Abstract
Models in economic analysis often assume sets or functions are convex. These convexity properties make solutions of optimization problem analytically convenient.
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Notes
- 1.
In the context of consumer theory y is replaced by a given utility level u and C is often called an expenditure function.
- 2.
An exception is the Leontief production function, \(f(\mathbf {x})=\min \{x_{1}/a_{1}, \ldots , x_{n}/a_{n}\}\), where a 1, …, a n > 0. In this case \(\nabla ^{2}_{\mathbf {p}}C(\mathbf {p}, y)\) is a zero matrix. Note that f is not differentiable in this case.
References
Carter, M. (2001). Foundations of mathematical economics. Cambridge: The MIT Press.
Rockafellar, R. T. (1970). Convex analysis. Princeton: Princeton University Press.
Starr, R. M. (2008). Shapley-Folkman theorem. The new Palgrave dictionary of economics, Second Edition. Houndmills: Palgrave Macmillan.
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Yu, K. (2019). Convex Analysis. In: Mathematical Economics. Springer Texts in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-030-27289-0_6
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DOI: https://doi.org/10.1007/978-3-030-27289-0_6
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