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Non‑convex sets have been incorporated in the theories of general economic equilibria, [2] of market failures, [3] and of public economics. [4] These results are described in graduate-level textbooks in microeconomics, [5] general equilibrium theory, [6] game theory, [7] mathematical economics, [8] and applied mathematics (for economists). [9]
Shephard's lemma is a result in microeconomics having applications in the theory of the firm and in consumer choice. [1] The lemma states that if indifference curves of the expenditure or cost function are convex, then the cost-minimizing point of a given good with price is unique.
Coquille board, also known as stipple board, is a type of drawing paper with a pebbled texture. The grain is impressed into the uncoated paper during manufacture. [ 1 ] Used with a soft lithographic crayon or carbon pencil , coquille produces a shading effect similar to hand stippling in a fraction of the time. [ 2 ]
In zero dimensions there is only the zero vector, while in one dimension all vectors are parallel, so in both these cases the product must be identically zero. The restriction to 0, 1, 3 and 7 dimensions is related to Hurwitz's theorem, that normed division algebras are only possible in 1, 2, 4 and 8 dimensions. The cross product is formed from ...
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics.Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods.
In econometrics, the equations of a structural form model are estimated in their theoretically given form, while an alternative approach to estimation is to first solve the theoretical equations for the endogenous variables to obtain reduced form equations, and then to estimate the reduced form equations. Let Y be the vector of the variables to ...
The vector triple product is defined as the cross product of one vector with the cross product of the other two. The following relationship holds: The following relationship holds: a × ( b × c ) = ( a ⋅ c ) b − ( a ⋅ b ) c {\displaystyle \mathbf {a} \times (\mathbf {b} \times \mathbf {c} )=(\mathbf {a} \cdot \mathbf {c} )\mathbf {b ...
Econophysics is a non-orthodox (in economics) interdisciplinary research field, applying theories and methods originally developed by physicists in order to solve problems in economics, usually those including uncertainty or stochastic processes and nonlinear dynamics.