Abstract
The importance of convexity of preferences and technology to many of the fundamental propositions of neoclassical economics, both positive and normative, is evidenced by scores if not hundreds of essays in this Dictionary. Two such propositions will suffice here. In general equilibrium theory the existence of competitive equilibrium is obtained by applying Brouwer’s fixed point theorem or one of its extensions, each of which depends upon a suitable convex-valued mapping of a convex set to itself. In welfare economics, the one-to-one nature of Edgeworth–Pareto optimality and competitive equilibrium is assured by the Theorem of the Supporting Hyperplane applied to an appropriate convex set.
This chapter was originally published in The New Palgrave: A Dictionary of Economics, 1st edition, 1987. Edited by John Eatwell, Murray Milgate and Peter Newman
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Newman, P. (1987). Convexity. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95121-5_565-1
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DOI: https://doi.org/10.1057/978-1-349-95121-5_565-1
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