interactions and stoehastic dominanee One of the eoncems in frarning decisions is interactions across decisions. Ralph is trying to secure an essential serviee from one of three possible subcontractors.

The total acquisition cost is uneertain. The eost possibilities and probabilities are summarized below.

first source second source third source 100 .10 .20 .30 600 .20 .20 .00 chapter 12 900 .70 .60 .70 Any randomness with the aequisition eost is independent of any other randomness in the settingo Let R denote the net revenue to Ralph exclusive of aequisition cost.
Also let x denote the net wealth associated with all other aetivities in Ralph's domain. So Ralph's utility evaluation is denoted U(x+R-C), where e is the above noted aequisition cost.
a] Suppose we know nothing about R or x and nothing about Ralph's utility funetion except more is preferred to less. It then tu ms out we ean immediately dismiss the first source. To see this, look at the difference between Ralph' s expeeted utility using the first versus the second souree, for any x and R combination:
(.1O-.20)U(x+R-100) + (.20-.20)U(x+R-600) + (.70-.60)U(x+R-900).
Notice the first source uncertainty puts more weight on the bad outcome (a cost of 900). The second source ean be viewed as taking the first source's cost uncertainty and moving some probability weight from a bad to a good outeome. This is ealled first order stoehastic dominance.
Now suppose we know x is rather large, but constant and R is 900. Also suppose U(·) is a square root funetion. With x so large Ralph is effectively risk neutraI in the sourcing decision. What, under risk neutrality, is the best ehoice?

Contrast this with the ease where x is zero.

b] Why is it, then, interactions with other decisions are irrelevant in eomparing the first and second sources here, but not in eomparing the second and third sources?

AppendixLO1