00:01
Have a 50 -50 chance of gaining or losing $1 ,000.
00:04
We have a policy that removes the risk costs 500.
00:08
At what level of wealth, w, will you be indifferent between taking the gamble or paying the insurance? we have a 50 -fitility function given as u of w equals negative 1 over w.
00:20
How to calculate the utility taking the gamble.
00:24
So eu would be calculated as 0 .5 times u, parentheses w, w, plus 1000 plus 0 .5 times u parentheses w minus 1 ,000.
00:38
We have a 50 with substitute u equals negative 1 over w.
00:45
So we have e u equals 0 .5 times negative 1 over w plus 1 ,000 plus 0 .5 times negative 5 over w minus 1 ,000.
01:01
You have a $50 to $500 insurance, your wealth becomes w minus 500.
01:07
You have a 50.
01:08
This condition is where you're indifferent when the expected utility of the gamble equals the utility of paying for the insurance.
01:15
So this would be written as negative 0 .5 times 1 over w plus 1 ,000, minus 0 .5 times 1 over w minus 1 ,000, equals negative 1 over w minus 500...