If there are two goods, if a consumer prefers more of each good to less, and if she has a diminishing marginal rate of substitution, then her preferences are convex.

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This statement is a key assumption of convex preferences, which state that the consumer is willing to give up a decreasing amount of one good in exchange for increasing amounts of the other good. This is known as a diminishing marginal rate of substitution, and it leads to a convex-shaped indifference curve.

If There Are Two Goods, If a Consumer Prefers More