# price elasticity of demand

• First, a good’s elasticity is not necessarily constant; it varies at different points along the demand curve because a 1% change in price has a quantity effect that may depend
on whether the initial price is high or low.

• [8][9] If a 1% rise in the price of gasoline causes a 0.5% fall in the quantity of cars demanded, the cross-price elasticity is As the size of the price change gets bigger,
the elasticity definition becomes less reliable for a combination of two reasons.

• Demand for a good is said to be inelastic when the elasticity is less than one in absolute value: that is, changes in price have a relatively small effect on the quantity
demanded.

• As a result, the relationship between elasticity and revenue can be described for any good:[38][39] • When the price elasticity of demand for a good is perfectly inelastic,
changes in the price do not affect the quantity demanded for the good; raising prices will always cause total revenue to increase.

• • When the price elasticity of demand is perfectly elastic, any increase in the price, no matter how small, will cause the quantity demanded for the good to drop to zero.

• [17][19] Point elasticity The point elasticity of demand method is used to determine change in demand within the same demand curve, basically a very small amount of
change in demand is measured through point elasticity.

• He described price elasticity of demand as thus: “And we may say generally:— the elasticity (or responsiveness) of demand in a market is great or small according as the amount
demanded increases much or little for a given fall in price, and diminishes much or little for a given rise in price”.

• [7] Since the price elasticity of demand is negative for the vast majority of goods and services (unlike most other elasticities, which take both positive and negative values
depending on the good), economists often leave off the word “negative” or the minus sign and refer to the price elasticity of demand as a positive value (i.e., in absolute value terms).

• For example, when demand is perfectly inelastic, by definition consumers have no alternative to purchasing the good or service if the price increases, so the quantity demanded
would remain constant.

• Two important special cases are perfectly elastic demand (= ∞), where even a small rise in price reduces the quantity demanded to zero; and perfectly inelastic demand (= 0),
where a rise in price leaves the quantity unchanged.

• A good with an elasticity of −2 has elastic demand because quantity demanded falls twice as much as the price increase; an elasticity of −0.5 has inelastic demand because
the change in quantity demanded change is half of the price increase.

• In terms of partial-differential calculus, point elasticity of demand can be defined as follows:[22] let be the demand of goods as a function of parameters price and wealth,
and let be the demand for good .

• [33] When the goods represent only a negligible portion of the budget the income effect will be insignificant and demand inelastic,[33] Necessity The more necessary a good
is, the lower the elasticity, as people will attempt to buy it no matter the price, such as the case of insulin for those who need it.

• In other words, we can say that the price elasticity of demand is the percentage change in demand for a commodity due to a given percentage change in the price.

• [13][29] Duration For most goods, the longer a price change holds, the higher the elasticity is likely to be, as more and more consumers find they have the time and inclination
to search for substitutes.

• For inelastic goods, because of the inverse nature of the relationship between price and quantity demanded (i.e., the law of demand), the two effects affect total revenue
in opposite directions.

• The price elasticity gives the percentage change in quantity demanded when there is a one percent increase in price, holding everything else constant.

• [27] A number of factors can thus affect the elasticity of demand for a good:[28] Availability of substitute goods The more and closer the substitutes available, the higher
the elasticity is likely to be, as people can easily switch from one good to another if an even minor price change is made;[28][29][30] There is a strong substitution effect.

• • When the price elasticity of demand is unit (or unitary) elastic, the percentage change in quantity demanded is equal to that in price, so a change in price will not affect
total revenue.

• Revenue is simply the product of unit price times quantity: Generally, any change in price will have two effects:[36] The price effect For inelastic goods, an increase in
unit price will tend to increase revenue, while a decrease in price will tend to decrease revenue.

• The fundamental equation for one product becomes and the corresponding equation for several products becomes Excel models are available that compute constant elasticity, and
use non-constant elasticity to estimate prices that optimize revenue or profit for one product[41] or several products.

• [3] The formula for the coefficient of price elasticity of demand for a good is:[4][5][6] where is the initial price of the good demanded, is how much it changed, is the initial
quantity of the good demanded, and is how much it changed.

• In the opposite case, when demand is perfectly elastic, by definition consumers have an infinite ability to switch to alternatives if the price increases, so they would stop
buying the good or service in question completely—quantity demanded would fall to zero.

• For example, Company X’s fish and chips would tend to have a relatively high elasticity of demand if a significant number of substitutes are available, whereas food in general
would have an extremely low elasticity of demand because no substitutes exist.

• This form of the equations shows that point elasticities assumed constant over a price range cannot determine what prices generate maximum values of ; similarly they cannot
predict prices that generate maximum or maximum revenue.

• • When the price elasticity of demand is relatively elastic, the percentage change in quantity demanded is greater than that in price.

• It may also be defined as the ratio of the percentage change in quantity demanded to the percentage change in price of particular commodity.

• [39] It is important to realize that price-elasticity of demand is not necessarily constant over all price ranges.

• Constant elasticity and optimal pricing If one point elasticity is used to model demand changes over a finite range of prices, elasticity is implicitly assumed constant
with respect to price over the finite price range.

• Arc Elasticity is a second solution to the asymmetry problem of having an elasticity dependent on which of the two given points on a demand curve is chosen as the “original”
point will and which as the “new” one is to compute the percentage change in P and Q relative to the average of the two prices and the average of the two quantities, rather than just the change relative to one point or the other.

• The above measure of elasticity is sometimes referred to as the own-price elasticity of demand for a good, i.e., the elasticity of demand with respect to the good’s own price,
in order to distinguish it from the elasticity of demand for that good with respect to the change in the price of some other good, i.e., an independent, complementary, or substitute good.

• [2] At an elasticity of 0 consumption would not change at all, in spite of any price increases.

• Effect on tax incidence Demand elasticity, in combination with the price elasticity of supply can be used to assess where the incidence (or “burden”) of a per-unit tax is
falling or to predict where it will fall if the tax is imposed.

• [3] That two-good type of elasticity is called a cross-price elasticity of demand.

• Non-constant elasticity and optimal pricing If the definition of price elasticity is extended to yield a quadratic relationship between demand units and price, then
it is possible to compute prices that maximize , , and revenue.

• • When the price elasticity of demand is relatively inelastic , the percentage change in quantity demanded is smaller than that in price.

• He used Cournot’s basic creating of the demand curve to get the equation for price elasticity of demand.

• )[37] The percentage change in quantity is related to the percentage change in price by elasticity: hence the percentage change in revenue can be calculated by knowing the
elasticity and the percentage change in price alone.

• If demand is inelastic, the good’s demand is relatively insensitive to price, with quantity changing less than price.

• Definition The variation in demand in response to a variation in price is called price elasticity of demand.

• The price elasticity of demand is ordinarily negative because quantity demanded falls when price rises, as described by the “law of demand”.

• [35] Effect on entire revenue A firm considering a price change must know what effect the change in price will have on total revenue.

• This is the approach taken in the definition of point elasticity, which uses differential calculus to calculate the elasticity for an infinitesimal change in price and quantity
at any given point on the demand curve:[20] In other words, it is equal to the absolute value of the first derivative of quantity with respect to price multiplied by the point’s price (P) divided by its quantity (Qd).

• But in determining whether to increase or decrease prices, a firm needs to know what the net effect will be.

• This is a price increase of 60% and a quantity decline of 20%, an elasticity of for that part of the demand curve.

• As a result, this measure is known as the arc elasticity, in this case with respect to the price of the good.

• If the price falls from \$16 to \$10 and the quantity rises from 80 units to 100, however, the price decline is 37.5% and the quantity gain is 25%, an elasticity of for the
same part of the curve.

• Hence, as the accompanying diagram shows, total revenue is maximized at the combination of price and quantity demanded where the elasticity of demand is unitary.

• Hence, suppliers can increase the price by the full amount of the tax, and the consumer would end up paying the entirety.

• One way to avoid the accuracy problem described above is to minimize the difference between the starting and ending prices and quantities.

• The linear demand curve in the accompanying diagram illustrates that changes in price also change the elasticity: the price elasticity is different at every point on the curve.

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