Definition of Elastic, Inelastic, and Unit Elastic Demand Show
By definition: 1. A product is elastic when its elasticity is greater than 1. 2.
A product is inelastic when its elasticity is less than 1. 3. A product is unit elastic when its elasticity is equal to 1.  Elasticity and Revenue When a product is elastic, and its price rises, what happens to the firm’s total revenue? A firm’s total revenue is equal to the number of products it sells times the price of the product. Therefore: Total Revenue = Price times Quantity For example, if a store sells 30 pairs of shoes at $10 each, then its revenue equals 30 times $10, or $300. If the store sells 20 pairs of shoes after the price increases to $25, then its total revenue equals 20 times $25, or $500. Thus, the store’s total revenue increases. In the above example, P (the price) increased, so, therefore, Q (the quantity demanded) decreased, and total revenue increased. Does a price increase always lead to total revenue increase? The answer is “no”. It depends on the product’s elasticity. Let’s look at the following example. A supermarket sells 50 oranges at $1 each. Its revenue equals 50 times $1 or $50. If the store sells 20 oranges after the price increases to $2, then its revenue equals 20 times $2, or $40. Thus, the store’s revenue decreases. If a product is elastic, the percentage change in the quantity demanded change is greater than the percentage change in the price. Therefore, for an elastic product, if the price increases, the percentage change in the quantity demanded decreases by a greater amount, and the firm’s revenue will decrease, and vice versa. If a product is inelastic, the percentage change in the quantity demanded change is smaller than the percentage change in the price. Therefore, for an inelastic product, if the price increases, the percentage change in the quantity demanded decreases by a smaller amount, and the firm’s revenue will increase, and vice versa. In summary: When a product is elastic and its price falls, total revenue increases. When a product is elastic and its price rises, total revenue decreases. When a product is inelastic and its price rises, total revenue increases. When a product is inelastic and its price falls, total revenue decreases. When a product is unit elastic and its price changes, total revenue remains constant. 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. How will an increase in price change total revenue?A price increase will therefore increase total revenue while a price decrease will decrease total revenue. Finally, when the percentage change in quantity demanded is equal to the percentage change in price, demand is said to be unit elastic.
When demand is elastic an increase in price will result in a decrease in total revenue?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. Different commodities may have different elasticities depending on whether people need them (necessities) or want them (accessories).
When demand is inelastic a price increase will increase total revenue?On the other hand, if the price for an inelastic good is increased and the demand does not change, the total revenue increases due to the higher price and static quantity demanded. However, price increases typically do lead to a small decrease in quantity demanded.
When demand is elastic an increase in price causes quantity demanded to and total revenue to?If the price rises and total revenue falls, the demand must be elastic. An increase in price leads to a fall in demand. For the fall in TR, decrease in quantity demand must be more than the increase in price.
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If demand is elastic, how will an increase in price change total revenue? explain.
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