Question

# 4. Prove the followings (30p)

A) When X is finite, show that u : R →R represents R ⇒ R is

rational(15p).

B) Theorem If A ⊂ B ⊂ X are nonempty and finite sets, and R is a rational preference relation on X, then

(.) (Optima are indifferent) x,y ∈ C^{R}(A) ⇒ x I y,

(.) (Larger menus are at least as good) C^{R}(B) R C^{R}(A)

(.) (Larger menu with disjoint optimum is strictly better) (C^{R}(B)∩C^{R}(A) = ∅) ⇒C^{R}(B) P C^{R}(A)).

### Recently Asked Questions

- The American Bar Association (ABA) is an example of a. industrial union b. a public employee union c. a craft union d. an employee association

- Joe is currently in consumer equilibrium by consuming cheese and crackers, such that the last cracker consumed yielded 8 utils and the last piece of cheese

- Suppose Carrie's utility function for clams is as follows: If she consumes 1 clam, she gets 10 units of total utility; for 2 clams, she gets 18 units of total