bradybrahmavihara

Let a, b, and c be bundles (vectors) of goods, such as (x, y) combinations above, with possibly different quantities of each respective good in the different bundles. The first assumption is necessary for a well-defined representation of stable preferences for the consumer as agent; the second assumption is convenient.

Rationality (called an ordering relationship in a more general mathematical context): Completeness + transitivity. For given preference rankings, the consumer can choose the best bundle(s) consistently among a, b, and c from lowest on up.

Continuity: This means that you can choose to consume any amount of the good. For example, I could drink 11 mL of soda, or 12 mL, or 132 mL. I am not confined to drinking 2 liters or nothing. See also continuous function in mathematics.

Of the remaining properties above, suppose, property (5) (convexity) is violated by a bulge of the indifference curves out from the origin for a particular consumer with a given budget constraint. Consumer theory then implies zero consumption for one of the two goods, say good Y, in equilibrium on the consumer's budget constraint. This would exemplify a corner solution. Further, decreases in the price of good Y over a certain range might leave quantity demanded unchanged at zero beyond which further price decreases switched all consumption and income away from X and to Y. The eccentricity of such an implication suggests why convexity is typically assumed.



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