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Paul Douglas explained that his first formulation of the Cobb–Douglas production function was developed in 1927; when seeking a functional form to relate estimates he had calculated for workers and capital, he spoke with mathematician and colleague Charles Cobb, who suggested a function of the form Y = AL β K 1−β, previously used by Knut Wicksell, Philip Wicksteed, and Léon Walras ...
The marginal product of capital (MPK) is the additional output resulting, ceteris paribus ("all things being equal"), from the use of an additional unit of physical capital, such as machines or buildings used by businesses. The marginal product of capital (MPK) is the amount of extra output the firm gets from an extra unit of capital, holding ...
The Modigliani–Miller theorem (of Franco Modigliani, Merton Miller) is an influential element of economic theory; it forms the basis for modern thinking on capital structure. [1] The basic theorem states that in the absence of taxes, bankruptcy costs, agency costs, and asymmetric information, and in an efficient market, the enterprise value ...
Zero to the power of zero. Zero to the power of zero, denoted by 00, is a mathematical expression that is either defined as 1 or left undefined, depending on context. In algebra and combinatorics, one typically defines 00 = 1. In mathematical analysis, the expression is sometimes left undefined. Computer programming languages and software also ...
Powers of a number with absolute value less than one tend to zero: b n → 0 as n → ∞ when | b | < 1. Any power of one is always one: b n = 1 for all n if b = 1. Powers of –1 alternate between 1 and –1 as n alternates between even and odd, and thus do not tend to any limit as n grows.
Remark: The above proof continues to work if is replaced by any prime with {,, …,}, the product becomes + and even vs. odd argument is replaced with a divisible vs. not divisible by argument. The resulting contradiction is that P − p j {\displaystyle P-p_{j}} must, simultaneously, equal 1 {\displaystyle 1} and be greater than 1 ...
Proof of work. Proof of work ( PoW) is a form of cryptographic proof in which one party (the prover) proves to others (the verifiers) that a certain amount of a specific computational effort has been expended. [1] Verifiers can subsequently confirm this expenditure with minimal effort on their part.
Marginal cost (MC) is the change in total cost per unit change in output or ∆ C /∆ Q. In the short run, production can be varied only by changing the variable input. Thus only variable costs change as output increases: ∆ C = ∆ VC = ∆ ( wL ). Marginal cost is ∆ ( Lw )/∆ Q. Now, ∆ L /∆ Q is the reciprocal of the marginal product ...