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  2. Implicit function theorem - Wikipedia

    en.wikipedia.org/wiki/Implicit_function_theorem

    The unit circle can be specified as the level curve f(x, y) = 1 of the function f(x, y) = x 2 + y 2.Around point A, y can be expressed as a function y(x).In this example this function can be written explicitly as () =; in many cases no such explicit expression exists, but one can still refer to the implicit function y(x).

  3. Implicit function - Wikipedia

    en.wikipedia.org/wiki/Implicit_function

    An implicit function is a function that is defined by an implicit equation, that relates one of the variables, considered as the value of the function, with the others considered as the arguments. [ 1 ] : 204–206 For example, the equation x 2 + y 2 − 1 = 0 {\displaystyle x^{2}+y^{2}-1=0} of the unit circle defines y as an implicit function ...

  4. Comparative statics - Wikipedia

    en.wikipedia.org/wiki/Comparative_statics

    Comparative statics results are usually derived by using the implicit function theorem to calculate a linear approximation to the system of equations that defines the equilibrium, under the assumption that the equilibrium is stable.

  5. Topkis's theorem - Wikipedia

    en.wikipedia.org/wiki/Topkis's_Theorem

    This example will show how using Topkis's theorem gives the same result as using more standard tools. The advantage of using Topkis's theorem is that it can be applied to a wider class of problems than can be studied with standard economics tools. A driver is driving down a highway and must choose a speed, s. Going faster is desirable, but is ...

  6. Monotone comparative statics - Wikipedia

    en.wikipedia.org/wiki/Monotone_comparative_statics

    Traditionally, comparative results in economics are obtained using the Implicit Function Theorem, an approach that requires the concavity and differentiability of the objective function as well as the interiority and uniqueness of the optimal solution. The methods of monotone comparative statics typically dispense with these assumptions.

  7. Economic model - Wikipedia

    en.wikipedia.org/wiki/Economic_model

    For example, inflation is a general economic concept, ... Regarding x as an implicitly defined function of t by this equation (see implicit function theorem), ...

  8. Another 1 million not deported because Biden granted ...

    www.aol.com/news/another-1-million-not-deported...

    For example, on Oct. 11, DHS extended TPS status to illegal foreign nationals from El Salvador, Honduras, Nepal, Nicaragua, and Sudan through March 9, 2025. Those registered through the program ...

  9. Function of several real variables - Wikipedia

    en.wikipedia.org/wiki/Function_of_several_real...

    The implicit function theorem of more than two real variables deals with the continuity and differentiability of the function, as follows. [4] Let ϕ(x 1, x 2, …, x n) be a continuous function with continuous first order partial derivatives, and let ϕ evaluated at a point (a, b) = (a 1, a 2, …, a n, b) be zero: