Example. Essential and substitutable expertise give different restrictions [ftip-00ON]
Example. Essential and substitutable expertise give different restrictions [ftip-00ON]
Let \(H,M\geq 0\) denote usable human and machine expertise. Under perfect substitution, effective expertise is \(E=H+\chi M\) with \(\chi >0\). The productive requirement \(E\geq E_{\min }>0\) is satisfied with \(H=0\) whenever \(M\geq E_{\min }/\chi \). Under essential complementarity, take \(E=\min \{H,\chi M\}\) instead. Then \(E\geq E_{\min }\) implies \(H\geq E_{\min }\). Both claims follow directly from the definitions.
A human-stock floor can therefore represent either an explicit social constraint or an indispensable productive input. The latter interpretation requires a complementarity premise. An economic model does not prove biological exclusivity merely by naming one coordinate human expertise. The organization and substitution of knowledge also depend on communication and access, as modeled by Ide and Talamàs.