Indifference Curve - Assumptions of Consumer Preference Theory

Assumptions of Consumer Preference Theory

• Preferences are complete. The consumer has ranked all available alternative combinations of commodities in terms of the satisfaction they provide him.
  • Assume that there are two consumption bundles A and B each containing two commodities x and y. A consumer can unambiguously determine that one and only one of the following is the case:
    • A is preferred to B ⇒ A p B
    • B is preferred to A ⇒ B p A
    • A is indifferent to B ⇒ A I B
      • Note that this axiom precludes the possibility that the consumer cannot decide, and that a consumer is able to make this comparison with respect to every conceivable bundle of goods.
• Preferences are reflexive
  • Means that if A and B are in all respect identical the consumer will recognize this fact and be indifferent in comparing A and B
    • A = B ⇒ A I B
• Preferences are transitive
  • If A p B and B p C then A p C.
  • Also A I B and B I C then A I C.
    • This is a consistency assumption.
• Preferences are continuous
  • If A is preferred to B and C is infinitesimally close to B then A is preferred to C.
  • A p B & C → B ⇒ A p C.
    • "Continuous" means infinitely divisible - just like there are infinite numbers between 1 and 2 all bundles are infinitely divisible. This assumption makes indifference curves continuous.
• Preferences exhibit strong monotonicity
  • if A has more of both x and y than B then A is preferred to B
    • this assumption is commonly called the "more is better" assumption
    • an alternative version of this assumption is strong monotonicity which requires that if A and B have the same quantity of one good, but A has more of the other, then A is preferred to B.

It also implies that the commodities are good rather than bad. Examples of bad commodities can be disease, pollution etc. because we always desire less of such things.

• Indifference curves exhibit diminishing marginal rates of substitution
  • The marginal rate of substitution tells how much 'y' a person is willing to sacrifice to get one more unit of 'x'.
  • This assumption assures that indifference curves are smooth and convex to the origin.
  • This assumption also set the stage for using techniques of constrained optimization because the shape of the curve assures that the first derivative is negative and the second is positive.
  • Another name for this assumption is the substitution assumption. It is the most critical assumption of consumer theory: Consumers are willing to give up or trade-off some of one good to get more of another. The fundamental assertion is that there is a maximum amount that "a consumer will give up, of one commodity, to get one unit of another good, in that amount which will leave the consumer indifferent between the new and old situations" The negative slope of the indifference curves represents the willingness of the consumer to make a trade off.
• There are also many sub-assumptions:
  • Irreflexivity - for no x is xpx
  • Negative transitivity - if xnot-py then for any third commodity z, either xnot-pz or znot-py or both.