Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 23

How should the assumption of completeness and transitivity be reflected in Figure? Specifically:
1. What does the assumption of completeness imply about all of the points in the figure?
2. If it were known that a particular point in the ''?'' area in Figure was preferred to point X*, Y*, how could transitivity be used to rank some other points in that area?
FIGURE More of Good is Preferred to Less
The darkly shaded area represents those combinations of X and Y that are unambiguously preferred to the combination X*, Y*. This is why goods are called ''goods''; individuals prefer having more of any good rather than less. Combinations of X and Y in the lightly shaded area are inferior to the combination X*, Y*, whereas those in the questionableareas may or may not be superior to X*, Y*.