intermediate micro economics notes - AXIOMS OF RATIONAL CHOICE

Axioms of Rational Choice

•Completeness
–if A and B are any two situations, an individual can always specify exactly one of these possibilities:
•A is preferred to B
•B is preferred to A
•A and B are equally attractive


•Transitivity
–if A is preferred to B, and B is preferred to C, then A is preferred to C
–assumes that the individual’s choices are internally consistent


•Continuity
–if A is preferred to B, then situations suitably “close to” A must also be preferred to B
–used to analyze individuals’ responses to relatively small changes in income and prices




Utility


•Given these assumptions, it is possible to show that people are able to rank in order all possible situations from least desirable to most
•Economists call this ranking utility
–if A is preferred to B, then the utility assigned to A exceeds the utility assigned to B


U(A) > U(B)


•Utility rankings are ordinal in nature
–they record the relative desirability of commodity bundles
•Because utility measures are not unique, it makes no sense to consider how much more utility is gained from A than from B
•It is also impossible to compare utilities between people


•Utility is affected by the consumption of physical commodities, psychological attitudes, peer group pressures, personal experiences, and the general cultural environment
•Economists generally devote attention to quantifiable options while holding constant the other things that affect utility
–ceteris paribus assumption



•Assume that an individual must choose among consumption goods x1, x2,…, xn
•The individual’s rankings can be shown by a utility function of the form:

utility = U(x1, x2,…, xn; other things)
–this function is unique up to an order-preserving transformation