Convexity is ubiquitous in economics, whether in financial modeling—the changes in capital, the value of an annuity, the dependence of a bond's price on the interest rate—or in other areas of microeconomics and macroeconomics. How can it be used to model consumer preferences? By introducing a relational structure for preferences...
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What do we mean by convexity?
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Ask a high-school student, "What is a convex function?", and they will very likely reply, "a function whose second derivative is positive", or make a gesture tracing the shape of a smile. Convexity does not depend on differentiability (for twice-differentiable functions, however, the first answer is relevant), while the gestured answer comes closer to the intrinsic definition.
