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If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Total revenue equals the good’s price multiplied by the quantity sold. Because the price elasticity of demand shows the relationship between price and quantity sold, the elasticity number captures all the information you need to anticipate changes in total revenue. If demand is inelastic (the price
elasticity of demand is between 0 and –1), the quantity sold does not change very much when price changes. As a result, a higher price causes a very small decrease in the quantity sold and total revenue increases. (The higher price you receive for the goods you sell more than offsets the slightly smaller number you sell.) On the other hand, charging a lower price does not cause much of an increase in quantity demanded; total revenue decreases. As these situations illustrate, when
demand is inelastic, price and total revenue change in the same direction; they both increase or decrease together. For an elastic demand (the price elasticity of demand is bigger than –1), the opposite situation occurs; price and total revenue move in opposite directions. (The higher price you receive isn’t enough to offset the decrease in the amount of goods you sell.) If you decrease the good’s price, a large increase occurs in quantity demanded, and total revenue increases. Thus,
when demand is elastic, price and total revenue change in opposite directions. Say that your vending machine company initially charges a $1.50 per bottle and sells 2,000 bottles per week. Decreasing the price to $1 increases sales to 4,000 bottles. The price elasticity of demand equals –1.67; demand is elastic. The price decrease increases total revenue from $3,000 to $4,000 because the $0.50 decrease in price is more than offset by selling 2,000 more bottles. Thus, price and total
revenue move in opposite directions given the elastic demand. Another useful concept is marginal revenue, the change in total revenue that occurs when one additional unit of a good is sold. The formula describing the relationship between marginal revenue, MR, and the price elasticity of demand, η, is Use this formula with the point price elasticity of demand. If your good is currently selling at price P, and you know the point price elasticity of demand η, you can quickly determine how much your revenue changes if you lower price to sell one additional unit of the good. Assume that your company charges a $1.25 per bottle of soft drink and the point price elasticity of demand is –5/3. To determine marginal revenue (the amount of revenue you add by selling one more bottle):
So the marginal revenue received when an additional bottle is sold is  About This ArticleThis article can be found in the category:
Topic 4 Part 1: Elasticity Learning ObjectivesBy the end of this section, you will be able to:
In Topic 4.1, we introduced the concept of elasticity and how to calculate it, but we didn’t explain why it is useful. Recall that elasticity measures responsiveness of one variable to changes in another variable. If you owned a coffee shop and wanted to increase your prices, this ‘responsiveness’ is something you need to consider. When you increase prices, you know quantity will fall, but by how much? Elasticities can be divided into three broad categories: elastic, inelastic, and unitary. An elastic demand is one in which the elasticity is greater than one, indicating a high responsiveness to changes in price. Elasticities that are less than one indicate low responsiveness to price changes and correspond to inelastic demand. Unitary elasticities indicate proportional responsiveness of either demand or supply, as summarized in the following table:
If we were to calculate elasticity at every point on a demand curve, we could divide it into these elastic, unit elastic, and inelastic areas, as shown in Figure 4.2a. This means the impact of a price change will depend on where we are producing. Feel free to calculate the elasticity in any of the regions, you will find that it indeed fits the description. To demonstrate, we have calculated the elasticities at a point in each of the zones: Point A = [latex]\frac{\Delta Q}{\Delta P}\cdot \frac{P}{Q}=\frac{9}{6.75}\cdot \frac{4.5}{3}=2[/latex] = Elastic Point B = [latex]\frac{\Delta Q}{\Delta P}\cdot \frac{P}{Q}=\frac{9}{6.75}\cdot \frac{3}{5}=0.8[/latex] = Inelastic Point C = [latex]\frac{\Delta Q}{\Delta P}\cdot \frac{P}{Q}=\frac{9}{6.75}\cdot \frac{3.375}{4.5}=1[/latex] = Unit Elastic In reality, the only point we need to find to determine which areas are elastic and inelastic is our point where elasticity is 1, or Point C. This isn’t as hard as it may seem. Since our formula is equal to the inverse of our slope multiplied by a point on the graph, it will only equal 1 when our point is equal to the slope of our graph. For a linear graph, this only occurs at the middle point, which is (4.5, 3.325) in this case. Why is This Useful?So far, we have determined how to calculate elasticity at and between different points, but why is this knowledge useful? Consider a coffee shop owner considering a price hike. The owner has two things to account for when deciding whether to raise the price, one that increases revenue and one that decreases it. Elasticity helps us determine which effect is greater. Referring back to our table:
These two effects work against each-other. To determine which outweighs the other we can look at elasticity: When our point is elastic our [latex]\%\;change\;in\;quantity > \%\;change\;in\;price[/latex] meaning if we increase price, our quantity effect outweighs the price effect, causing a decrease in revenue. When our point is inelastic our [latex]\%\;change\;in\;quantity < \%\;change\;in\;price[/latex] meaning if we increase price, our price effect outweighs the quantity effect, causing a increase in revenue. This information is summarized in Figure 4.2b: The first thing to note is that revenue is maximized at the point where elasticity is unit elastic. Why? If you are the coffee shop owner, you will notice that there are untapped opportunities when demand is elastic or inelastic. If elastic: The quantity effect outweighs the price effect, meaning if we decrease prices, the revenue gained from the more units sold will outweigh the revenue lost from the decrease in price. If inelastic: The price effect outweighs the quantity effect, meaning if we increase prices, the revenue gained from the higher price will outweigh the revenue lost from less units sold. The effects of price increase and decrease at different points are summarized in Figure 4.2c. What about ExpenditureYou will notice that expenditure is mentioned whenever revenue is. This is because a dollar earned by the coffee shop corresponds to a dollar spent by the consumer. Therefore, if the firm’s revenue is rising, then the consumer’s expenditure is rising as well. You must understand how to answer questions from both sides. SummaryElasticity is used to measure the responsiveness of one variable to another. This responsiveness can be labelled as elastic (e > 1), unit elastic (e = 1), and inelastic (e < 1). We can apply this to the demand curve, with unit elastic corresponding to the middle of the demand curve (x-intercept/2 , y-intercept/2). Everything to the left is elastic and everything to the right is inelastic. This information can be used to maximize revenue or expenditure, with the understanding that when elastic, the quantity effect outweighs the price effect, and when inelastic, the price effect outweighs the quantity effect. GlossaryElasticwhen the elasticity is greater than one, indicating that a 1 percent increase in price will result in a more than 1 percent increase in quantity; this indicates a high responsiveness to price.Inelasticwhen the elasticity is less than one, indicating that a 1 percent increase in price paid to the firm will result in a less than 1 percent increase in quantity; this indicates a low responsiveness to price.Unitary elasticwhen the calculated elasticity is equal to one indicating that a change in the price of the good or service results in a proportional change in the quantity demanded or suppliedExercises 4.2Use the demand curve diagram below to answer the following TWO questions. 1. What is the own-price elasticity of demand as price decreases from $8 per unit to $6 per unit? Use the mid-point formula in your calculation. a) Infinity. 2. At what point is demand unit-elastic? a) P = $6, Q = 12. 3. Which of the following statements about the relationship between the price elasticity of demand and revenue is TRUE? a) If demand is price inelastic, then increasing price will decrease revenue. 4. Suppose BC Ferries is considering an increase in ferry fares. If doing so results in an increase in revenues raised, which of the following could be the value of the own-price elasticity of demand for ferry rides? a) 0.5. 5. Use the demand diagram below to answer this question. Note that P × Q equals $900 at every point on this demand curve. Which of the following statements correctly describes own-price elasticity of demand, for this particular demand curve? I. Demand is unit elastic at a price of $30, and elastic at all prices greater than $30. a) I and II only. 6. Suppose that, if the price of a good falls from $10 to $8, total expenditure on the good decreases. Which of the following could be the (absolute) value for the own-price elasticity of demand, in the price range considered? a) 1.6. 7. Consider the demand curve drawn below. At which of the following prices and quantities is revenue maximized? a) P = 40; Q = 0. Why do price and total revenue go in the same direction when the demand for the product is inelastic?Why do price & total revenue go in the same direction when the demand for the product is inelastic? Elastic items aren't necessary, so when prices go up or down, quantity demanded also changes.
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.
When the changes in price and total revenue are in the same direction price elasticity is equal to?The price elasticity exactly equals 1 and total revenue and price move in the same direction.
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.
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Why do price and total revenue go in the same direction when the quantity demanded for the product is inelastic?
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