Read this article to learn about price elasticity and slope of the demand curve!
It is essential and important to distinguish between the slope of the demand curve and its price elasticity. It is often thought that the price elasticity of demand can be known by simply looking at the slope of a demand curve, that is, a flatter demand curve has greater price elasticity and a steeper curve has lower price elasticity of demand.
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But this is a wrong notion because the slope of a demand curve is different from its price elasticity of demand. In order to understand the difference between the two, let us analyse the formula for price elasticity of demand.
Ep = ∆q/∆p x p/q
Where its first part, ∆q/∆p, is the reciprocal of the slope of the demand curve, and the second part, p/q is the ratio of the price to quantity.
The slope of a demand curve, whether it is flat or steep, is based on absolute changes in price and quantity, that is,
Slope of demand curve = ∆p/∆q = 1/ ∆q/∆p
On the other hand, the price elasticity of demand is concerned with relative changes in price and quantity, that is,
Ep = ∆ q/q / ∆ p/p
Thus the slope of the demand curve and its price elasticity are different because
1/∆q/∆p ≠ ∆q/q / ∆p/p
Further, as is clear from the slope of the linear demand curve DC is constant throughout its length, whereas the price elasticity of demand varies between ∞ and О on its different points. Thus it is clear that the slope of the demand curve is different from its price elasticity. This fact can also be verified by measuring price elasticities on two demand curves of the same or different slopes.
(a) Two straight line demand curves originating from the same point. There are two straight line demand curves NM and NS in Figure 11.6. At a glance, the curve NS is flatter than NM. Therefore, it appears that its price elasticity is higher than the other curve. But this is not a reality. If we draw a line PV passing through these curves and touching the vertical axis at point P, the elasticity at point T on the NM curve according to the point formula is:
MT/TN = OP/PN
Similarly, elasticity at point V on the NS curve is:
SV/VN = Op/PN, Therefore, MT/TN = SV/VN = OP/PN = 1.
Thus elasticity is equal on both points T and V of the two curves. We may conclude that if two linear demand curves originate from the vertical axis at the same point, such as N, they have exactly equal elasticities at every single price.
(b) Two straight line demand curves originating from different points which are neither parallel nor intersecting. Figure 11.7 shows two demand curves NM and RS. Of these, the curve NS is flatter and so it looks more price elastic. But this is wrong. To prove it, draw a line from point P of the vertical axis which passes through these curves at point A and В respectively. Thus price elasticity at point A on the NM curve is MA/AN = OP/PN and at point В on the RS curve is SB/BR = OP/PR. Since OP/PN > OP/PR, therefore, MA/AN > SB/BR. It means that price elasticity of demand is less than 1 at point В on the demand curve RS and greater than 1 at point A on the NM curve.
(c) Two parallel straight line demand curves. Two parallel straight line demand curves appear to have the same slope and hence the same price elasticity. This view is wrong. To prove, let NM and RS be two parallel straight line demand curves. Draw a line PT which passes through these straight lines at point L and T respectively, as shown in Figure 11.8. According to the point formula, elasticity at point L on the NM curve is ML/LN = OP/PN. Similarly, elasticity at point T on the RS curve is ST/TR = OP/PR.
Since OP/PN > OP/PR therefore ML/LN > ST/TR. It means greater elasticity at point L on the line NM than at point T on the line RS. In other words, the curve which is nearer to the origin has greater elasticity than which is farther from the origin. Thus even two parallel straight line demand curves have different elasticities at each and every point.
(d) Two points on a curved demand curve. Let us take points A and В on a curved demand curved D in Figure 11.9. Elasticity at point В is MB/BN, and at point A is SA/AR. Since SA/AR is greater than MB/BN, elasticity at point A is greater than unity and at point В it is less than unity.
The above cases prove that the price elasticity of demand cannot be ascertained by simply looking at the slope of a demand curve.
Exceptions:
However, there are three exceptional cases when price elasticity can be known from the slope of the demand curve.
(1) When price and quantity are identical, it can be said by looking at the slopes of the two intersecting demand curves which one is more or less elastic. This is explained in Figure 11.10 where the slope of the RS curve shows that it is flatter and that of the NM curve shows it be steeper. Both intersect at point K so that they have identical price OP and identical quantity OQ.
Price elasticity on the RS curve at point K is SK/KR = OP/PR. Similarly, elasticity at point K on the NM curve is MK/KN = OP/PN. But OP/PR > OP/PN. Therefore, SK/KR > MK/KN.
Thus the flatter curve RS has greater elasticity than the steeper curve NM at point K.
(2) If the demand curve is vertical, its price elasticity is zero, as shown in Figure 11.10 (D).
(3) If the demand curve is horizontal, its price elasticity is infinite, as shown in Figure 11.10(E)
Cross Elasticity of Demand:
The cross elasticity of demand is the relation between percentage change in the quantity demanded of a good to the percentage change in the price of a related good. The cross elasticity of demand between good A and В is
It can also be measured with the formula of arc elasticity with the difference that here price and quantity refer to different goods.
Let us suppose that when the price of tea is Rs 8 per kg, 100 kg. of coffee is bought, but when the price rises to Rs. 10, the demand for coffee increases to 120 kg. According to this formula the coefficient of cross
Or less than unity. There are two types of related goods: substitutes and complementaries.
Cross Elasticity of Substitutes:
In the case of substitutes, the cross elasticity is positive and large. The higher the coefficient Eba, the better substitutes the goods are. If the price of butter rises, it will lead to increase in the demand for jam; similarly a fall in the price of butter will cause a decrease in the demand for jam.
If a change in the price of good A leads to more than proportionate change in the demand for good B, the cross elasticity is high (Eba > 1). In Figure 11.11 Panel (A) price of good A is taken on Y-axis and the quantity of good В on X-axis, the change in the amount demanded of good В, ∆ qb is more than proportionate to the change in the price of А, ∆ pa, cross elasticity is high. Such goods are close substitutes.
The cross elasticity of demand is unity (Eba =1) when a change in the price of good A causes the same proportionate change in the quantity of good B. This is shown in Panel (В) where ∆ qb (the change in the quantity of B) and ∆ pa (the change in price of A) are equal.
The cross elasticity is less than unity, (Eba< 1) when the quantity demanded of good В changes less than proportionately in response to the change in the price of good A as in Panel (C). It means that goods A and В are poor substitutes for each other.
When the change in the price of good A has no effect whatsoever on the demand for good B, the cross elasticity of demand is zero. Panel (D) shows that with the change in the price of A, from a to a1 the demand for В remains unchanged as OD (Eba = 0). Such goods are unrelated to each other, like butter and mango.
In case the two goods are perfect substitutes, the cross elasticity of demand will be infinite, Eba = ∞. A fall in the price of butter may reduce the demand for jam to nothing. The demand curve for good В (jam) will coincide with the Y-axis.
Though the cross elasticity of demand for substitutes varies between zero and infinity, it may also be negative. If the price of A falls, the demand for A being inelastic, then less of A will be purchased because it is cheaper, and more of В will be bought. In Figure Panel (E) fall in the price of good A from a1 to a leads to a rise in the demand for В from b1 to b. The slope of the DD curve shows negative cross elasticity.
Cross Elasticity of Complementary Goods:
If two goods are complementary (jointly demanded), rise in the price of one leads to a fall in the demand for the other. Rise in the prices of cars will bring a fall in their demand together with the demand for petrol. Similarly, a fall in the prices of cars will raise the demand for petrol. Since the price and demand vary in the opposite direction, the cross elasticity of demand is negative.
If the change in quantity demanded В is exactly in the same proportion as the change in the price of A, the cross elasticity is unity (Eba =1), as in 11.12 Panel (А), ∆qb/∆pa = 1.
In the case of complementary goods, cross elasticity is greater than unity (Eba > 1), when the change in the demand for В good (<$EDELTA>qb) is more than proportionate to the change in the price of good A, ∆ pa as shown in Panel (B) i.e. ∆ qb/ ∆ pa > 1.
The cross elasticity is less than unity (Eba < 1), when the change in the quantity of В is less in response to a change in the price of A as shown in Panel (С), ∆qb/∆pa< 1.
The cross elasticity of demand is zero (Eba = 0 ), when the change in the price of A causes no change whatsoever in the purchases of В, ∆qb/∆ pa = 0. In Panel (D), fall in the price of good A from a to a, leaves the demand OD of good В unchanged.
It is infinity (Eba=0 ) when an infinitesimal change in the price of A causes an infinitely large change in purchase of В. ∆qb/∆pa= ∞. The price of A remains almost the same (OD) and the demand for В increases from b to b1 as in Panel (E).
Some Conclusions:
We may draw certain inferences from this analysis of the cross elasticity of demand.
(a) The cross elasticity between two goods, whether substitutes or complementaries, is only a one-way traffic. The cross elasticity between butter and jam may not be the same as the cross elasticity of jam to butter. A 10% fall in the price of butter may cause a fall in the demand for jam by 5%. But a 10% fall in the price of jam may lower the demand for butter by 2%. It shows that in the first case the coefficient is 0.5 and in the second case 0.2. The superior the substitute whose price changes, the higher is the cross elasticity of demand.
This rule also applies in the case of complementary goods. If the price of car falls by 5%, the demand for petrol may go up by 15% giving a high coefficient of 3. But a fall in the price of petrol by 5% may lead to a rise in the demand for cars by 1% giving a low coefficient of 0.2.
(b) Cross elasticities for both substitutes and complementaries vary between zero and infinity. Generally cross elasticity for substitutes is positive, but in exceptional circumstances it may also be negative.
(c) Commodities which are close substitutes have high cross elasticity and commodities with low cross elasticities are poor substitutes for each other. This distinction helps to define an industry. If some goods have high cross elasticity, it means that they are close substitutes. Firms producing them can be regarded as one industry. A good having a low cross elasticity in relation to other goods may be regarded a monopoly product and its manufacturing firm becomes in industry by itself. But high or low cross elasticities do not lay down any set rules for determining the boundary of an industry. They are simply guidelines.