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Marginal revenue

 
Sci-Tech Dictionary: marginal revenue
(′mär·jən·əl ′rev·ə′nü)

(industrial engineering) The extra revenue achieved by selling an extra unit of output.


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Financial & Investment Dictionary: Marginal Revenue
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Change in total revenue caused by one additional unit of output. It is calculated by determining the difference between the total revenues produced before and after a one-unit increase in the rate of production. As long as the price of a product is constant, price and marginal revenue are the same; for example, if baseball bats are being sold at a constant price of $10 apiece, a one-unit increase in sales (one baseball bat) translates into an increase in total revenue of $10. But it is often the case that additional output can be sold only if the price is reduced, and that leads to a consideration of Marginal Cost-the added cost of producing one more unit. Further production is not advisable when marginal cost exceeds marginal revenue since to do so would result in a loss. Conversely, whenever marginal revenue exceeds marginal cost, it is advisable to produce an additional unit. Profits are maximized at the rate of output where marginal revenue equals marginal cost.

Wikipedia: Marginal revenue
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In microeconomics, Marginal Revenue (MR) is the extra revenue that an additional unit of product will bring. It is the additional income from selling one more unit of a good; sometimes equal to price.[1] It can also be described as the change in total revenue/change in number of units sold.

More formally, marginal revenue is equal to the change in total revenue over the change in quantity when the change in quantity is equal to one unit (or the change in output in the bracket where the change in revenue has occurred)

This can also be represented as a derivative. (Total revenue) = (Price Demanded) times (Quantity) or TR=P \cdot Q. Thus, by the product rule:

MR=\frac{dTR}{dQ}=\frac{dP}{dQ} \cdot Q + \frac{dQ}{dQ} \cdot P=P + Q \cdot \frac{dP}{dQ}.

For a firm facing perfectly competitive markets, price does not change with quantity sold (\frac{dP}{dQ}=0), so marginal revenue is equal to price. For a monopoly, the price received will decline with quantity sold (\frac{dP}{dQ}<0), so marginal revenue is less than price. This means that the profit-maximizing quantity, for which marginal revenue is equal to marginal cost will be lower for a monopoly than for a competitive firm, while the profit-maximizing price will be higher. When marginal revenue is positive, Price elasticity of demand [PED] is elastic, and when it is negative, PED is inelastic. When marginal revenue is equal to zero, price elasticity of demand is equal to -1.

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Maximizing profits using MR

Regardless of market structure firm maximized profit by producing where MR = MC. There are exceptions. If variable costs are zero or nominal the firm should seek to maximize revenue rather than follow the profit-max rule (MR = MC). For examples of pure pricing circumstance see Samuelson $ Marks, Managerial Economics 4th ed. (Wiley 2003) at 100.

Example

Assume the inverse demand function has the form P = 120 - .5Q. [2]Total revenue equals price times quantity. Multiplying the inverse demand function by Q to derive the total revenue function gives: TR = (120 - 0.5Q) x Q = 120Q - 0.5Q². The marginal revenue function is the first derivative of the total revenue function or MR = 120 - Q. Note that the MR function has the same y-intercept as the inverse demand function, the x-intercept of the MR function is one-half the value of the inverse demand function and the slope of the MR function is twice that of the inverse demand function. This relationship holds true for all linear demand equations. The importance of being able to quickly calculate MR is that the profit maximizing conditions for firms regardless of market structure is to produce where marginal revenue equals marginal cost. To derive MC you take the first derivative of the total cost function. then equate MR to MC and solve for Q. Thus assume that the firm's cost function is C = 420 +60Q + Q2[3]. The first derivative of the cost function is MC = 60 +2Q. Equating MR and MC gives: 120 - Q = 60 +2Q. Solving for Q - Q = 20. to find the profit maximizing price simply plug Q into the price equation: P = 120 -.5Q = 120 = .5(20) = 120 - 10 = 110.

References

  1. ^ Sullivan, Arthur; Steven M. Sheffrin (2003). Economics: Principles in action. Upper Saddle River, New Jersey 07458: Pearson Prentice Hall. pp. 112. ISBN 0-13-063085-3. http://www.pearsonschool.com/index.cfm?locator=PSZ3R9&PMDbSiteId=2781&PMDbSolutionId=6724&PMDbCategoryId=&PMDbProgramId=12881&level=4. 
  2. ^ Samuelson & Marks, Managerial Economics 4th ed. (Wiley 2003) at 57.
  3. ^ Samuelson & Marks, Managerial Economics 4th ed. (Wiley 2003) at 57

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Sci-Tech Dictionary. McGraw-Hill Dictionary of Scientific and Technical Terms. Copyright © 2003, 1994, 1989, 1984, 1978, 1976, 1974 by McGraw-Hill Companies, Inc. All rights reserved.  Read more
Financial & Investment Dictionary. Dictionary of Finance and Investment Terms. Copyright © 2006 by Barron's Educational Series, Inc. All rights reserved.  Read more
Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Marginal revenue" Read more