Search results
Results From The WOW.Com Content Network
Marginal cost and marginal revenue, depending on whether the calculus approach is taken or not, are defined as either the change in cost or revenue as each additional unit is produced or the derivative of cost or revenue with respect to the quantity of output. For instance, taking the first definition, if it costs a firm $400 to produce 5 units ...
In calculus, Rolle's theorem says that if a real-valued function f is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists a c in the open interval (a, b) such that f(c) is a maximum or a minimum and the gradient at x = c is zero, meaning f ′ (c) = 0.
Price and total revenue have a negative relationship when demand is elastic (price elasticity > 1), which means that increases in price will lead to decreases in total revenue. Price changes will not affect total revenue when the demand is unit elastic (price elasticity = 1). Maximum total revenue is achieved where the elasticity of demand is 1.
[1] [3] [8] The marginal revenue (the increase in total revenue) is the price the firm gets on the additional unit sold, less the revenue lost by reducing the price on all other units that were sold prior to the decrease in price. Marginal revenue is the concept of a firm sacrificing the opportunity to sell the current output at a certain price ...
The Lagrange multiplier theorem states that at any local maximum (or minimum) of the function evaluated under the equality constraints, if constraint qualification applies (explained below), then the gradient of the function (at that point) can be expressed as a linear combination of the gradients of the constraints (at that point), with the ...
The marginal profit per unit of labor equals the marginal revenue product of labor minus the marginal cost of labor or M π L = MRP L − MC L A firm maximizes profits where M π L = 0. The marginal revenue product is the change in total revenue per unit change in the variable input assume labor. [10] That is, MRP L = ∆TR/∆L.
The derivatives provide detailed information for such optimizers, but are even harder to calculate, e.g. approximating the gradient takes at least N+1 function evaluations. For approximations of the 2nd derivatives (collected in the Hessian matrix), the number of function evaluations is in the order of N².
If the domain X is a metric space, then f is said to have a local (or relative) maximum point at the point x ∗, if there exists some ε > 0 such that f(x ∗) ≥ f(x) for all x in X within distance ε of x ∗. Similarly, the function has a local minimum point at x ∗, if f(x ∗) ≤ f(x) for all x in X within distance ε of x ∗.