1.What is the minimum amount of money that you would accept with certainty before you would switch to the gamble as discussed at the start of section 4D in my notes?

2.Suppose my utility function is My car is worth $9000, and there is a 6% chance of a road accident that reduces the value of the car to $1600.I'm thinking about getting insurance.

2a) What is the expected value of my car?

2b) What is my expected utility from the car?

2c) What is my certainty equivalent?

2d) How much am I willing to pay for insurance?

Part 4D - Risk Preferences

Now, how does this relate to risk aversion?Take the same graph above, and think now that instead of just giving you money each day, I give you a single gamble today.I'll flip a coin.Heads, you get $10,000,000.Tails, you get nothing.Or, you can just have $5,000,000 right now.Would you choose to take the five million, or flip the coin?

Most of us would choose the five million dollars, and for the same reasons discussed here.The first million is a LOT better than the second million, so why gamble with it?Isn't the same thing as being given $5,000,000, and then taking it to Vegas and betting it all on red?It is... so most people wouldn't do something like that.Graphically, it has to do with that square root graph shown above (or Figure 6.1 in the Ahlerston textbook, which looks about the same).Here is a screenshot of that.

You can see points a, b, c, d, and e in that figure.The idea is that, flipping the coin, you will either be at point a (lose) or point b (win).These values of zero and 10 map to utility values of 0 and 3.2.

The idea of risk aversion comes from points c and d.If you have the gamble, your expected wealth is the average of the two payments (5), and your expected utility is the average of the utilities (1.6), which gets you to point c.But if you had 5 with certainty, then your utility (happiness) would be greater; you would be at point d!

A risk averse person, therefore, would choose the 5 with certainty.