Editing Marginal revenue (section)

==Relationship between marginal revenue and elasticity==
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><ref name=":2">{{Cite web|date=2020-02-27|title=3.3: Marginal Revenue and the Elasticity of Demand|url=https://socialsci.libretexts.org/Bookshelves/Economics/Book%3A_The_Economics_of_Food_and_Agricultural_Markets_(Barkley)/03%3A_Monopoly_and_Market_Power/3.03%3A_Marginal_Revenue_and_the_Elasticity_of_Demand|access-date=2020-10-27|website=Social Sci LibreTexts|language=en}}</ref><ref name=":3">{{Cite web|last=Rekhi|first=Samia|date=2016-05-16|title=Marginal Revenue and Price Elasticity of Demand|url=https://www.economicsdiscussion.net/price-elasticity/marginal-revenue-and-price-elasticity-of-demand/19728|access-date=2020-10-27|website=Economics Discussion|language=en-US}}</ref>

:<math>R=P(Q)\cdot Q,</math>
:Taking the first order derivative of total revenue: 
:<math>\left ( \frac{dR}{dQ} \right )= \left ( \frac{dQ}{dQ} \right )\cdot P  + \left ( \frac{dP}{dQ} \right ) \cdot Q</math>

:<math>MR = dR/dQ = P + \frac{dP}{dQ} \cdot Q = P + \left(\frac{dP}{dQ} \frac{Q}{P}\right) \cdot P = P \cdot \left(1 + \frac{1}{e} \right),</math>

where ''R'' is total revenue, ''P''(''Q'') is the inverse of the demand function, and ''e'' < 0 is the [[price elasticity of demand]] written as <math>e = \left(\frac{dQ}{dP}\frac{P}{Q}\right)</math>.<ref name=":2" />

Monopolist firm, as a price maker in the market, has the incentives to lower prices to boost quantities sold.<ref name=":1" /> The price effects occur when a firm raises its products' prices and increased revenue on each unit sold. The quantity effect, on the other hand, describes the stage when prices increased and consumers quantity demanded reduce. Firms' pricing decision, therefore, is based on the tradeoff between the two outcomes by considering elasticity.<ref>{{Cite book |author=Paul Krugman |author2=Robin Wells |author3=Iris Au |author4=Jack Parkinson |title=Microeconomics |date=2013 |publisher=Worth Publishers |isbn=978-1-4292-4005-5 |edition=3rd |location=New York |oclc=796082268}}</ref>

When a monopolist firm is facing an [[Inelastic demand]] curve (e<1), it implies that a percentage change in quantity is less than the percentage change in price. By increasing quantity sold, the firm is forced to accept a reduction of price for all the current and previous production units,<ref name=":7" /> resulting in a negative marginal revenue (MR). As such, as consumers are less sensitive and responsive to lower prices movement and so the expected product sales boost is highly unlikely and firms lose more profits due to reduction in marginal revenue. A rational firm will have to maintain its current price levels instead or increase the price for profit expansion.<ref name=":2" /><ref name=":4">{{Cite book |author=Pemberton, Malcolm |author2=Rau, Nicholas |title=Mathematics for economists : an introductory textbook |date=2011 |publisher=Manchester University Press |isbn=978-0-7190-8705-9 |edition=3rd |location=Manchester |oclc=756276243}}</ref><ref name=":5">{{Cite web|title=Leibniz: The elasticity of demand|url=http://www.core-econ.org/the-economy/book/text/leibniz-07-08-01.html|access-date=2020-10-27|website=www.core-econ.org|language=en}}</ref>

Increases in consumer's responsiveness to small changes in prices leads represents an elastic demand curve (e>1), resulting in a positive marginal revenue (MR) under monopoly competition. This signifies that a percentage change in quantity outweighs the percentage change in price. Firms in the imperfect competition market that lower prices by a small portion benefit from a large percentage increase in quantity sold and this generates greater marginal revenue. With that, a rational firm will recognize the value of price effects under an elastic demand function for its products and would avoid increasing prices as the quantity (demand) lost would be amplified due to the elastic demand curve.<ref name=":2" /><ref name=":4" /><ref name=":5" />

If the firm is a perfect competitor, where quantity produced and sold has no effect on the market price, then the price elasticity of demand is negative infinity and marginal revenue simply equals the (market-determined) price <math>(MR = P)</math>.<ref name=":2" /><ref name=":5" />

Therefore, it is essential to be aware of the elasticity of demand. A monopolist prefers to be on the more elastic end of the demand curve in order to gain a positive marginal revenue. This shows that a monopolist reduces output produced up to the point where marginal revenue is positive.<ref name=":2" /><ref name=":3" />