Abstract
We now construct a generalization of the notions studied in the previous chapters. Consider some set \(\mathcal{L}\) of elements \(\mathbf{x},\mathbf{y},\mathbf{z},\ldots \). We call \(\mathcal{L}\) a linear space
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Notes
- 1.
In mathematics, a space is an abstract set of points with some additional structure. Mathematical spaces are often considered as models for real physical spaces. In addition to linear spaces, there are so-called Euclidean spaces, metric spaces, topological spaces and many others.
- 2.
Although widely used in economics, constant returns to scale assumption does not correspond to reality in many instances. It has been observed, particularly in manufacturing industry, that as the scale of production increases per unit input requirements may decline. This is the case of ‘increasing returns to scale’.
On the other hands, in some instances, production may also be subject to ‘decreasing returns to scale’. Such phenomenon is observed in agriculture and occasionally in ‘oversized enterprises’.
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© 2011 Springer-Verlag Berlin Heidelberg
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Aleskerov, F., Ersel, H., Piontkovski, D. (2011). Linear Spaces. In: Linear Algebra for Economists. Springer Texts in Business and Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20570-5_6
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DOI: https://doi.org/10.1007/978-3-642-20570-5_6
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