ECO 3145 Lecture 3: Lecture 3.pdf

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Y is explicitly expressed as a function of the x"s: general function. We say that the equation defines a general-function relationship between y and the x"s strictly speaking it is the left-hand side which is the function. ; i. e. if it is possible to isolate y from all other variables. If yes, does the implicit function have a closed-form solution?1 i. ) ii. ) iii. ) iv. ) comments: notice the importance of specifying the domain of the general function (domain and range of the implicit function) 1 see gabriel archinard and bernard guerrien, analyse math matique pour conomistes 3e dition (paris : Economica, 1988), p. 301 for a discussion of equation (iv. Implicit function theorem: the case of a single equation: the problem the possibility that an implicit function may exist but not have a closed-form solution presents particular challenges the following questions are relevant in this context: i. )

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