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(11)this implies that the preference order is complete

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(1)

|MRS|

(2)

here

x1 = x2

indifference curves are L shaped and form a 90° degree angle at the point of intersection with straight line of desired consumptopn ratio

(3)

D

at D

(4)

if indifference curves cross there is a

(5)

general convex combination

(6)
(7)

strictly

(8)
(9)

no convexity no concavity

(10)

is a

utility function representing a preference order

XX XXXXXX

XX XX

XXXXX XX

---- --- ---

(11)

this implies that the preference order is complete. Similar argument applies for transitivity. We can conclude that a preference order can be represented by a utility function only if it is complete and transitive.

(12)

Remark: and increasing transformation (also called positive monotonic transformation) preserves ORDER.

This implies that if f(u) is an increasing function, then f(u(x1,x2)) is a utility function representing the same preferences represented by u(x1,x2).

NO!!

(13)

Proof: Because u(x1,x2) ia a utility function representing the given preference order and f(u) is increasing:

V(x1, x2) is another utility function representing the same preferences.

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