Homework on Adverse Selection in Insurance Markets

The Excel workbook for this assignment is now available. I'm sorry for the delay. Please use the comments area for this post to ask questions about the homework.

I think I'm missing something pretty easy, but I'm not sure how I am supposed to get the slope of a 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.

Not yet no because I'm not sure where the expected coverage is coming from or what that equation would be. I do know how to invert the relationship and figure out things from there, just missing what expected coverage is.

Well, for the slope of the fair insurance line, it's not even an equation, you just have to invert the number. For low risk, it gives you a percentage so you just invert the figure in a decimal form.

What I cannot figure out is question 3 where it asks for utility of wealth minus expected loss as a certainty.

For question #3, it is asking you to calculate total utility using the utility function given in the Excel spreadsheet. Right above it you calculate expected loss - so take initial wealth minus expected loss as they tell you and plug it in to the utility function!

It may be natural to think of the premium as a function of the coverage -

premium = fixed load + (variable load)*coverage

However, in the graph the premium is on the horizontal axis and the coverage is on the vertical axis, so to make sense of the relationship as plotted the premium function must be inverted.

For fair insurance with no fixed load, the premium equals the expected coverage. But note that the premium is plotted on the x-axis, so you need to solve for the coverage as a function of the premium, by inverting the relationship.

The ballgame starts at 7. I will be offline during the game.

I am having trouble with the question about what the expected utility is when there is no insurance available. I tried entering 20000 and 10000 for x in the utility function, but they are both not working. I am not sure what to plug in for x. If someone could help me out, that would be great!

Thank you! I figured it out. For the question immediately after that, is the question asking if there is no insurance available, will the certainty amount of the original lottery be the same, whether or not there is insurance available?

I am at a lost on the 5th question finding the certainty equivalent of the original lottery. Wouldn't it be (20000-1350) ? Given that was the certainty equation for the original lottery

u(CE)= E(u(x)). Therefore to find the CE you must take u inverse and evaluate that at E(u(x). Note that since u(x) = x^a, u inverse evaluated at x is x^(1/a).

I'm not sure how you use the inverse in that situation however because of how large the numbers I'm getting are. Using x^(1/a) for me is the equivalent of x^(1/.005) -> x^200 which isn't a feasible number. Not sure where I'm going wrong?

I only have one question left and its the separating policy for low risk types (the last question on the first half). Every time I press the arrows my mac freezes. Is anybody else having this problem?

I think I'm missing something pretty easy, but I'm not sure how I am supposed to get the slope of a 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.

ReplyDeleteDid you get the answer? If not, I can assist you further

DeleteNot yet no because I'm not sure where the expected coverage is coming from or what that equation would be. I do know how to invert the relationship and figure out things from there, just missing what expected coverage is.

DeleteWell, for the slope of the fair insurance line, it's not even an equation, you just have to invert the number. For low risk, it gives you a percentage so you just invert the figure in a decimal form.

DeleteWhat I cannot figure out is question 3 where it asks for utility of wealth minus expected loss as a certainty.

Hope this helps

Thanks, finally figured it out.

DeleteFor question #3, it is asking you to calculate total utility using the utility function given in the Excel spreadsheet. Right above it you calculate expected loss - so take initial wealth minus expected loss as they tell you and plug it in to the utility function!

What do you mean by inverting the number/relationship?

DeleteIt may be natural to think of the premium as a function of the coverage -

Deletepremium = fixed load + (variable load)*coverage

However, in the graph the premium is on the horizontal axis and the coverage is on the vertical axis, so to make sense of the relationship as plotted the premium function must be inverted.

For fair insurance with no fixed load, the premium equals the expected coverage. But note that the premium is plotted on the x-axis, so you need to solve for the coverage as a function of the premium, by inverting the relationship.

ReplyDeleteThe ballgame starts at 7. I will be offline during the game.

I am having trouble with the question about what the expected utility is when there is no insurance available. I tried entering 20000 and 10000 for x in the utility function, but they are both not working. I am not sure what to plug in for x. If someone could help me out, that would be great!

ReplyDelete

DeleteThe calculation you must do is (1-p)*u(2000) + p*u(1000) You are computing an expected utility, not the utility of some amount for certain.

Thank you! I figured it out. For the question immediately after that, is the question asking if there is no insurance available, will the certainty amount of the original lottery be the same, whether or not there is insurance available?

DeleteI'm struggling to figure out how to find P. If someone could help explain to find the value of P I would appreciate it. Thanks

DeleteI am at a lost on the 5th question finding the certainty equivalent of the original lottery. Wouldn't it be (20000-1350) ? Given that was the certainty equation for the original lottery

ReplyDeleteI will answer this algebraically.

ReplyDeleteu(CE)= E(u(x)). Therefore to find the CE you must take u inverse and evaluate that at E(u(x). Note that since u(x) = x^a, u inverse evaluated at x is x^(1/a).

I'm not sure how you use the inverse in that situation however because of how large the numbers I'm getting are. Using x^(1/a) for me is the equivalent of x^(1/.005) -> x^200 which isn't a feasible number. Not sure where I'm going wrong?

ReplyDeleteI figured this one out, if anyone needs any further help let me know!

DeleteYes, how did you figure this one out? I tried to do the inverse as well, and it is not working for me!

DeleteWhen using the inverse, as Professor Arvan said, plug in the answer you got for the Expected Utility for the values, not the values of W and L.

DeleteThat is correct. u takes income as its argument an gives utility back. u inverse takes utility as its argument and gives income back.

DeleteThank you! that helped me a lot!

DeleteI am confused on how to calculate the "risk premium" - what is the equation I need to use to find expected dollar amount?

ReplyDeleteThe risk premium is the expected dollar value of the lottery less the certainty equivalent.

DeleteI only have one question left and its the separating policy for low risk types (the last question on the first half). Every time I press the arrows my mac freezes. Is anybody else having this problem?

ReplyDelete