Effects of Shifts in Both Supply and Demand on Equilibrium Price and Quantity:

(1) Simultaneous Shifts in Demand and Supply:

We have so far discussed the effects of changes in demand and supply on equilibrium price separately. Let us now consider a case in which changed in demand and supply take place, simultaneously. This can be better explained with the help of the following diagram.

Diagram/Figure:

In the figure (8.11) DD^/and SS^/ are the original demand and supply curves. When demand rises, the whole of demand curve DD¹, shifts upward and it intersects the old supply curve SS^/ at point F. The new equilibrium price is now equal to FK.

But if supply also increases with the rise in demand, the new equilibrium price will be established at a point where  the new supply  curve intersects the new demand curve. In our diagram, when changes in both supply and demand take place, the new equilibrium price is established at point N. NT becomes the new equilibrium price and OT the new equilibrium amount.

(2) When Supply is Greater Than Rise in Demand:

The new equilibrium price can be higher or  lower than the original price. It all depends upon the relative changes in demand and supply. If the rise in supply is greater than the rise in demand, the price will be lower than the original price. In Fig. (8.12), the price has fallen from EQ to E^/Q^/.

(3) Increase in Demand But Decrease in Supply:

If the change in demand is relatively higher than that of supply, the new equilibrium price will be higher than the original price as is shown in fig. 8.13. The equilibrium price has increased from EQ to E^/Q^/.

Effects of Shifts in Supply on Market Equilibrium:

Just as we have discussed the effects of changes in demand on price, we can also explain the effects of changes in supply on the equilibrium price.

We assume here that the demand curve remains fixed and a change takes place in the supply of a commodity.

The change in the supply of a commodity will result in shifting. Supply curve upward or downward from the original supply curve. When supply rises, demand remaining the same, the supply curve shifts downward from the original curve, i.e., it lies on the right side of the original curve. In case of fall in supply, demand remaining the same, the supply curve moves upward, i.e., it shifts to the left side of the original curve. This  can be also illustrated graphically.

Diagram/Figure:

In the diagram (8.8) the demand curve DD^/ is assumed as fixed and change takes place only in the supply curve. SS^/ shifts, to the right side of the original curve, when supply rise. The S¹S² supply curve was to the left side of the original supply curve when supply falls. PM is the initial position of the equilibrium price and OM the initial equilibrium amount. When supply increases, OK becomes the new equilibrium amount and NK the new equilibrium price. When supply falls, OD is the new equilibrium amount and FD the new equilibrium price.

Here again a question can be asked that if supply rises, will it effect the quantity in greater proportion or the price. The answer is that it depends upon elasticity of demand. If demand is perfectly elastic, see in fig. (8.9) the price will not be affected and quantity demanded will, however, increase with the increase in supply. The price remains unaltered OD.

Inelastic Demand:

If the demand is perfectly inelastic, then with a fall in supply, the quantity demanded will remain unaffected and the price will go up.

With inelastic demand curve, when supply decreases there is no change in the quantity. It remains OM (figure 8.10). The price, on the other hand, rises from ML to MK and then with further fall in supply, it increases to MZ. ln practice, the elasticity of demand is neither perfectly elastic nor perfectly inelastic. It is either equal to unity, greater than unity or less than unity.

If the elasticity of demand is equal to unity, the quantity and price will be affected in equal proportion with a rise or fall in supply.

If elasticity is greater than unity, there will be greater change in quantity and less change in price.

If elasticity of demand is less than unity, then the price is affected more than the quantity demanded.

Effects of Changes in Demand on Equilibrium Market:

We know that if the price rises, other things remaining the same, people buy less of that commodity and if price falls, people buy more of that commodity. Let us now discuss the effects of changes in demand on equilibrium price. 

                             

A change to demand can take place independently of change in price, i.e., price remaining the same, people may purchase more or less of the commodity. When larger quantity is demanded at the same old price or the same old quantity is demanded at a higher price we say, the demand has risen. In such a case, the whole of demand curve rises above the original demand curve. In case of a fall in demand, the whole of the demand curve falls below the original demand curve.

In order to study the effect of the changes in demand on equilibrium price, let us assume that no change takes place in the supply schedule, i.e., it remains fixed. If demand rises, more quantity will be purchased at a higher price. On the other hand, if demand falls, less commodity will be purchased at a lower price. This can also be illustrated in the following diagram.  

Diagram/Figure: 

In the figure (8.2) DD^/ is the original demand curve. PM is the equilibrium price and OM the equilibrium amount. When demand rises, supply remaining the same, the equilibrium amount increases from OM to OG and the equilibrium price rises from PM to FG. In case of fall of in demand, which is indicated by D²D² curve, the quantity demanded decreases from OM to OK and the equilibrium price falls from PM to LK.

Now a question can be asked that when the demand rises, does it affect more on the price or on the quantity of the commodity to be sold? The answer to this simple question, is that if the supply is perfectly elastic, a rise in demand will increase the quantity but will not affect the price. If the supply is perfectly inelastic, then a rise in demand will affect the price but not the quantity. This can be shown with the help of the diagram. In case of perfect elastic supply, (Fig. 8.3) when demand rises, the supply increases from OK to OI with further rise in demand D²D² the supply increases from OI to ON.

Supply Perfectly Inelastic:

In fig. 8.4, the supply is perfectly inelastic. A rise in demand affects the price which rises from RM to KM and with the further rise in demand to LM. The quantity supplied remains the same OM.

In the the world in which we live, the supply is seldom perfectly elastic or perfectly inelastic. It is either equal to unity or greater than unity, or less than unity. We will, therefore, examine these, cases now. If elasticity of supply is to unity and demand rises, the price and quantity will change in equal proportion.

(i) Elasticity of Supply is Equal to Unity:

The quantity and price change in equal proportion with a rise in demand as is clear in fig. 8.5. 

(ii) Elasticity of Supply Greater Than Unity:

If the elasticity of supply is greater than unity, a rise in demand will affect the supply which will change in greater proportion than the price as is obvious from the following fig. 8.6.

In fig. (8.6) when demand rises, KL quantity supplied is greater in proportion than PN price.

(iii) Elasticity of Supply Less Than Unity:

If the elasticity of supply is less than unity, a rise in demand will change the price in greater proportion than the quantity as shown in fig. 8.7.

In fig. 8.7 the proportionate change in quantity demanded KL is less than the change in price RN.

Equilibrium of Demand and Supply:

Meaning and Definition:

The price of a commodity in the market is determined by the interaction of the forces of demand and supply. By"demand for a commodity" at a given price is meant:

"The total quantity of that commodity which buyers will take at different prices per unit of time".

While "supply of a commodity" at a given price refers to:

"That quantity of the commodity which sellers are willing to offer for sale at different prices per unit of time".

If we construct a list or table of the different amounts of the commodity which consumers purchase at different prices in the market, we get the market demand schedule. Similarly, supply schedule is a list or a table of different amounts of the commodity that are offered for sale in the market at different prices per unit of time.

In the market, there are large number of buyers and sellers. It is the desire of every buyer in the market to purchase a commodity at the lowest possible price while the sellers wish to sell it at the highest possible price.

When buyers compete among themselves for the purchase of particular commodity, the price of that commodity goes up and when there is competition amongst the sellers, the price comes down.

Equilibrium Price:

The price of a commodity tends to settle at a point where the quantity demanded is exactly equal to the quantity supplied. The price at which the buyers and sellers are willing to buy and sell an equal amount of commodity, is called the, equilibrium price. We illustrate the above proposition with the help of a schedule and a curve.

Schedule:

                                                

Quantity Supplied (Cooking Oil Kg) Per Week	Price (Dollars)	Quantity Demanded (Cooking Oil Kg) Per Week
800 600 500 450	19 18 17 16	100 250 400 450
350 100	15 14	500 700

If we study the above schedule carefully, we will find that when the price of cooking oil is $16 per kilogram, the total quantity demanded in a week is exactly equal to the total quantity supplied. So $16 is the equilibrium price for the period and the equilibrium amount, i.e. the quantity demanded and offered for sale is 450 kilograms of cooking oil is:

Equation:

 Q^d = Q^s

If the conditions assumed above remain the same, then there can be no equilibrium price other than $16.

Example:

For instance, if the price of cooking oil happens to rise to$18 per kilogram. At this price, the sellers are anxious to sell 600 kilograms of ghee but the buyers are willing to, buy only 250 kilograms. The sellers will compete with one another to dispose off this surplus stock. The competition among the sellers will result in lowering the price. When the price comes down to $16 (i.e., the equilibrium price), then the whole of the stock will be sold.

Conversely, if the price happens to fall to $14 per kilogram, the buyers would like to buy 700 kilograms of cooking oil, but the sellers are willing to sell only 100 kilograms. The buyers, in order to buy more cooking oil at a lower price will compete among themselves. This competition among the buyers will increase the price of ghee. Finally, the price will be reestablished at the equilibrium price which is $16.

Diagram/Figure:

  

The determination of the equilibrium price can be proved graphically.

In the figure (8.1) DD^/ is the demand curve which, represents the different amount of .the commodity that are purchased in the market at different prices, SS^/ is the supply cure which indicate, the amount of the commodity that is offered for sale at different prices per unit of time.

MN is the equilibrium price i.e., $16 and ON 450 kg. is the equilibrium amounts. If the price is below the equilibrium price ($16), there are upward pressure on price due to the resulting shortage of good. In case, the price is above the. equilibrium, there is a downward pressure on price caused by the resulting surplus of good. If is only at price MN, the buyers take of the market exactly what sellers place on the market.

Measurement of Elasticity of Supply:

Definition and Explanation:

Elasticity of supply can be measured on the very same lines as we measured the elasticity of demand. Elasticity of supply can either be equal to unity or greater than unity or less than unity.

Equal to Unity:

If a, change in the quantity supplied, and a change in the price vary in equal proportion, the ratio will be equal to one and the elasticity of supply will be equal to unity.

Diagram/Figure and Schedule:

This is shown with the help of the schedule and the diagrams given below:

Price ($)	Quantity Supplied (Kg)
1	10
2	20
3	30

If the supply curve is a straight line and is also equal to unity, it will pass through the origin as is shown in Fig. 7.6. If the point on the arc supply curve is such that the tangent passes through the origin, the elasticity at the point will also be equal to unity as is shown in Fig. 7.7.

Greater than Unity:

If a change of 1 percent in price leads to more than 1 percent change in supply, the elasticity is said to be greater than unity.

This is shown with the help of the schedule and the diagrams given below:

Price ($)	Quantity Supplied (Kg)
1	10
2	25
3	45

In Fig. 7.8, the supply curve SS^/ cuts the Y-axis, the elasticity is greater than unity. If the supply curve is an arc, then the point on the curve whose tangent cuts the price axis will have elasticity greater than unity as is shown in diagram 7.9.

Less than Unity:

If a 1 percent change in price is accompanied by less than 1 percent change in supply, the elasticity of supply is said to be less than unity.

Price ($)	Quantity Supplied (Kg)
1	10
2	15
3	17

If the supply curve cuts the X-axis, the elasticity will be less that unity as is shown in fig. 7.10, and Fig. 7.11. The tangent at point C intersects the X-axis at the point d. This means elasticity of supply is less than one.

Determinants/Factors of Price Elasticity of Supply:

The main determinants/factors which determine the degree of price elasticity of supply are as under:

          

(i) Time period. Time is the most significant factor which affects the elasticity of supply. If the price of a commodity rises and the producers have enough time to make adjustment in the level of output, the elasticity of supply will be more elastic. If the time period is short and the supply cannot be expanded after a price increase, the supply is relatively inelastic.

(ii) Ability to store output. The goods which can be safety stored have relatively elastic supply over the goods which are perishable and do not have storage facilities.

(iii) Factor mobility. If the factors of production can be easily moved from one use to another, it will affect elasticity of supply. The higher the mobility of factors, the greater is the elasticity of supply of the good and vice versa.

(iv) Changes in marginal cost of production. If with the expansion of output, marginal cost increases and marginal return declines, the price elasticity of supply will be less elastic to that extent.

(v) Excess supply. When there is excess capacity and the producer can increase output easily to take advantage of the rising prices, the supply is more elastic. In case the production is already up to the maximum from the existing resources, the rising prices will not affect supply in the short period. The supply will be more inelastic.

     

(vi) Availability of infrastructure facilities. If infrastructure facilities are available for expanding output of a particular good in response to the rise in prices, the elasticity of supply will be relatively more elastic.

(vii) Agricultural or industrial products. In agriculture, time is required to increase output in response to rise in prices of goods. The supply of agricultural goods is fairly inelastic. As regards the supply of manufactured consumer goods, it is comparatively easy to increase production in a short period.

Therefore, the supply of consumer goods is fairly more elastic; In case of supply of aero planes or any other heavy machinery, the supply is relatively inelastic as it takes time to manufacture heavy machinery.      

Categories/Types of Price Elasticity of Supply:

Definition and Explanation:
(1) Infinitely Elastic Supply:
When the amount supplied at the ruling price is infinite, we say the supply is infinitely elastic. An infinitely elastic supply curve is a horizontal straight line as is shown in the figure 7.1.
Diagram/Figure and Example:

In this diagram 7,1, when the price is OP, the producer supplies an infinite amount of goods if the price falls slightly below OP then nothing will be supplied by him.
(2) Elastic Supply:
When the percentage change in the amount of a good supplied is greater than the percentage change in price that generated it. the supply is then said to be elastic supply.
For example, if the price of oranges increases from $5 to $6 and the quantity supplied rises from 150 to 600 oranges, the supply will be elastic.

In the diagram 7.2 SS^/ supply curve is elastic and the numerical value for elasticity is greater than 1.
(3) Unitary Elasticity:
When the percentage change in the quantity supplied is exactly equal to percentage change in price that evoked it, the supply is said to have elasticity equal to unity, the elasticity of supply is equal to 1.

In the diagram 7.3 SS^/ supply curve drawn through the origin has unit elasticity of supply.
(4) Inelastic Supply:
When the percentage change in the quantity supplied is less than the percentage change in the price that generated it, the supply is said to be inelastic. The inelasticity of supply is less than 1.

In this figure 7.4 SS^/ supply curve (which is steeper than the elastic supply curve) shows that with a significant change in price, the quantity offered for sale is not very much affected.
(5) Perfectly Inelastic Supply:
In perfectly inelastic-supply, the quantity supplied does not change as price changes. The elasticity of supply in other words is zero.
For example, if the price of a painting by an artist who has died, rises from $10 thousand to $50 thousand, the supply of the painting cannot be increased. Diagram 7.5 shows the perfectly inelastic supply.

There are five degrees of price elasticity of supply:

Price Elasticity of Supply:

Definition and Explanation:

Price elasticity of demand measures the degree of responsiveness of demand for a product due to a change in the price of that product.

"Price elasticity of supply measures how responsive producers are to a change in the price of good. It is defined as a measure of the responsiveness of quantity supplied to change in price".

Measurement and Formula:

It is measured by dividing the percentage change in quantity supplied by the percentage change in price. Thus the Percentage Method formula is:

E^s = Percentage Change in Quantity Supplied

        Percentage Change in Price

It can also be written as:

E^s = ΔQ/Q

                                                                                 ΔP/P

E^s = ΔQ x P

                                                                                ΔP    Q

Just like demand, supply can also be elastic or inelastic.

Elastic Supply:

Elasticity of supply represents the extent of change in supply in response to a change in price. If the amount supplied is highly responsive to a change in price, the supply is said to be elastic.

Inelastic Supply:

If the amount offered for sale is less affected by price change, then the supply is said to be inelastic.

Relation Between Price and Supply:

The elasticity of supply is great or small accordingly as the amount offered for sale increases much or little for a given rise in price. Boulding in his book "Economic Analysis" writes:

"The relation between a price and the quantity of supply is rather like the relation between a whistle and a dog, the louder the whistle, the faster comes the dog; raise the price and quantity supplied increase. If the dog is responsive in Economic terminology; elastic-quite a small crescendo in the whistle will send him bounding along. If the dog is unresponsive or inelastic, we may have to whistle very loudly before he comes along at all".

Importance of Elasticity of Demand:

(1) Theoretical Importance:

The concept of elasticity of demand is very useful as it has got both theoretical and practical advantages. As regards its importance in the academic interest, the concept, is very helpful in the theory of value. In the words of Keynes:

"The concept of elasticity is so important that in the provision of terminology and apparatus to aid thought, I do not think, Marshall did any greater service than by the explicit introduction of the idea of the elasticity".

(2) Practical Importance:

(i) Importance in taxation policy. As regards its practical advantages, the concept has immense importance in the sphere of government finance. When a finance minister levies a tax on a certain commodity, he has to see whether the demand for that commodity is elastic or inelastic.

If the demand is inelastic, he can increase the tax and thus can collect larger revenue. But if the demand of a commodity is elastic, he is not in a position to increase the rate of a tax. If he does so, the demand for that commodity will be, calculated and the total revenue reduced.

(ii) Price discrimination by monopolist. If the monopolist finds that the demand for his commodities is inelastic, he will at once fix the price at a higher level in order to maximize his net profit. In case of elastic demand, he will lower the price in order to increase, his sale and derive the maximum net profit. Thus we find that the monopolists also get practical advantages from the concept of elasticity.

    

(iii) Price discrimination in cases of joint supply. The concept of elasticity is of great practical advantage where the separate, costs of Joint products cannot be measured. Here again the prices are fixed on the principle. "What the traffic will bear" as is being done in the railway rates and fares.

(iv) Importance to businessmen. The concept of elasticity is of great importance to businessmen. When the demand of a good is elastic, they increases sale by towering its price. In case the demand' is inelastic, they are then in a position to charge higher price for a commodity.

(v) Help to trade unions. The trade unions can raise the wages of the labor in an industry where the demand of the product is relatively inelastic. On the other hand, if the demand, for product is relatively elastic, the trade unions cannot press for higher wages.

(vi) Use in international trade. The term of trade between two countries are based on the elasticity of demand of the traded goods.

(vii) Determination of rate of foreign exchange. The rate of foreign exchange is also considered on the elasticity of imports and exports of a country. 

                                               .

(viii) Guideline to the producers. The concept of elasticity provides a guideline to the producers for the amount to be spent on advertisement. If the demand for a commodity is elastic, the producers shall have to spend large sums of money on advertisements for increasing the sales.

(ix) Use in factor pricing. The factors of production which have inelastic demand can obtain a higher price in the market then those which have elastic demand. This concept explains the reason of variation in factor pricing.

Factors Determining Price Elasticity of Demand:

The price elasticity of demand is not the same for all commodities. It may be or low depending upon number of factor. These factors which influence price elasticity of demand, in brief, are as under:

        

(i) Nature of Commodities. In developing countries of the world, the per capital income of the people is generally low. They spend a greater amount of their income on the purchase of necessaries of life such as wheat, milk, course cloth etc. They have to purchase these commodities whatever be their price. The demand for goods of necessities is, therefore, less elastic or inelastic. The demand for luxury goods, on the other hand is greatly elastic.

For example, if the price of burger falls, its demand in the cities will go up.

(ii) Availability of Substitutes. If a good has greater number of close substitutes available in the market, the demand for the good will be greatly elastic.

For examples, if the price of Coca Cola rises in the market, people will switch over to the consumption of Pepsi Cola, which is its close substitute. So the demand for Coca Cola is elastic.

(iii) Proportion of the Income Spent on the Good. If the proportion of income spent on the purchase of a good is very small, the demand for such a good will be inelastic.

For example, if the price of a box of matches or salt rises by 50%, it will not affect the consumers demand for these goods. The demand for salt, maker box therefore will be inelastic. On the other hand, if the price of a car rises from $6 lakh to $9 lakh and it takes a greater portion of the income of the consumers, its demand would fall. The demand for car is, therefore, elastic.

(iv) Time. The period of time plays an important role in shaping the demand curve. In the short run, when the consumption of a good cannot be postponed, its demand will be less elastic. In the long run if the rise price persists, people will find out methods to reduce the consumption of goods. So the demand for a good in the, long run is elastic, other things remaining constant.

For example if the price of electricity goes up, it is very difficult to cut back its consumption in the short run. However, if the rise in price persists, people will plan substitution gas heater, fluorescent bulbs etc. so that they use less^electricity. So the electricity of demand will be greater (E_d = > 1) in the long run than in the short run.

(5) Number of Uses of a Good. If a good can be put to a number of uses, its demand is greater elastic (E_d > 1).

For example, if the price of coal falls, its quantity demanded will rise considerably because demand will be coming from households, industries railways etc.

(6) Addition. If a product is habit forming say for example, cigarette, the rise in its price would not induce much change in demand. The demand for habit forming good is, therefore, less elastic.

(7) Joint Demand. If two goods are Jointly demand, then the elasticity of demand depends upon the elasticity of demand of the other Jointly demanded good.

For example, with the rise in price of cars, its demand is slightly affected, then the demand for petrol will also be less elastic.

Types of Elasticity of Demand:

The quantity of a commodity demanded per unit of time depends upon various factors such as the price of a commodity, the money income of the prices of related goods, the tastes of the people, etc., etc.

Whenever there is a change in any of the variables stated above, it brings about a change in the quantity of the commodity purchased over a specified period of time. The elasticity of demand measures the responsiveness of quantity demanded to a change in any one of the above factors by keeping other factors constant. When the relative responsiveness or sensitiveness of the quantity demanded is measured to changes, in its price, the elasticity is said be price elasticity of demand.

When the change in demand is the result of the given change in income, it is named as income elasticity of demand. Sometimes, a change in the price of one good causes a change in the demand for the other. The elasticity here is called cross electricity of demand. The three main types of elasticity of demand are now discussed in brief.

(1) Price Elasticity of Demand:

Definition and Explanation:

The concept of price elasticity of demand is commonly used in economic literature. Price elasticity of demand is the degree of responsiveness of quantity demanded of a good to a change in its price. Precisely, it is defined as:

"The ratio of proportionate change in the quantity demanded of a good caused by a given proportionate change in price".

Formula:

The formula for measuring price elasticity of demand is:

Price Elasticity of Demand = Percentage in Quantity Demand

                                       Percentage Change in Price

                                                         E_d = Δq X P

                                                                Δp    Q

Example:

Let us suppose that price of a good falls from $10 per unit to $9 per unit in a day. The decline in price causes the quantity of the good demanded to increase from 125 units to 150 units per day. The price elasticity using the simplified formula will be:

E_d = Δq X P

                                                                                Δp    Q

Δq = 150 - 125 = 25

Δp = 10 - 9 = 1

Original Quantity = 125

Original Price = 10

E_d = 25 / 1 x 10 / 125 = 2

The elasticity coefficient is greater than one. Therefore the demand for the good is elastic.

Types:

The concept of price elasticity of demand can be used to divide the goods in to three groups.

(i) Elastic. When the percent change in quantity of a good is greater than the percent change in its price, the demand is said to be elastic. When elasticity of demand is greater than one, a fall in price increases the total revenue (expenditure) and a rise in price lowers the total revenue (expenditure).

(ii) Unitary Elasticity. When the percentage change in the quantity of a good demanded equals percentage in its price, the price elasticity of demand is said to have unitary elasticity. When elasticity of demand is equal to one or unitary, a rise or fall in price leaves total revenue unchanged.

(iii) Inelastic. When the percent change in quantity of a good demanded is less than the percentage change in its price, the demand is called inelastic. When elasticity of demand is inelastic or less than one, a fall in price decreases total revenue and a rise in its price increases total revenue.

(2) Income Elasticity of Demand:

Definition and Explanation:

Income is an important variable affecting the demand for a good. When there is a change in the level of income of a consumer, there is a change in the quantity demanded of a good, other factors remaining the same. The degree of change or responsiveness of quantity demanded of a good to a change in the income of a consumer is called income elasticity of demand. Income elasticity of demand can be defined as:

"The ratio of percentage change in the quantity of a good purchased, per unit of time to a percentage change in the income of a consumer".

Formula:

The formula for measuring the income elasticity of demand is the percentage change in demand for a good divided by the percentage change in income. Putting this in symbol gives.

                             

E_y = Percentage Change in Demand

       Percentage Change in Income

Simplified formula:

E_y = Δq X P

                                                                               Δp    Q

Example:

A simple example will show how income elasticity of demand can be calculated. Let us assume that the income of a person is $4000 per month and he purchases six CD's per month. Let us assume that the monthly income of the consumer increase to $6000 and the quantity demanded of CD's per month rises to eight. The elasticity of demand for CD's will be calculated as under:

Δq  =  8 - 6 = 2                                   

Δp = $6000 - $4000 = $2000

Original quantity demanded = 6

Original income = $4000

E_y = Δq / Δp x P / Q = 2 / 200 x 4000 / 6 = 0.66

The income elasticity is 0.66 which is less than one.

Types:

When the income of a person increases, his demand for goods also changes depending upon whether the good is a normal good or an inferior good. For normal goods, the value of elasticity is greater than zero but less than one. Goods with an income elasticity of less than 1 are called inferior goods. For example, people buy more food as their income rises but the % increase in its demand is less than the % increase in income.

             

(3) Cross Elasticity of Demand:

Definition and Explanation:

The concept of cross elasticity of demand is used for measuring the responsiveness of quantity demanded of a good to changes in the price of related goods. Cross elasticity of demand is defined as:

"The percentage change in the demand of one good as a result of the percentage change in the price of another good".

Formula:

The formula for measuring, cross, elasticity of demand is:

E_xy = % Change in Quantity Demanded of Good X

          % Change in Price of Good Y

               

The numerical value of cross elasticity depends on whether the two goods in question are substitutes, complements or unrelated.

Types and Example:

(i) Substitute Goods. When two goods are substitute of each other, such as coke and Pepsi, an increase in the price of one good will lead to an increase in demand for the other good. The numerical value of goods is positive.

For example there are two goods. Coke and Pepsi which are close substitutes. If there is increase in the price of Pepsi called good y by 10% and it increases the demand for Coke called good X by 5%, the cross elasticity of demand would be:

E_xy = %Δq_x / %Δp_y =  0.2

Since E_xy is positive (E > 0), therefore, Coke and Pepsi are close substitutes.

(ii) Complementary Goods. However, in case of complementary goods such as car and petrol, cricket bat and ball, a rise in the price of one good say cricket bat by 7% will bring a fall in the demand for the balls (say by 6%). The cross elasticity of demand which are complementary to each other is, therefore, 6% / 7% = 0.85 (negative).

    

(iii) Unrelated Goods. The two goods which a re unrelated to each other, say apples and pens, if the price of apple rises in the market, it is unlikely to result in a change in quantity demanded of pens. The elasticity is zero of unrelated goods.

Measurement of Price Elasticity of Demand:

There are three methods of measuring price elasticity of demand:

(1) Total Expenditure Method.

(2) Geometrical Method or Point Elasticity Method.

(3) Arc Method.

These three methods are now discussed in brief:

(1) Total Expenditure Method/Total Revenue Method:

Definition, Schedule and Diagram:

The price elasticity can be measured by noting the changes in total expenditure brought about by changes in price and quantity demanded.

(i) When with a percentage fall in price, the quantity demanded increases so
much that it results in the increase in total expenditure, the demand is
said to be elastic (E_d > 1).

For Example:

Price Per Unit ($)	Quantity Demanded	Total Expenditure ($)
20	10 Pens	200.0
10	30 Pens	300.0

The figure (6.6) shows that at price of $20 per pen, the quantity demanded is ten pens, the total expenditure OABC ($200). When the price falls down to $10, the quantity demanded of pens is thirty. The total expenditure is OEFG ($300).

Since OEFG is greater than OABC, it implies that change in quantity demanded is proportionately more than the change in price. Hence the demand is elastic (more than one) E_d > 1.

(ii) When a percentage fall in price raises the quantity demanded so much as to
leave the total expenditure unchanged, the elasticity of demand is said to be
unitary (E_d = 1).

For Example:

Price Per Pen ($)	Quantity Demanded	Total Expenditure ($)
10	30	300
5	60	300

The figure (6.7) shows that at price of $10 per pen, the total expenditure is OABC ($300). At a lower price of $5, the total expenditure is OEFG ($300).

Since OABC = OEFG, it implies that the change in quantity demanded is proportionately equal to change in price. So the price elasticity of demand is equal to one, i.e., E_d = 1.

(iii) When a percentage fall in price raises the quantity demanded of a good so as to cause the total expenditure to decrease, the demand is said to be inelastic or less than one, i.e., E_d < 1.

For Example:

Price Per Pen ($)	Quantity Demanded	Total Expenditure ($)
5	60	300
2	100	200

In the fig (6.8) at a price of $5 per pen the quantity demanded is 50 pens. The total expenditure is OABC ($300). At a lower price of $2, the quantity demanded is 100 pens.

The total expenditure is OEFG ($200). Since OEFG is smaller than OABC, this implies that the change in quantity demanded is proportionately less than the change in price. Hence price elasticity of demand is less than one or inelastic.

Note:

As the demand curve slopes downward, therefore, the coefficient of price elasticity of demand is always negative. The economists for convenience sake, omit the negative sign and express the price elasticity of demand by positive number.

(2) Geometric Method/Point Elasticity Method:

"The measurement of elasticity at a point of the demand curve is called point elasticity".

The point elasticity of demand method is used as a measure of the change in the quantity demanded in response to a very small changes in price. The point elasticity of demand is defined as:

"The proportionate change in the quantity demanded resulting from a very small proportionate change in price".

Measurement of Geometric/Point Elasticity Method:

(i) Measurement of Elasticity on a Linear Demand Curve:

The price elasticity of demand can also be measured at any point on the demand curve. If the demand curve is linear (straight line), it has a unitary elasticity at the mid point. The total revenue is maximum at this point.

Any point above the midpoint has an elasticity greater than 1, (E_d > 1). Here, price reduction leads to an increase in the total revenue (expenditure). Below the midpoint elasticity is less than 1. (E_d < 1). Price reduction leads to reduction in the total revenue of the firm.

Graph/Diagram:

The formula applied for measuring the elasticity at any point on the straight line demand curve is:

E_d    =     %∆q    X     p

              %∆p           q

The elasticity at each point on the demand curve can be traced with the help of point method as:

E_d = Lower Segment

                                                                         Upper Segment

In the figure (6.9) AG is the linear demand curve (1). Elasticity of demand at its mid point D is equal to unity. At any point to the right of D, the elasticity is less than unity (E_d < 1) and to the left of D, the elasticity is greater than unity (E_d > 1).

(1) Elasticity of demand at point D = DG = 400 = 1 (Unity).
                                                     DA     400

(2) Elasticity of demand at point E = GE = 200 = 0.33 (<1).
                                                     EA    600

(3) Elasticity of Demand at point C = GC = 600 = 3 (>1).
                                                      CA    200

(4) Elasticity of Demand at point C is infinity.

(5) At point G, the elasticity of demand is zero.

Summing up, the elasticity of demand is different at each point along a linear demand curve. At high prices, demand is elastic. At low prices, it is inelastic. At the midpoint, it is unit elastic.

(ii) Measurement of Elasticity on a Non Linear Demand Curve:
If the demand curve is non linear, then elasticity at a point can be measured by drawing a tangent at the particular point. This is explained with the help of a figure given below:

In figure 6.10, the elasticity on DD^/ demand curve is measured at point C by drawing a tangent. At point C:

E_d = BM = BC = 400 = 2 (>1).
        MO    CA    200

Here elasticity is greater than unity. Point C lies above the midpoint of the demand curve DD^/. In case the demand curve is a rectangular hyperbola, the change in price will have no effect on the total amount spent on the product. As such, the demand curve will have a unitary elasticity at all points.

(3) Arc Elasticity:

Normally the elasticity varies along the length of the demand curve. If we are to measure elasticity between any two points on the demand curve, then the Arc Elasticity Method, is used. Arc elasticity is a measure of average elasticity between any two points on the demand curve. It is defined as:

"The average elasticity of a range of points on a demand curve".

Formula:

Arc elasticity is calculated by using the following formula:
-

E_d = ∆q X P¹ + P²

                                                                           ∆p    q¹ + q²

Here:

∆q denotes change in quantity.

∆p denotes change in price.

q¹ signifies initial quantity.

q² denotes new quantity.

P¹ stands for initial price.

P² denotes new price.

Graphic Presentation of Measuring Elasticity Using the Arc Method:

In this fig. (6.11), it is shown that at a price of $10, the quantity of demanded of apples is 5 kg. per day. When its price falls from $10 to $5, the quantity demanded increases to 12 Kgs of apples per day. The arc elasticity of AB part of demand curve DD^/ can be calculated as under:

E_d = ∆q X P¹ + P²

                                                                           ∆p    q¹ + q²

E_d = 7 X 10 + 5 = 7 X 15 = 7 X 15 = 21 = 1.23
        5     5 + 12   5    17    5    17    17

The arc elasticity is more than unity.