Handout 4: Elasticity of Demand and Supply

Elasticity of Demand and Supply

It should be clear from one’s understanding of supply and demand curves, that changes in price are related to changes in the quantities supplied and demanded. Sometimes however a particular price change will have a large effect and sometimes a smaller effect. Elasticity measures this sensitivity of the movement of these curves to price changes.

Elasticity is a central concept in the theory of supply and demand. In this context, elasticity refers to how strongly the quantities supplied and demanded respond to various factors, including price and other determinants. One way to define elasticity is the percentage change in one variable (the quantity supplied or demanded) divided by the percentage change in the causative variable. For discrete changes this is known as arc elasticity, which calculates the elasticity over a range of values. In contrast, point elasticity uses differential calculus to determine the elasticity at a specific point. Elasticity is a measure of relative changes.

Often, it is useful to know how strongly the quantity demanded or supplied will change when the price changes. This is known as the price elasticity of demand or the price elasticity of supply, respectively. If a monopolist decides to increase the price of its product, how will this affect the amount of their good that customers purchase? This knowledge helps the firm determine whether the increased unit price will offset the decrease in sales volume. Likewise, if a government imposes a tax on a good, thereby increasing the effective price, knowledge of the price elasticity will help us to predict the size of the resulting effect on the quantity demanded.

Elasticity is calculated as the percentage change in quantity divided by the associated percentage change in price. For example, if the price moves from $1.00 to $1.05, and as a result the quantity supplied goes from 100 pens to 102 pens, the quantity of pens increased by 2%, and the price increased by 5%, so the price elasticity of supply is 2%/5% or 0.4.

Since the changes are in percentages, changing the unit of measurement or the currency will not affect the elasticity. If the quantity demanded or supplied changes by a greater percentage than the price did, then demand or supply is said to be elastic. If the quantity changes by a lesser percentage than the price did, demand or supply is said to be inelastic. If supply is perfectly inelastic; that is, has zero elasticity, then there is a vertical supply curve.

Short-run supply curves are not as elastic as long-run supply curves, because in the long run firms can respond to market conditions by varying their holdings of physical capital, and because in the long run new firms can enter or old firms can exit the market.

Elasticity in relation to variables other than price can also be considered. One of the most common to consider is income. How strongly would the demand for a good change if income increased or decreased? The relative percentage change is known as the income elasticity of demand.

(Wikipedia)

The elasticity of demand.

The first aspect that one should take into account when developing a yardstick to measure the sensitivity of demand curves to changes in price, is to not attempt to directly equate the two variables. The size of the change in price or quantity can only be measured with reference to the original price or quantity. For example a change in price of R1 would be relatively large if the original price was R5; but be infinitesimally small if the original price was R 10 000. The same with quantity. Therefore in the determination of elasticity the proportional (relative) change of quantity is compared with the proportional (relative) change in price.

So, elasticity of demand =

So if P is the original price and ΔP (Delta P) the change in price, then

is larger than

(e is referred to here as the elasticity coefficient)

The first thing to note that although e is in fact negative the absolute value is used.

(Q and P have different signs – for example as price goes down = negative; price goes up = positive, this is however disregarded in e). the second is that there are five cases of elasticity that need to be recognised: a) If the relative change in quantity demanded is smaller than the relative change in price, the value of the elasticity coefficient will be between 0 and 1. b) if they are equal it will be 1; and c) if

is the proportional change in price. So if Q is the original quantity and ΔQ the change in quantity, then

is the proportional change in quantity.

As a result then the above equation of elasticity (e)can be stated as follows:

elasticity will be greater than 1. Then there are two limits d) the first where e=0 and e) when e = (infinity).

Generally speaking elasticity varies from point to point on a straight line demand curve -because of the differential changes in the relative proportions. It has little to do with the slope – it has everything to do with the relationship between the relative quantities and the relative prices (this will be explained fully in a future handout - send me an email if you wish to know more about elasticity now).

The elasticity of supply.

The definition of the elasticity of supply is similar to the definition of the elasticity of demand. Again the size of the change in price or quantity can only be measured with reference to the original price or quantity.

The elasticity of supply can thus be described as:.

Elasticity of supply =

(equation 2)

(e is referred to here as the elasticity coefficient)

The line S2 above is a perfectly inelastic supply curve which runs parallel with the axis OP – the elasticity of supply here is equal to zero which means that irrespective the price the quantity supplied remains the same (ΔQ =0 for any change in P)

The curve S1 is perfectly elastic – a very small change in P would lead to an infinitely large change in the quantity supplied. It is important to note that the two limiting cases of elasticity both supply and demand curves are the same. A perfectly elastic curve is in both cases parallel to the horizontal curve and a perfectly inelastic curve is parallel to the vertical axis OP

The first thing to note that although e is in this case positive since both price and quantity move in the same direction. The second is that there are also five cases of elasticity that need to be recognised:

The two limits are where e=0 and e = (infinity).

These are represented in figure 2

Another elasticity sometimes considered is the cross elasticity of demand, which measures the responsiveness of the quantity demanded of a good to a change in the price of another good. This is often considered when looking at the relative changes in demand when studying complements and substitute goods. Complements are goods that are typically utilized together, where if one is consumed, usually the other is also. Substitute goods are those where one can be substituted for the other, and if the price of one good rises, one may purchase less of it and instead purchase its substitute.

Cross elasticity of demand is measured as the percentage change in demand for the first good divided by the causative percentage change in the price of the other good. For an example with a complement good, if, in response to a 10% increase in the price of fuel, the quantity of new cars demanded decreased by 20%, the cross elasticity of demand would be -2.0. (Wikipedia)

Charl Heydenrych - January 2011