point on I1. A negative slope and transitivity exclude indifference curves crossing, since straight lines from the origin on both sides of where they crossed would give opposite and intransitive preference rankings. (Strictly) convex. With (2), convex preferences imply that the indifference curves cannot be concave to the origin, i.e. they will either be straight lines or bulge toward the origin of the indifference curve. If the latter is the case, then as a consumer decreases consumption of one good in successive units, successively larger doses of the other good are required to keep satisfaction unchanged. 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, formally written as A p B B is preferred to A, formally written as B p A A is indifferent to B, formally written as A I B This axiom precludes the possibility that the consumer cannot decide, It assumes that a consumer is able to make this comparison with respect to every conceivable bundle of goods. Preferences are reflexive This means that if A and B are identical in all respects 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 if 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 sufficiently close to B then A is preferred to C. A p B and C → B ⇒ A p C. "Continuous" means infinitely divisible - just like there are infinitely many 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 requires that if A and B have the same quantity of one good, but A has more