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[[File:Average and marginal revenue.svg|thumb|right|upright=2|Typical marginal revenue R' and average revenue (price) <R> curves for a firm that is not in [[perfect competition]]]] |
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In [[microeconomics]], '''marginal revenue''' (R') is the additional revenue that will be generated by increasing product sales by one unit.<ref name="Essentials">Bradley R. chiller, "Essentials of Economics", New York: McGraw-Hill, Inc., 1991.</ref><ref name="MicroTheory">Edwin Mansfield, "Micro-Economics Theory and Applications, 3rd Edition", New York and London:W.W. Norton and Company, 1979.</ref><ref name="IntermediateMicro">Roger LeRoy Miller, "Intermediate Microeconomics Theory Issues Applications, Third Edition", New York: McGraw-Hill, Inc, 1982.</ref><ref name="IndustrialOrg">Tirole, Jean, "The Theory of Industrial Organization", Cambridge, Massachusetts: The MIT Press, 1988.</ref><ref name="EconDictionary">John Black, "Oxford Dictionary of Economics", New York: Oxford University Press, 2003.</ref> It can also be described as the [[total revenue|unit revenue]] the last item sold has generated for the firm.<ref name="IntermediateMicro" /><ref name="EconDictionary" /> In a [[perfect competition|perfectly competitive]] market, the additional revenue generated by selling an additional unit of a good is equal to the price the firm is able to charge the buyer of the good.<ref name="IntermediateMicro" /><ref>O'Sullivan & Sheffrin (2003), p. 112.</ref> This is because a firm in a [[perfect competition|competitive market]] will always get the same price for every unit it sells regardless of the number of units the firm sells since the firm's sales can never impact the industry's price.<ref name="Essentials" /><ref name="IntermediateMicro" /> However, a [[monopoly]] determines the entire [[industry]]'s sales.<ref name="Essentials" /> As a result, it will have to lower the price of all units sold to increase sales by 1 unit.<ref name="Essentials" /><ref name="IntermediateMicro" /> Therefore, the marginal revenue generated is always lower than the price the firm is able to charge for the unit sold, since each reduction in price causes unit revenue to decline on every good the firm sells.<ref name="Essentials" /><ref name="IntermediateMicro" /> 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. |
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A firms profits will be maximized when marginal revenue (MR) equals [[Marginal cost|marginal cost (MC)]]. If <math>MR > MC</math> then a firm should increase output for more profits, if <math>MR < MC</math> then a firm should decrease output for additional profits. A firm should choose the output level which is profit maximizing under perfect competition theory <math>MR = MC</math>.<ref>{{Cite book|url=https://www.worldcat.org/oclc/432989728|title=Managerial economics : a strategic approach|last=David.|first=Prentice,|last2=1962-|first2=Waschik, Robert G.,|date=2010|publisher=Routledge|year=|isbn=9780415495172|location=|pages=33|oclc=432989728}}</ref> |
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== Definition == |
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Marginal revenue is equal to the ratio of the change in revenue for some change in quantity sold to that change in quantity sold. This can also be represented as a derivative when the change in quantity sold becomes arbitrarily small. More formally, define the revenue function to be the following |
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:<math>R(q)=P(q)\cdot q </math>. |
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By the [[product rule]], marginal revenue is then given by |
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:<math>R'(q)=P(q) + P'(q)\cdot q</math>. |
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For a firm facing perfect competition, price does not change with quantity sold (<math>P'(q)=0</math>), so marginal revenue is equal to price. For a [[monopoly]], the price decreases with quantity sold (<math>P'(q)<0</math>), so marginal revenue is less than price (for positive <math>q</math>). |
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==Marginal revenue curve== |
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The marginal revenue curve is affected by the same factors as the demand curve - changes in income, change in the prices of complements and substitutes, change in populations. These factors can cause the R curve to shift and rotate.<ref>Landsburg, S Price 2002. p. 137.</ref> |
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==Relationship between marginal revenue and elasticity== |
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The relationship between marginal revenue and the [[price elasticity of demand|elasticity of demand]] by the firm's customers can be derived as follows:<ref>Perloff (2008) p. 364.</ref> |
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:<math> R' = \frac{dR}{dQ} </math> |
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:<math> R' = \langle R \rangle + \left( \frac{d \langle R \rangle}{dQ} \right) Q </math> |
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:as <math> \langle R \rangle = P </math> |
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:<math> R' = \langle R \rangle \left[ 1 + \frac{d \langle R \rangle}{dQ} \frac{Q}{\langle R \rangle} \right] </math> |
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:<math> R' = \langle R \rangle (1 + 1 / e_{\langle R \rangle})</math> |
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where e is the [[price elasticity of demand]]. If demand is inelastic (e<sub><R></sub> < 1) then R' will be negative, because to sell a marginal (infinitesimal) unit the firm would have to lower the selling price so much that it would lose more revenue on the pre-existing units than it would gain on the incremental unit. If demand is elastic (e<sub><R></sub> > 1) R' will be positive, because the additional unit would not drive down the price by so much. If the firm is a perfect competitor, so that it is so small in the market that its quantity produced and sold has no effect on the price, then the price elasticity of demand is negative infinity, and marginal revenue simply equals the (market-determined) price. |
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==Marginal revenue and rule-of-thumb pricing== |
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Profit maximization requires that a firm produces where marginal revenue equals marginal costs. Firm managers are unlikely to have complete information concerning their marginal revenue function or their marginal costs. Fortunately, the profit maximization conditions can be expressed in a “more easily applicable form” or rule of thumb. |
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:R' = C' |
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:R' = <R>(1 + 1/e<sub><R></sub>) |
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:MC = <R>(1 + 1/e<sub><R></sub>) |
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:MC = <R> + <R>/e<sub><R></sub> |
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:(<R> - C')/ <R> = - 1/e<sub><R></sub><ref name="Pindyck, R 2001 p. 334">Pindyck, R & Rubinfeld, D (2001) p. 334.</ref> |
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Markup is the difference between price and marginal cost. The formula states that markup as a percentage of price equals the negative of the inverse of elasticity of demand.<ref name="Pindyck, R 2001 p. 334"/> Alternatively, the relationship can be expressed as: |
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:<R> = C'/(1 + 1/e<sub><R></sub>) |
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Thus if e<sub><R></sub> is - 2 and mc is $5.00 then price is $10.00. |
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(<R> - C')/ <R> = - 1/e<sub><R></sub> is called the Lerner index after economist Abba Lerner.<ref name="Perloff">Perloff (2008) p. 371.</ref> The Lerner index is a measure of market power - the ability of a firm to charge a price that exceeds marginal cost. The index varies from zero to 1. The greater the difference between price and marginal cost the closer the index value is to 1. The Lerner index increases as demand becomes less elastic.<ref name="Perloff"/> |
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'''Example''' |
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If a company can sell 10 units at $20 each or 11 units at $19 each, then the marginal revenue from the eleventh unit is (11 × 19) - (10 × 20) = $9. |
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==See also== |
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{{Portal|Economics}} |
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* [[Cost curve]] |
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* [[Profit maximization]] |
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==Notes== |
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{{Reflist}} |
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==References== |
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* Landsburg, S 2002 Price Theory & Applications, 5th ed. South-Western. |
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* Perloff, J., 2008, Microeconomics: Theory & Applications with Calculus, Pearson. {{ISBN|9780321277947}} |
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* Pindyck, R & Rubinfeld, D 2001: Microeconomics 5th ed. Page Prentice-Hall. {{ISBN|0-13-019673-8}} |
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* Samuelson & Marks, 2003 Managerial Economics 4th ed. Wiley |
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* O'Sullivan, Arthur; Sheffrin, Steven M. (2003). Economics: Principles in Action. Pearson Prentice Hall. {{ISBN|0-13-063085-3}}. |
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[[Category:Revenue]] |
[[Category:Revenue]] |
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[[Category:Marginal concepts]] |
[[Category:Marginal concepts]] |
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