Q3.2 I understand the concepts of first and second order dominance, but I don't understand what they are doing in these two questions, especially why they factorize and then conclude that it is true? Can someone please explain the memo? Thanks
Can you say that it is true because for values 0<w<1, the equation is <= 0, which makes mathematically sense?
Because first and second order dominance means that the CDF (for first order) or its integral (for second order) of one function is always equal to or greater than the other function. So what they do is subtract Function B from Function A, and then prove that for all values within the given range, this difference is always non-positive (if there was a positive value for any value of w between 0 to 1 inclusive, then that order of dominance does not hold). By factorizing Function B out, it makes it easier to show the part of Function A is indeed smaller then or equal to one, and hence the inequality holds true for all w within the range.
