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What is price elasticity of demand? Elasticity of demand is a measure used in economics to determine the sensitivity of demand of a product to price changes. In theory, this measurement can work on a wide range of products, from low priced items like pencils to more significant purchases like cars. Because of this diversity of products, elasticity of demand looks at percent changes in price rather than absolute changes; for example, a \$10 increase for a pack of pencils would be outrageous, while a \$10 increase for a new car would likely go unnoticed. Ultimately, the equation used to determine elasticity of demand can be simply thought of as: how do a price increase of X% affect the demand of product Y? A higher demand elasticity means that consumers are more responsive to changes in the price of the product. How to determine elasticity of demand Given that elasticity of demand calculates the relationship between change in price and change in demand, we can begin to derive the formula: |$\frac{\text{Percent change in demand}}{\text{Percent change in price}}| = |\frac{∆q/q}{∆p/p}$| This can be further simplified as: |$\frac{∆q}{q} \cdot \frac{p}{∆p}| = |\frac{p}{q} \cdot \frac{∆q}{∆p}$| In the above equation ∆p refers to change in price, while ∆q represents the corresponding change in the quantity of the product demanded. Absolute values are used when determining the coefficient of elasticity, because the correlation between price increase and quantity demand can be assumed to always be negative. For small changes in price, $\frac{∆q}{∆p}$ can be approximated by the derivative $\frac{dq}{dp}$. This means that we can determine elasticity of demand, E, by substituting in the derivatives of ∆q and ∆p into the above formula. Therefore, E = |$\frac{p}{q} \cdot \frac{dq}{dp}$| Important values for elasticity of demand The word “coefficient” is used to describe the values for price elasticity of demand (E). Different coefficient values have various implications for the price elasticity of demand of products:
The more the demand for a product decreases in relation to the change in price, the more elastic that good is considered. Application The demand curve for a product is given by $q = 2000−4p^2$, where p = price. What is the elasticity of the product when the price is \$10? To solve this problem, first find $\frac{dq}{dp}$. Using the power rule, we know that $\frac{dq}{dp} = -8p$. We plug this, as well as the price, into the equation, yielding: $E = |\frac{10}{q} \cdot (-8)$| To find q, we go back to our original equation. $q = 2000−4p^2 = 2000−4(10)^2 = 1,600$ Now we have all of the components needed to calculate the price elasticity of demand at price = /$10. $E = |\frac{10}{400} \cdot (-8)| = .2$ Considering the values of E described above, we know that the product is inelastic at p=10. Another way to think of this is that a 1% increase in price will correspond with an approximately .2% decrease in quantity demand. Sources: Applied Calculus 5th Edition (Hughes-Hallet, Gleason, Lock, Faith, et al.) – section 4.6 https://www.tutor2u.net/economics/reference/price-elasticity-of-demand https://www.extension.iastate.edu/AGDM/wholefarm/pdf/c5-207.pdf https://www.intelligenteconomist.com/price-elasticity-of-demand/ What happens when the price elasticity of demand increases?A product with high price elasticity of demand will see demand fall sharply when prices rise. For the product with high elasticity of demand, the downward-sloping demand curve appears flatter, and for every change in price, there is a large change to the quantity demanded.
What is the absolute value of the price elasticity of demand?Again, as with the elasticity of demand, the elasticity of supply is not followed by any units. Elasticity is a ratio of one percentage change to another percentage change—nothing more—and we read it as an absolute value. In this case, a 1% rise in price causes an increase in quantity supplied of 3.5%.
What would be the absolute value of the elasticity if demand is unit elastic?Demand elasticity of a good with unit elastic demand is 1 (strictly speaking, elasticity equals -1 since the demand curve is downward sloping; but in most cases, elasticity is calculated as an absolute value).
What happens when the price of an inelastic good increases?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.
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The absolute value of the price elasticity of demand for a good increases when
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