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A curve connecting the tangency points is called the expansion path because it shows how the input usages expand as the chosen level of output expands. In economics , an expansion path (also called a scale line [ 1 ] ) is a path connecting optimal input combinations as the scale of production expands. [ 2 ]
An expansion, [6] which converges more rapidly for all real values of x than a Taylor expansion, is obtained by using Hans Heinrich Bürmann's theorem: [7] = (() () ()) = (+ =). where sgn is the sign function.
This condition makes sense: at a particular input combination, if an extra dollar spent on input 1 yields more output than an extra dollar spent on input 2, then more of input 1 should be used and less of input 2, and so that input combination cannot be optimal. Only if a dollar spent on each input is equally productive is the input bundle optimal.
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
When G is d-regular, a linear algebraic definition of expansion is possible based on the eigenvalues of the adjacency matrix A = A(G) of G, where A ij is the number of edges between vertices i and j. [5] Because A is symmetric, the spectral theorem implies that A has n real-valued eigenvalues λ 1 ≥ λ 2 ≥ … ≥ λ n.
An isoquant (derived from quantity and the Greek word isos, ίσος, meaning "equal"), in microeconomics, is a contour line drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more inputs.
Extensive growth, in economics, is growth in the quantity of output produced based on the expansion of the quantity of inputs used.It contrasts with intensive growth, which arises from inputs being used more productively.
Negative testing is done to check that the product deals properly with the circumstance for which it is not programmed. The fundamental aim of this testing is to check how bad data is taken care of by the systems, and appropriate errors are shown to the client when bad data is entered. Both positive and negative testing play an important role.