When the mathematical concept of genericity was arrived at in economics, it was meant more or less as a synonym for generality. Referring to constant return production economies, we will argue that this is not always the case. In particular, the representation of technology that is mathematically generic is not at all general for economists. We will see that in cases that are economically general, but not mathematically generic, activity-level indeterminacy may occur. In these cases, Kehoe’s index theorem, a well-known result of the application of the differentiable approach to production economies, becomes unusable.
Fratini, S.M. (2008). ECONOMIC GENERALITY VERSUS MATHEMATICAL GENERICITY: ACTIVITY-LEVEL INDETERMINACY AND THE INDEX THEOREM IN CONSTANT RETURNS PRODUCTION ECONOMIES. METROECONOMICA, 59(2), 266-275 [10.1111/j.1467-999X.2007.00305.x].
ECONOMIC GENERALITY VERSUS MATHEMATICAL GENERICITY: ACTIVITY-LEVEL INDETERMINACY AND THE INDEX THEOREM IN CONSTANT RETURNS PRODUCTION ECONOMIES
FRATINI, SAVERIO MARIA
2008-01-01
Abstract
When the mathematical concept of genericity was arrived at in economics, it was meant more or less as a synonym for generality. Referring to constant return production economies, we will argue that this is not always the case. In particular, the representation of technology that is mathematically generic is not at all general for economists. We will see that in cases that are economically general, but not mathematically generic, activity-level indeterminacy may occur. In these cases, Kehoe’s index theorem, a well-known result of the application of the differentiable approach to production economies, becomes unusable.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
