In economics, the total revenue test is a means for determining whether demand is elastic or inelastic. If an increase in price causes an increase in total revenue, then demand can be said to be inelastic, since the increase in price does not have a large impact on quantity demanded. If an increase in price causes a decrease in total revenue, then demand can be said to be elastic, since the increase in price has a large impact on quantity demanded. Show
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Mathematical explanation[edit]The mathematical link between them comes from the formula of the price elasticity of demand: where stands for Price, for quantity demanded, for change in quantity demanded, and for change in price.[1] Here the minus sign converts the result to a non-negative number, as is conventional but not universal. Using the idea of limits for infinitesimal changes in price and therefore in quantity, the formula becomes Total revenue is given by . Since quantity demanded Q is a function of price P, total revenue can be rewritten as The derivative of total revenue with respect to P is thus: But , so . After both multiplying and dividing by , the equation can be rewritten as: The last step is to substitute the elasticity of demand for to obtain: .To find the elasticity of demand using the mathematical explanation of the total revenue test, it's necessary to use the following rule: If demand is elastic, , then : price and total revenue move in opposite directions. If demand is inelastic, , then : price and total revenue change in the same direction. If demand is unit elastic, , then : an increase in price has no influence on the total revenue. Graphical explanation[edit]Total revenue, the product price times the quantity of the product demanded, can be represented at an initial point by a rectangle with corners at the following four points on the demand graph: price (P1), quantity demanded (Q1), point A on the demand curve, and the origin (the intersection of the price axis and the quantity axis). The area of the rectangle anchored by point A is the measure of total revenue. When the price changes the rectangle changes. The change in revenue caused by the price change is called the price effect, and the change In revenue in the opposite direction caused by the resulting quantity change is called the quantity effect. When the price changes from to the magnitude of the price effect is represented by the rectangle and the magnitude of the quantity effect is given by rectangle . The price effect is the loss of revenue from selling the original quantity at the lower price; the quantity effect is the added revenue earned at the new price on the newly induced units sold. So, if the area of the rectangle giving the price effect is greater than the area of the rectangle giving the quantity effect, demand is inelastic: . If the reverse is true, demand is elastic: . If the sizes are equal, demand is unit elastic (or unitary elastic).[2] References[edit]
Why do price and total revenue go in the same directions when the demand for the good is elastic?Answer and Explanation:
The price and the total revenue move in the opposite direction when the demand is elastic because, with elastic demand, the decrease in the quantity demanded is greater than the increase in the price. Thus, when the demand is elastic, an increase in price decreases the total revenue.
Why do price and total revenue go in the same direction when the quantity demanded for the product is inelastic?When demand is inelastic, total revenue changes in the same direction as prices, since the price change more than compensates for the change in quantity, which is represented by a steep demand curve. Hence, raising prices increases revenue.
What happens to price and revenue when demand is inelastic?If price changes by a larger percentage than quantity demanded (i.e., if demand is price inelastic), total revenue will move in the direction of the price change. If price and quantity demanded change by the same percentage (i.e., if demand is unit price elastic), then total revenue does not change.
Why does total revenue increase when demand is inelastic?However, if demand is inelastic at the original quantity level, then should the company raise its prices, the percentage increase in price will result in a smaller percentage decrease in the quantity sold—and total revenue will rise.
What happens when demand is inelastic?"Inelastic" is an economic term referring to the static quantity of a good or service when its price changes. Inelastic demand means that when the price goes up, consumers' buying habits stay about the same, and when the price goes down, consumers' buying habits also remain unchanged.
When demand is elastic price and total revenue move in which direction?In general, demand is elastic in the upper half of any linear demand curve, so total revenue moves in the direction of the quantity change. Moving from point A to point B implies a reduction in price and an increase in the quantity demanded. Demand is elastic between these two points.
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Why do price and total revenue go in the same directions when the demand for the good is inelastic?
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