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In microeconomics, marginal profit is the increment to profit resulting from a unit or infinitesimal increment to the quantity of a product produced. Under the marginal approach to profit maximization , to maximize profits, a firm should continue to produce a good or service up to the point where marginal profit is zero.
= economic profit. Profit maximization means that the derivative of with respect to Q is set equal to 0: ′ + ′ = where P'(Q) = the derivative of the inverse demand function. C'(Q) = marginal cost–the derivative of total cost with respect to output.
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 ...
The marginal revenue function has twice the slope of the inverse demand function. [9] The marginal revenue function is below the inverse demand function at every positive quantity. [10] The inverse demand function can be used to derive the total and marginal revenue functions. Total revenue equals price, P, times quantity, Q, or TR = P×Q ...
In economics, calculus allows for the determination of maximal profit by calculating both marginal cost and marginal revenue, as well as modeling of markets. [ 5 ] In signal processing and machine learning, discrete calculus allows for appropriate definitions of operators (e.g., convolution), level set optimization and other key functions for ...
Under certain assumptions, the production function can be used to derive a marginal product for each factor. The profit-maximizing firm in perfect competition (taking output and input prices as given) will choose to add input right up to the point where the marginal cost of additional input matches the marginal product in additional output.
The marginal cost can also be calculated by finding the derivative of total cost or variable cost. Either of these derivatives work because the total cost includes variable cost and fixed cost, but fixed cost is a constant with a derivative of 0.
Calculus can be applied to understand how quickly a drug is eliminated from a body or how quickly a cancerous tumor grows. [65] In economics, calculus allows for the determination of maximal profit by providing a way to easily calculate both marginal cost and marginal revenue. [66]: 387