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'[[File:Average and marginal revenue.svg|thumb|right|Typical marginal revenue and average revenue (price) curves for a firm that is not in [[perfect competition]]]] In [[microeconomics]], '''marginal revenue''' (MR) is the additional revenue that will be generated by increasing product sales by 1 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 price the firm is able to charge the buyer of the good.<ref>Sullivan & Sheffrin (2003), p. 112.</ref><ref name="IntermediateMicro" /> 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="IntermediateMicro" /><ref name="Essentials" /> 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="IntermediateMicro" /><ref name="Essentials" /> Therefore the Marginal Revenue generated is always less (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="IntermediateMicro" /><ref name="Essentials" /> 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. <BR/> <BR/> == Definition == 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. This can also be represented as a derivative when the units of output are arbitrarily small. (Total revenue) = (Price that can be charged consistent with selling a given quantity) times (Quantity) or :<math>TR=P(Q) \cdot Q</math>. Thus, by the [[product rule]]: :<math>MR=\frac{dTR}{dQ}=\frac{dP}{dQ} \cdot Q + \frac{dQ}{dQ} \cdot P= Q \cdot \frac{dP}{dQ} + P.</math> For a firm facing perfectly competitive markets, price does not change with quantity sold (<math>\frac{dP}{dQ}=0</math>), so marginal revenue is equal to price. For a [[monopoly]], the price received will decline with quantity sold (<math>\frac{dP}{dQ}<0</math>), so marginal revenue is less than price. This means that the [[profit maximization|profit-maximizing]] quantity, for which marginal revenue is equal to [[marginal cost]] (MC) will be lower for a monopoly than for a competitive firm, while the profit-maximizing price will be higher. When demand is [[price elasticity of demand|elastic]], marginal revenue is positive, and when demand is inelastic, marginal revenue is negative. When the price elasticity of demand is equal to 1, marginal revenue is equal to zero. ==Marginal revenue curve== 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 MR curve to shift and rotate.<ref>Landsburg, S Price 2002. p. 137.</ref> ==Relationship between marginal revenue and elasticity== The relationship between marginal revenue and the elasticity of demand by the firm's customers can be derived as follows:<ref>Perloff (2008) p. 364.</ref> :MR = dTR/dQ :MR = P+Q(dP/dQ) :MR = P[1 + (dP/dQ) (Q/P)] :MR = P(1 + 1/PED) where PED is the price elasticity of demand. If demand is inelastic (PED < 1) then MR 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 (PED > 1) MR 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. ==Marginal revenue and rule of thumb pricing== Profit maximization requires that a firm produce 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. :MR = MC :MR = P(1 + 1/PED) :MC = P(1 + 1/PED) :MC = P + P/PED :(P - MC)/ P = - 1/PED<ref>Pindyck, R & Rubinfeld, D (2001) p. 334.</ref> 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>Pindyck, R & Rubinfeld, D (2001) p. 334.</ref>Alternatively, the relationship can be expressed as: :P = MC/(1 + 1/PED) Thus if PED is - 2 and MC is $5.00 then price is $10.00. (P - MC)/ P = - 1/PED 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"/> '''Real life example:''' if you can sell 10 units at $20 each or 11 units at $19 each, then your marginal revenue from the eleventh unit is (11 × 19) - (10 × 20) = $9. ==See also== * [[Cost curve]] * [[Profit maximization]] ==Notes== {{Reflist}} ==References== * Landsburg, S 2002 Price Theory & Applications, 5th ed. South-Western. * Perloff, J., 2008, Microeconomics: Theory & Applications with Calculus, Pearson. ISBN 978032127794 * Pindyck, R & Rubinfeld, D 2001: Microeconomics 5th ed. Page Prentice-Hall. ISBN 0-13-019673-8 * Samuelson & Marks, 2003 Managerial Economics 4th ed. Wiley * Sullivan, Arthur; Steven M. Sheffrin (2003). Economics: Principles in action. Pearson Prentice Hall. ISBN 0-13-063085-3. [[Category:Microeconomics]] [[Category:Marginal concepts]] [[Category:Economics terminology]] [[ar:إيراد حدي]] [[ca:Ingrés marginal]] [[de:Grenzerlös]] [[es:Ingreso marginal]] [[fr:Revenu marginal]] [[ko:한계 수입]] [[it:Ricavo marginale]] [[he:פדיון שולי]] [[hu:Határbevétel]] [[nl:Marginale opbrengst]] [[ja:限界収益]] [[pl:Przychód krańcowy]] [[pt:Renda marginal]] [[ru:Предельный доход]] [[sr:Маргинални приход]] [[sv:Marginalintäkt]] [[zh:边际收益/temp]]'