Final answer:
The Implicit Function Theorem suggests that in the vicinity of a suitable point, a function can be represented as an explicit function either of the form y = g(x) or x = h(y), depending on the application and the nature of the original function.
Step-by-step explanation:
Using the Implicit Function Theorem, we can conclude that a function f(x, y) can be locally described by the graph of explicit functions in some neighborhood of a point (a, b), assuming that partial derivatives exist and meet specific criteria at that point. By the theorem, if ∂f/∂y ≠ 0, we are guaranteed the existence of a function which can either be of the form y = g(x) or x = h(y), depending on the context of the problem and the function being considered. For instance, if we have a function of x and y which can be solved for y in terms of x near the point of interest, y = g(x) is a suitable form. Conversely, if it is more appropriate to solve for x in terms of y, then x = h(y) would be the valid form.
An implicit function is one where the relationship between the variables is not given in the standard form y=f(x), instead, the function is implied by an equation involving both x and y. When applying the Implicit Function Theorem, we typically look for regions where the function behaves nicely and can be described by such explicit functions. In economic models, this concept is essential, as mathematical functions often describe relationships or definitions within the model.