00:01
In this video, we are going to focus on this very problem where we have been given to assume that the attribute x takes positive value such that we have here the value of u of x, basically u1 of x to be equals to 1 minus e raised to the power negative x.
00:20
And then here we can say that we have u2x and that is equal to x squared.
00:27
So, it can be written like this.
00:29
And now here we have u3 or x and that is going to be here equals to under root of x.
00:37
So firstly, we have to sketch these utility function.
00:41
So the sketch of these very functions will look like over here as such.
00:47
And from this very sketch, we can say that this black line denotes the graph of u2.
00:53
This is u2 of x that is equals to x square and then this very red line denotes the graph of u3 that is u3 of x is equal to under root of x and then this blue line denotes the graph of we can say u1 that is equals to 1 minus e raise to the power negative of x and hence from this very value we can say that here here the x -axis, this one is representing change in certain, let's write change in certain and it will be compensation.
01:36
So it is c -o -m -p -e -n, s -a -t -i -o -n, and this very graph or basically this very axis which is y -axis is denoting change in utility.
01:49
So it is here going to be change in utility.
01:53
Which can be written over here as u -t -i -l -i -t -y and it is denoted with delta x.
02:01
So from this very information we can say that this very graph help us to understand that yes, the decision -maker preferences are taken as risk averse...
