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Convexity is an important topic in economics. [1] In the Arrow–Debreu model of general economic equilibrium, agents have convex budget sets and convex preferences: At equilibrium prices, the budget hyperplane supports the best attainable indifference curve. [2] The profit function is the convex conjugate of the cost function.
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The Bank (2001) – A mathematician discovers a formula to predict fluctuations in the stock market. Cube (1997) – Six people, including Leaven, a math student, awake in a deathtrap based on mathematical principles. Fermat's Room (2007) – Three mathematicians and one inventor are invited to a house under the premise of solving a great ...
Non-convexity (economics) is included in the JEL classification codes as JEL: C65. In economics, non-convexity refers to violations of the convexity assumptions of elementary economics. Basic economics textbooks concentrate on consumers with convex preferences (that do not prefer extremes to in-between values) and convex budget sets and on ...
Jan 1, 2017 · Convexity is a property of real vector spaces, and its domain of application in economic analysis is not just Euclidean spaces but also the infinite dimensional vector spaces which arise in the study of uncertainty and dynamics, where infinite numbers of goods are required. Nonetheless, this brief exposition will be confined to Euclidean spaces.
- Lawrence E. Blume
A function with this property is said to be concave concave function A function of two variables for which the line segment between any two points on the function lies entirely below the curve representing the function (the function is convex when the line segment lies above the function). . An implication of concavity (and its algebraic ...
Definitions. The twin notions of concavity and convexity are used widely in economic theory, and are also central to optimization theory. A function of a single variable is concave if every line segment joining two points on its graph does not lie above the graph at any point. Symmetrically, a function of a single variable is convex if every ...
