting me know - very unfortunate. I will see if I can fix it for the students downloading it later tonight.
DeleteI fixed it - I hope.
DeleteFor use on the 4th and 5th questions, what is the implication of the fixed load and no insurance available? I think I'm just missing something, but I'm not sure what we are supposed to do on those questions.
ReplyDeleteIn the first graph the insurance line goes through the origin (no premium, no coverage). The origin clearly gives the insurance company zero profit. Since the insurance is fair, all points on that insurance line give zero expected profit. Note that the indifference curve for the insured is tangent to the insurance line at the full coverage point and has a positive intercept on the coverage axis (when the premium is zero). Having no premium but that amount of coverage gives the same expected utility as the full coverage point. This clearly shows the insured is better off than he would be if he didn't purchase any insurance. So in the first graph all the gains for trade are captured by the insured.
DeleteIn the second graph, the first graph is reproduced but now there is another insurance line, where the fixed load equals the risk premium, so buying insurance with full coverage leaves the insured indifferent to not purchasing any insurance at all. On that insurance line, there is a positive intercept on premium axis, equal to the risk premium. In that case the insurance company captures all the gains from trade.
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DeleteI'm having difficulty with the 3rd question. I thought it would be =(D20^D25)?
ReplyDeleteFor b71 you have to first subtract the expected loss before you plug it into the utility function.
DeleteI am having trouble with B71, that's the expected loss for low risk type. I think I might be missing something.
DeleteThe expected loss is the probability of loss times the loss.
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ReplyDeleteI'm confused where the probability of no insurance comes from for number 4
ReplyDeleteThe expected utility with no insurance is simply (1-p)U(W) + pU(W-L).
DeleteI am having a hard time with the #6th question (cell B148). I understand the the premium is F +VI but I just can't figure it out...
ReplyDeletewere you able to understand #5?
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