ELASTICITY OF DEMAND AND SUPPLY
Introduction
The concept of elasticity measures how much the quantity demanded or supplied will be affected by a change in any of the determinants of demand and supply. The law of demand and supply explains that demand and supply will change due to a change in the price of the commodity, but it does not explain the rate of the change. Economists use the concept of elasticity to measure how much demand and supply responds to changes in its determinants.
The Concept of Elasticity of Demand
Elasticity of demand measures the responsiveness of quantity demanded to changes in the own-price of the good, consumer income and price of other related goods. Thus, elasticity of demand may be defined as the degree of responsiveness of demand to changes in any one of the influencing factors. (e.g.: Price, taste or income). From this definition we can identify three kinds of elasticity of demand:
• Price elasticity of demand
• Income elasticity of demand
• Cross elasticity of demand
Price Elasticity of Demand
The law of demand states that the quantity demanded increases as price falls and vice versa. By how much quantity demanded will increase or decrease as price changes is measured by the price elasticity of demand (PED). Price elasticity of demand is defined as the degree of responsive of a percentage change in quantity demanded of a commodity as a result of a percentage change in price. In order words, it means the extent to which the quantity demanded of a commodity will change if there is a change in the price of that commodity. This may be expressed mathematically as
?
= Percentage change in quantity demanded of good X
???Percentage change in price of good X
?
= 
?Where 
= price elasticity of demand; Q = original quantity; P = original price?
??
= change in quantity demanded (
)
??
= change in price of the good (
-
)
NB: Ed is always negative i.e. Ed < 0. This is so because a typical demand curve is negatively sloped.
Example:
Assume a business firm has been selling 100cumputers per day. It reduces price by charging GH¢8.00 instead of the usual price GH¢ 10.00. If society recognizes this change in price and sales increased to 140 computers. We may calculate the coefficient of the price elasticity of demand as follows:
??
= 10,?
= 8,??
= 100,?
= 140
??
= 
- 
8 – 10 = -2,??
= 
- 
140 -100 = 40
??
??
= 
Price elasticity of demand may be different on the same demand curve. This is illustrated in the diagram below. That is points on the demand curve may have different elasticities of demand. This is because elasticity is calculated at a price. The coefficients of the elasticity are interpreted as follows.
??
= 1 represents unitary elastic
??
< 1 represents inelastic
??
> 1 represents elastic demand
??
= 0 represents perfectly inelastic demand
?`?
represents infinitely/perfectly elastic
Estimating Price Elasticity of Demand:
Two ways of estimating price elasticity of demand are pointand arc price elasticity of demand.
Point price-elasticity of demand
This is the measure of price-elasticity of demand at a point (price) on the demand curve, and it normally used to measure the elasticity of demand on the demand curve when the change in demand is very small. Point elasticity of demand is calculated by dividing the percentage change in quantity demanded by the percentage change in the price of the commodity. In effect the point elasticity of demand is measured as price elasticity of demand.
??
= 
Arc price elasticity of demand
This refers to the measure of price-elasticity of demand over an arc of a demand curve. This is the measure price elasticity between two points or over a range. It is used when the change on the demand curve is very large. Hence we will be interested in finding the average of the proportionate change in quantity demanded and the price of the commodity. The formula for this is as follows:
??
EXAMPLE (1)
The table below is a hypothetical demand schedule in which price (P) is in dollars and quantity demanded (Qd) is in liters,
P?10?20?30?40?50?60
Qd?50?44?38?32?26?20
(i) Find the price-elasticity of demand (Ed) at each price.
(ii)?If P rises from $20 to $50, calculate the
?(a) ?price-elasticity of demand
?(b)?arc-price elasticity of demand.
SOLUTION
(i) "Point elasticity” is involved in this part of the question (since we are measuring Ed at each price). The calculations can be presented in a table as follows:
| | Ed = ?Qd x P1 where ?Qd = 44 – 50 = – 6 = –3 ? P Q1 ? P 20 – 10 10 5 |
| | –3 x 10 = – 3 or – 0.12 5 50 25 |
| | –3 x 20 = – 3 or – 0. 27 5 44 11 |
| | –3 x 30 = – 9 or – 0. 47 5 38 19 |
| | –3 x 40 = – 3 or – 0.75 5 32 4 |
| | –3 x 50 = –15 or – 1.15 5 26 13 |
| | –3 x 60 = – 9 = – 14 or –1. 8 5 20 5 5 |
??
?
(ii)?(a) Ed = ?Qd x P1
? P Q1
? = 26 – 44 x 20
50 – 20 44
= 18 x 20 = – 3 ( or – 0.27 )
30 44 11
(b) Arc - Ed = ?Qd x P1 + P ? P Q1 + Q 2
? = 18 x 20 + 50
30 44 + 26
?? = 18 x 70 = – 3 ( or – 0.6 )
?30 70 5
EXAMPLE (2)
(a)?The gradient (slope) of a non-linear demand curve at the point
A (50 units, ¢53) is – 2. 12. Determine the coefficient of price-elasticity of demand at A.
(b)?The price elasticity of demand for a commodity is –8/15. If the new price and quantity demanded of the commodity are ¢30 and 60 kg respectively, find its original price, given that the original quantity demanded was 50 kg.
(c) ? By what percentage should Qd change in response to a 20 % fall in P if
? Ed = – 1. 25?
SOLUTION
(a)?Ed at (Q1, P1) = dQd x P1
dP Q1
?Where dQd = reciprocal of the slope of the demand curve at the point
dP
Therefore Ed at A (50 units, ¢53)
= –1 x 53 = – 0.5
2.12 50
? ?
(b) Let P1 = original price
?Then
?Ed ?= ?Qd x P1
? P Q1
??– 8 = 60 – 50 x P1
15? 30 – P1 50
?– 8 = 10P1 15? 1500 – 50 P1
?
– 8 (1500 – 50P1) = 150P1
– 12000 + 400P1) = 150P1
250P1 = 120,00P1
250
(c) Ed = Percentage change in Qd
Percentage change in P
Therefore – 1. 25 = x = x 20% – 0. 20
?x = (1. 25) x (. 0 .2) = 0. 25 = 25 % increase in Qd
Example (3)
Assume that a consumer bought 5Apples at GH¢4.00 per fruit but 20 apples at the price of GH¢2.00 per fruit. Calculate
i. The point price elasticities at the two different prices
ii. The arc price elasticity of demand
Graphical Representation of Price Elasticity of Demand
The description of price elasticity of demand is based on the co-efficient or numerical value of elasticity. The various price elasticities can be represented graphically as demonstrated below.
Elastic demand curve
D
0 
Qty dd
In the above figure, price elasticity of demand is greater than one (i.e. ped > 1). It means that a small change in price leads to a more than proportionate change in quantity demanded.
Inelastic demand curve
0 
Qtydd
In the above figure, price elasticity of demand is less than one (i.e. Ped < 1). This means that a greater change in price leads to a small change in quantity demanded. Observe that in this case the change in quantity 
is less than the corresponding change
.
Unit elasticity of demand
0 
Qty dd
The above figure illustrates the case of Unit Elasticity of Demand. This is because a change in price brings in the same amount of change in quantity demanded (i.e. Ped = 1). Such a demand curve is referred to as a rectangular hyperbola because all areas under it are equal.
Perfectly inelastic curve
D
0 
Qtydd
In the above case, price elasticity of demand is equal to zero. At different prices quantity demanded remains unchanged or constant. A change in price has brought in practically no change in quantity demanded. That is, ped = 0.
Perfectly elastic demand curve P
D
0 
Qty dd
With reference to the above, price elasticity of demand is infinity (i.e. Ped = 
) It means that at the same price consumers are willing to buy any quantity of the commodity 
or 
etc. But if the Price moves above
, quantity demanded will tend to be zero.
Determinants of Price - Elasticity of Demand
Whether a commodity has elastic demand or inelastic demand will depend upon various factors. The following are some of these factors.
1.?The Availability of Close Substitutes
Commodities that have close substitutes tend to be elastic in demand because a change in price will result in a greater change in the quantity demanded of them, because it is easier for consumers to switch from that good to others. For example, Milo and Bourvita are easily substitutable; an increase in the price of Milo relative to that of bourvita will make a lot of consumers shift to bourvita. This will lead to a great change in quantity demanded of Milo. However, commodities that have no close substitutes, for example, salt or egg will tend to be inelastic in demand. The reason is that no matter the price level, consumers will buy almost the same quantity because they have no other alternative.
2.?The Degree of Necessity
The level of elasticity of demand for a commodity will also depend upon whether the commodity is a necessity or a luxury. Necessities are those commodities that we need as human beings to live. Thus, no matter their price, consumers will have to buy them. That is, almost the same quantity. Necessities are therefore inelastic in demand, because, consumers have no choice but to continue to buy them. Examples of such goods are food, clothing and shelter.
There are also those commodities that are luxuries and consumers can do without them. Luxury goods have close substitute. For example: expensive car or a gold necklace. Consumers will therefore reduce or change the quantity they demand of them greatly if their prices increase or change. Such luxuries are therefore elastic in demand. However, we must note that not all commodities that are inelastic in demand which are necessities. For example, cigarettes and alcoholic beverages such as beer tend to be inelastic in demand but they are not necessities.
3. Length of time:
In the short-run the demand for certain commodities tends to be inelastic because consumers have not got sufficient time to look round for substitutes. This is the case when the price of a commodity increases. Such commodities become elastic in the long-run when consumers now have sufficient time to locate substitutes for them.
4.?Proportion of Consumer’s Income Spent on the Commodity
Whether a commodity is elastic or inelastic in demand will depend upon the proportion of the consumer’s income being spent on the commodity. When a consumer spends an insignificant (small) proportion of his income on a commodity an increase in price of the commodity will not affect how much he buys of it. The demand for the commodity will therefore be inelastic. But when a consumer spends a greater proportion of his income on a commodity, a further increase in the price of that commodity will lead to the consumer reducing greatly how much he buys of that commodity. Demand will therefore be elastic.
5.?Number of possible uses
Some commodities have so many uses and others have limited uses. For example, a black pair of shoes can be used for various occasions. But a white pair of shoes is used on limited occasions. Commodities that have many uses tend to have elastic demand. This is because a change in their prices will affect a great number of people who uses them. But commodities that serve limited uses are said to have inelastic demand because a charge in price will affect only a limited number of users.
6.?Habit
Habit formation also determines the elasticity of demand for a commodity. People who form the habit of consuming certain commodities will have inelastic demand for such commodities. This is because no matter the price, they will tend to buy almost the same quantity. But people who do not form the habit for such commodities will have elastic demand for them. For example, smokers tend to have inelastic demand for cigarettes.
7.?The Number of New Buyers
The elasticity of demand for a commodity also depends upon the number of new buyers. There are some commodities that are only bought once. For example, a Television set. These are durable commodities. As consumers buy them they leave the market for a long time. If a large number of people have already acquired such a commodity, a change in price will only affect a small number of people who are new buyers. Demand will therefore be inelastic. However, if the number of new buyers is a large one, a change in price, for example a decrease in price for the commodity will lead to a great increase in quantity demanded. Demand will therefore be elastic.
8.?Consumers Income
Normally, the poor in society will have elastic demand for most commodities. As price increases for these commodities, the poor complain and therefore may stop buying or buy a small amount of these commodities. The rich may tend to have inelastic demand because a change in price, for example an increase in price, will not have any significant effect on how much they buy of the commodity.
Uses or Application of Price Elasticity of Demand
1. Generating of Government Revenue:
One way by which Governments generate revenue for development purposes is through taxation on goods and services. However, the government’s tax policy maker must consider the elasticity of demand for the commodities he intends taxing in other to raise revenue. It must be noted that a tax on a commodity increases the price of that commodity. If a commodity is elastic in demand and a tax is levied on it, quantity demanded of it will reduce greatly and lesser total revenue will be raised for government. But if the commodity is inelastic in demand, consumers will tend to buy almost the same quantity of the commodity despite the increase in price as a result of taxation. Total revenue will be higher for the government. Therefore, in a taxation policy to raise revenue, the tax policy maker must tax commodities that are inelastic in demand if he really wants more revenue for government.
2. Price Fixing by Businessmen:
Producers or businessmen want to maximize their profit. In order to maximize profit, they have to sell at a price that will give them more revenue. In fixing prices, the producer takes into consideration the elasticity of demand for his product. When the demand for the product is elastic and the producer fixes a higher price, total revenue will reduce because quantity demanded will decrease greatly. However, if the demand for a commodity is inelastic he can fix a higher price because consumers will not change greatly how much they buy of the commodity. The producer’s total revenue and profit will therefore be high. Note that to get high revenue from a commodity which is elastic in demand, lower prices should be fixed by the producer.
3. Restricting Imports
A government of a country may want to reduce the importation of certain commodities into the country. One way the government could reduce the imports is to increase import duties on such commodities. The increase in import duties will lead to an increase in the price of the imports. The aim here is to make the commodity expensive for local consumers and therefore reduce their demand. But to achieve this aim, import duties can only work if the demand for the imports is elastic. But if the demand for the imports is inelastic the policy will not work because local consumers will continue to buy the imported commodities at the higher price.
4. Devaluation:
This is defined as the deliberate reduction in the value of a country’s currency in relation to other countries’ currencies. Devaluation is normally done to solve a country’s balance of payment deficit. The aim is therefore to reduce imports and increase exports. Whether devaluation will work to achieve such an objective will depend upon the elasticity of demand for imports and foreigner’s elasticity of demand for exports. Devaluation will be successful only when demand for imports is elastic and foreigners demand for exports is also elastic.
5. Wage Increase:
In granting wage increases to trade unions, the employer would have to consider the elasticity of demand for the final product. If the demand for the final product is elastic, the employer cannot shift so much of the increased cost, due to wage increase, to the consumer. The more inelastic the demand for the product the easier it becomes for the producer to shift the cost of production in the form of higher prices to the consumers. In this case the producer will be willing to grant wage increase to trade unions.
Cross Elasticity of Demand
Economist use cross elasticity of demand to measure how the quantity demanded of one good change as the price of another good change. Cross Elasticity of demand (Ey) refers to a percentage change in the quantity demanded of one good as a result of percentage change in the price of a substitute or a complement good while all other factors influencing demand remain constant. Cross Elasticity of demand can be positive, negative or zero. If the estimated cross elasticity of demand is positive then the goods are substitutes but when it is negative the two commodities are complement. When the value is zero then the goods are unrelated.
The formula is presented as:
= Percentage change in quantity demanded of commodity X
Percentage change in the price of commodity Y
????
Example: Assume price of Milo increased from GH¢8.00 to GH¢10.00. The quantity demanded of Ovaltine increased from 5 to 7 tins. Compute the cross-price elasticity of demand.
Determinants of Cross Elasticity of Demand
The main determinant of cross elasticity of demand is the relationship between the two commodities as to whether they are substitutes or complements.
Importance of Cross Elasticity of Demand
• Classification of goods into substitutes and complements
• For forecasting the effect of pricing decision of a firm on the sale of another
Income Elasticity of Demand
This is defined as the percentage change in the quantity demanded as a result of a percentage change in consumer income. The concept of income elasticity of demand holds price constant and measures the change in quantity demanded that results from a change in consumer income. Goods with positive values are described as normal goods, for an increase in income the quantity purchased will increase. The income elasticity of normal goods can be greater than 1 (elastic) or less than 1 (inelastic). When it is negative the good is called an inferior good. it means for an increase in income the quantity purchased will decline or for a decrease in income the quantity purchased will increase.
The formula is presented as:
????
Example: Assume that a consumer’s income increases from GH¢450.00 to GH¢500.00 and the quantity he buys of kenkey decreased from 5 to 4balls. Compute the income elasticity of demand.
Quantity Demanded Reacts to Changes in Income
It is true to say that as income increases; more of a commodity will be demanded. However, this is not always the case. When income increases, the quantities demanded of different commodities tend to react differently to increase income. There are three main cases to be considered here.
1.?There are those commodities whose quantity demanded will increase as income increases. The more the income increases the more we turn to buy these items. Examples are luxury goods such as video, ornaments etc. The general term for such commodities is superior or normal goods.
2.?They are those commodities whose quantity demanded will initially increase with increases in income. After a point, any further increase in income will leave quantity demanded constant. A typical example is salt. As consumer’s income increases he may increase the number of dishes he enjoys, calling for more quantities of salt. At a certain level of income, the consumer can no longer increase the number of dishes so that the demand for salt will remain constant, no matter the level of his income. Such commodities are referred to as necessities.
3. Again, there are some commodities whose quantity demanded will increase with increases in income. But after a level of income the quantity demanded of them tends to decrease. These are known as inferior goods like our basic foodstuffs such as gari, etc. The figure below illustrates these three cases.
Inferior Goods
0 Income
Angels was the first person to study the relationship between quantity demanded and incomes. The above curves are referred to as Angels Curves. Angels propounded a law which states that, as consumers’ income increases they turn to spend less on food.
This law is expressed in proportionate terms, meaning that as income increases consumers in absolute terms will spend more on food as compared to the previous. But if we talk of proportions, his spending will be less.
Determinants of Income Elasticity
i. The Degree of Necessity of the good: If a commodity is a normal good, its income elasticity of demand is positive, but if it is an inferior good, the income elasticity of demand is negative. Necessities such as a basic food item tend to have a low positive income elasticity that is greater than zero but less than unity, while luxuries have a high positive income elasticity of demand which is greater than one.
ii. The level of income of the consumer: In an economy where the levels of income are high relative to the general price level, the demand for commodities tends to be relatively income inelastic. The level of income determines whether a commodity is inferior or normal in a country.
iii. The time period: In the short run the demand for a commodity tends to be more elastic than in the long run. This is because it takes time for people to adjust their demand in response to change in income.
The Importance of Income Elasticity
i. Important to the businessman: If sellers know the income elasticity of demand for their products they will be able to predict what will happen to their total revenue in times of changing incomes, e.g. if demand for a product is income elastic then in times of rising incomes sellers can expect a significant rise in demand and in revenue. This helps sellers to know what to sell.
For products which have an income inelastic demand then the rise in incomes will increase demand but not by much – sellers can expect a small rise in revenue.
When income increases, for inferior products which have negative income elasticity of demand, demand would fall and so would revenue.
On the other hand, in a period of falling incomes, say in a recession, the demand for inferior goods and services should rise.
ii. Important to Government: The government would also be able to predict changes in revenue from taxes on products. Goods with high income elasticity will increase the source of revenue to the government as income rises, since these goods will be bought in greater proportion.
iii. Classification of Goods: Income elasticity of demand is used to classify goods into Normal, Inferior and Necessities
Elasticity of Supply
Price elasticity of supply measures the responsiveness of producers to changes in price. It is the percentage change in quantity supplied as a result of a percentage change in price. In other words, it refers to the extent to which the quantity supplied of a commodity will change should there be a change in the price of a said commodity. Supply elasticity is calculated in the same way as the demand elasticity but instead of using quantity demanded we apply quantity supplied or produced.
Measurement of Price Elasticity of Supply
Price elasticity of supply can be measured by making use of any one of the following two formulae;
?Es = percentage change in quantity supplied of a commodity
? Percentage change in price of a commodity
??Es =
Es is always positive for a normal supply curve.
Example: Assume the price of kenkey has changed from 1.00 to 2.00 per ball and quantity supplied changed from 20 to 22balls. Calculate price elasticity of supply.
After we have calculated the price elasticity of supply we may get results which range from zero to infinity. The result will be zero if the commodity is perfectly inelastic in supply. A result of less than one indicates that the commodity is fairly inelastic in supply. Unit elasticity of supply is a term we use when we get a result of just one. A commodity will be elastic or fairly elastic in supply when the result is greater than one. A perfectly elastic supply is the case when we get an answer of infinity. The numerical value of elasticity of supply could be explained in one of the following ways:
Es>1, supply is said to be price elastic. This means that a one percent change in the price of a commodity leads to more than proportionate change in quantity supplied.
.
0 
Qty ss
Es = 1, supply is said to be unitary elastic supply. This implies a one percent change in the price of a commodity leads to an equal proportionate change in the quantity supplied. Graphically any straight-line supply curve which passes through the origin has unitary elasticity of supply.
P
0 
Qty ss
Es<1 supply is said to be fairly inelastic supply. This means that a one percent change in the price of a commodity leads to less than proportionate change in quantity supplied.
0 
Qty ss Es =
, a commodity is said to have perfectly elastic supply curve when quantity supplied changes in response to no change in price. That is at the prevailing price producers are prepared to supply any quantity at all.
P
S
0 
Qty ss Es =0, perfectly inelastic supply, implies a given change in price causes no change in quantity supplied. That is quantity supplied remains constant as price varies.
P
0 
Qty ss Determinants of Elasticity of Supply
Some commodities are elastic in supply and others inelastic in supply. Whether a commodity is elastic or inelastic in supply will depend upon any one of the following factors:
a. The number of Markets served by the Producer; When a producer serves two or more markets his supply to any one of such markets will tend to be elastic. This is because the producer can easily reduce his supply to a market that asks for price reduction and sell more to the other which does not ask for price reduction. For example, if a producer supplies markets A and B and consumers in market A are demanding price reduction, he can easily reduce his supply to it. This makes the supply to market A elastic. But when a producer serves a single market his supply to such a market will be inelastic.
b. The Number of Factors of Production Under the Control of the Producer
When a producer controls a large proportion of the factors used in producing a commodity, his supply of the commodity will be elastic. Because he controls his resources, he can easily or quickly bring them together to increase supply. Supply will be inelastic when the producer does not control the resources used in producing a commodity. It will take some time for him to assemble these resources to increase supply.
c. Time Needed to Produce a Commodity
Some commodities will take a longer time to produce. Such commodities, for example agricultural products are said to be inelastic in supply in the short run. Other commodities can be increased in supply within short period for example manufactured goods. In general, manufactured goods are elastic in the short period. In the long run both agricultural and manufactured goods supplies are said to be elastic. Note that the supply of agricultural goods tends to be inelastic in the short period because of the gestation period involved in their production
d. The Cost of Production
When cost of production increases faster than price increases, when there is a price increase, producers may not want to increase the supply because the slow price increases cannot compensate them for the increasing cost. Supply in this case will tend to be inelastic but when price increases move faster than cost of production, as output is increased, supply tends to be elastic.
e. The Number of Different Products Produced by Producer
When a producer produces different items, the supply facing each one producer will tend to be elastic. The reason is that the producers can easily switch from one product to another
f. How Easy it is to Substitute Other Factors of Production for the Production of a Commodity
It must be noted that factors of production are not perfect substitutes for one another. Although we can substitute capital for labour, this substitution has limits. The more difficult it is to substitute a factor of production for another in the production of a commodity the more inelastic the supply will be.
g. The Time Period
The time dimension is a very important factor that determines the elasticity of supply of a commodity. Generally, the longer the time period within which firms have to respond to a price change, the more elastic is supply. Thus, supply is more price elastic in the long run than in the short run.
Importance or use of Elasticity of Supply
There are various uses to which we can put our knowledge of price elasticity of supply.
a.?In Determining How Much Incentive to give Producers to Increase output
The Government of a country may want the supply of certain commodities to be increased to meet a prevailing high demand. The Government policy maker therefore must find ways of encouraging producers to increase production. Some of the ways available include giving incentives and subsidies to producers. How much incentive the policy maker should give to producers will depend on the elasticity of supply of the commodity under consideration. If a commodity is fairly inelastic in supply more incentives would have to be given to increase supply. But no amount of incentive will work if the commodity is perfectly inelastic in supply.
a. To Determine the Extent to which the price of a commodity will change should there be a change in the conditions of demand:
The extent to which the price of a commodity will change should there be a change in demand depends on the price elasticity of supply of the commodity. When a commodity is inelastic in supply, a change in demand will bring about a greater change in price than if the commodity is elastic in supply.
b. To Determine Whether Devaluation will work in Solving a Country’s Balance of Payment problem
A country devalues her currency to make her exports cheaper for foreign buyers. Assuming demand for exports increase in the country devaluing capable of increasing supply? This will depend upon the elasticity of supply of the export of the devaluing country. When the supply of exports is inelastic the devaluing country cannot take advantage of any increased demand by foreign buyers. It means therefore that devaluation can only work when the country’s export is elastic in supply.
c. To Determine the Incidence of Taxation
To determine the incidence of indirect taxation, that is who bears the final burden of a tax, we have to consider the relative elasticity of supply and demand for a commodity.
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