How are elasticity of demand, marginal revenue, and total revenue connected? - Economics Stack Exchange most recent 30 from economics.stackexchange.com 2019-07-23T06:51:54Z https://economics.stackexchange.com/feeds/question/17617 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://economics.stackexchange.com/q/17617 0 How are elasticity of demand, marginal revenue, and total revenue connected? Nora https://economics.stackexchange.com/users/14037 2017-07-28T08:38:06Z 2017-07-28T09:53:48Z <p>I am completely new to economics, and am looking at some old exam papers. The question is as following:</p> <p>"<em>In a normal marked, where there is a negative correlation between quantity and price, which of the following are true for elasticity of demand, marginal revenue, and total revenue?</em>"</p> <p><strong>The correct alternative was:</strong></p> <p><strong>d)</strong> When the absolute value of elasticity is 1, the marginal revenue is 0, and total revenue is maximized </p> <p><strong>I was wondering:</strong> </p> <p>Why is the total revenue maximized when marginal revenue is 0? I know that, usually, total revenue is maximized when marginal revenue = marginal cost. In this case, however, no information is given about the marginal cost, so it does not make sense to me that it should be 0. </p> <p>Also, is the marginal revenue always 0, when elasticity is exactly equal to 1? How does that make sense?</p> https://economics.stackexchange.com/questions/17617/-/17618#17618 1 Answer by EnergyNumbers for How are elasticity of demand, marginal revenue, and total revenue connected? EnergyNumbers https://economics.stackexchange.com/users/44 2017-07-28T09:53:48Z 2017-07-28T09:53:48Z <p>Marginal cost is irrelevant to total revenue. It's relevant to profit, but not total revenue.</p> <p>Total revenue is just price x quantity.</p> <p>Marginal revenue is a monotonic decreasing function. That is, as quantity increases, marginal revenue decreases. So, let's take the quantity Q to be the point at which marginal revenue is zero.</p> <p>For quantities below Q, marginal revenue is positive, so total revenue increases with quantity.</p> <p>For quantities above Q, marginal revenue is negative, so total revenue decreases with quantity.</p> <p>Hence Q is the turning point of the curve: it is the point of maximum total revenue.</p> <p>Elasticity of 1 means that a tiny % change, $\Delta$ in price in one direction (equivalent to multiplying price by $1+\Delta$), will be met by a reciprocal proportional change in quantity in the other direction, equivalent to multipying it by $\frac{1}{1+\Delta}$: that's straight from the definition of elasticity. </p> <p>So total revenue, the product of price and quantity, remains the same:</p> <p>$$(1+\Delta) P \times \frac{1}{(1+\Delta)} Q = P \times Q$$</p> <p>Hence marginal revenue always 0, when elasticity is exactly equal to 1.</p>