DEMAND, SUPPLY AND ELASTICITY

2.1 Fundamental Concepts 

Demand and supply are basic concepts in economic analysis. This is because economics is fundamentally concerned with ends and means. The quantities of various goods demanded are expected to bring satisfaction of different wants or ends, the supply of these goods is conditioned by the availability or scarcity of resources which act as the means of production. Both the terms ‘demand’ and ‘supply’ have technical implications. By demand, we mean the quantity of any commodity that ‘buyers are willing and have the ability to buy.’ Both the conditions must be satisfied together before goods can be demanded. One who smokes wishes to purchase cigarettes but he must have enough money or resources to do so. Similarly, a quantity of a commodity is said to be supplied only when a seller is willing to sell it at the market price. 

The two concepts of demand and supply are, however, relative in nature and conveniently interchangeable. For example, a person may visit a distant wholesale market and purchase 50 small cans of beer at a somewhat lower price than what he would have paid in the local market. Therefore 50 cans of beer can be said to be his demand for the commodity. On his way home he meets a friend B who requests for 10 cans of beer at a particular price. If the bargain is acceptable, A will sell 10 cans to B, which will consist of his (that is A’s) ‘supply’ and the remaining 40 cans will then be his demand. Later on if a close relative of A (say C) requests him to part with 5 cans of beer on a ‘no profit no loss’ basis, then that becomes a further part of his ‘supply’ and his demand is reduced to 35 cans of beer. Similarly a shopkeeper who begins with 200 cans of beer (which is his supply) may retain 10 cans for himself and for his family members (this is known as self-consumption). In that case, his supply is reduced to 190 cans and demand would be 10 cans.

Finally demand and supply are mutually opposing concepts, in the sense that demand is an inverse (falling) function of the price, while supply is a direct (rising) function of the price. This is explained in the following sections.

Demand Schedule, Function and Law

D(demand) qd	Schedule P
10	0
8	1
4	2
1	3
0	4

(A) Demand Schedule : The various quantities demanded of a particular commodity are presented here in a schedule. At arbitrarily chosen prices, the quantity of a commodity an individual consumer is expected to demand, is explained by the schedule. Since quantity demanded (q_d) depends on the relevant prices of goods, the two can be expressed in the form of an algebraic function as well. The schedule shows that as price goes on rising (from zero to 4) the quantity demanded goes on falling (from 10 to zero).

The scheduled information has been presented in the form of a demand curve in Figure 2 (below). In the figure, the units of quantity of the goods have been measured along the horizontal axis (OX) and the respective prices have been shown along the vertical axis (OY). The curve intersects OY axis at point A which shows highest price at which quantity demanded is zero. On the contrary the curve intersects OX axis at point B showing largest quantity demanded where price is zero. Both OA and OB are said to be intercept quantities when one of the variables assumes zero value. Note that demand curve is sloping downward. This follows the law of demand (given below). But the demand curve of such a shape is obvious from the fact that quantities demanded and price in the demand schedule hold an inverse relationship.

Quantity Demanded q_d
Figure 2

(B) Demand Function: The price-demand relationship shown above can be expressed in the form of a demand function as follows:

q_d = 10 - 3P

On substitution of any scheduled value of P we get the relevant value of the quantity demanded. Thus when P = 1 then q_d =10 - 3 (1) = 7 or when P = 3, then q_d = 10 - 3 (3) = 1 etc.

(C) Law of demand: The law of demand explains the inverse relation between quantity and price in general. It can be stated as follows:

"Ceteris Paribus (other things remaining equal), the quantity of a good demanded will rise (expand) with every fall in its price and the quantity of a good demanded will fall (contract) with every rise in its price."

In a functional form this can be stated as,

q_d = f (P) [ Y, Ps, N, Z ]_const.

This explains that q_d, the quantity of a good demanded functionally depends on its price P. However, the quantity demanded is also causally related to other factors such as income of an individual (Y), prices of substitutes (Ps), number of members in the family (N) and the tastes of the consumer (Z). In order to satisfy price-demand relation, the effect of these other variables has been restrained by assuming them to be constant.

Initially, the law of demand was based on the principle of diminishing marginal utility (DMU). But in that case it was implied that utility is cardinally or absolutely measurable. There were other practical difficulties in the DMU approach as well. Therefore recently attempts have been made to place the law of demand on the empirical and realistic basis. One such attempt is in the form of Indifference Curve (IC) analysis. Under the IC approach it is enough to measure utility in ordinal or relative terms. 

(D) Rise or Fall and Increase or Decrease in demand: On a given demand curve as we move downwards from point A in the direction of B, the quantity demanded goes on rising with every successive fall in price. On the contrary, moving from point B to A shows a fall in the quantity demanded with every successive rise in the price. Marshall has called this process rise and fall or expansion and contraction in the demand. Therefore, in this case the price of the quantity (and the change in it) plays an important part. Here, a change in the quantity demanded is indicated with movement along the demand curve (up or down accordingly). This change is subject to the ceteris paribus condition.

On the other hand, other factors are also likely to alter the quantity demanded. This can be expressed by a shift in the curve. Such an upward shift in the demand curve (Figure 3) has been shown by a new and higher demand curve (A₁B₁) in the figure.

Figure 3

At a given price OP on the original demand curve (AB), the quantity demanded is Oq but on the new demand curve (A₁B₁) it has increased to Oq1. On the other hand, if we begin with the A₁B₁ demand curve as the initial demand curve and consider demand to have reduced (to AB) then the quantity demanded reduces from Oq1 to Oq. Such a change in the demand, arising out of a shift in the demand curve is known as an increase (if it is towards the right of the original demand curve) and a decrease (if it is towards the left of the original demand curve) in the demand, respectively. 

The demand curve may shift and quantity demanded may increase or decrease, due to changes in a number of factors (apart from price), say the income (Y) of a consumer (when he becomes richer or poorer). A similar effect can be noticed with a rise or fall in the price of substitute (Ps) goods. For instance, tea and coffee or soaps of different brands are substitutes of each other. Therefore a rise in price of pasta may result in a reduction in the consumption of pasta and simultaneously an increase in the consumption of bread to that extent and vice versa. Or the demand curve may shift and quantity demanded may increase at the old price if there is a sudden increase in the number of members in a family (N), (say because of the unexpected arrival of guests). Finally, a shift in the demand curve may also be the result of the change in the tastes of a consumer. A cigarette or liquor consumer may become addicted because of which his demand for such goods will rise remarkably even at the old price.

There is an important difference between the change in the quantity demanded of a particular commodity and change in the demand for that commodity. While the former is influenced by the single factor: price, the latter is influenced by various other factors apart from price. A change in the quantity demanded is represented by a movement along the demand curve, while a change in the demand is represented by a shift of the curve (towards the left in case of a decrease and towards the right in case of an increase).

Supply Schedule, Function and Law

(A) Supply Schedule: Just as goods are demanded by consumers, they are supplied by manufacturers or sellers. At any point of time quantity supplied by them is a function of the market price. Several such prices can be related to the relevant quantities supplied: this would give the supply schedule. In the given schedule, as price of the goods rises (from zero to 3) the quantity supplied also rises (from zero to 6 units).

Supply Schedule
qs	P
0	0
2	1
4	2
6	3

(B) Supply Function: Supply is a direct function of the price and it rises or falls with the price. This is because the law of supply is based on the behavior of the cost of production. Assuming that manufacturers

begin at the point where cost of production is minimal any further production and supply of goods can be possible only at an increasing additional or marginal cost per unit. Hence they can afford to supply more only at a rising price. Further, logically any seller would be willing to sell more goods if the price were to rise. The quantity supplied at the given range of prices as above can be presented in the form of an algebraic function:

q_s = 2P

With the help of the function we can find the quantity supplied at any randomly chosen prices. For instance, when P = 3, q_s = 6 or when P = 2, q_s = 4 etc.

(C) Law of Supply: The law of supply can be stated as follows:

"Ceteris paribus, the quantity of a good supplied will rise (expand) with every rise in its price and the quantity of a good supplied will fall (contract) with every fall in its price."

In a functional form this can be stated as :
q_s = f (P) [T, R, P] _const.

The quantity of a commodity supplied is thus a function of its own price. There exists a direct relationship between the quantity supplied and the price of a commodity. It is subject to the condition that other things should remain constant. In this case ‘other things’ include mainly two things. These are technical conditions or methods of production (T) and the prices and quantities of the resources supplied (RP). With improved technical conditions, supply can be increased at the same old price, since the cost of production can now be reduced. Similarly with an enhanced supply of resources and a reduction in the prices of resources such as land, labor, raw materials etc. an increasing quantity of the commodity can be supplied at a constant or even falling price.

Figure 4

Figure 4 is the graphical representation (the supply curve) of the supply schedule. It begins at the point of origin where both quantity supplied and price are zero in value, and then it continuously rises upwards. This upward sloping curve indicates the positive relationship between supply and price: there is a rise in the quantity supplied with every successive rise in the price.

(D) Expansion or contraction and increase or decrease: Changes in the quantity supplied as a result of movement along the same supply curve has been described by Marshall as rise and fall or expansion and contraction of quantity supplied of the commodity. But if the supply curve shifts left or right of the original curve, the changes in supply of the good are known as increase or decrease.

Figure 5

In figure 5 we notice such a shift in the supply curve. On the original supply curve (OS) the quantity of goods supplied at price OP is Oq but when the supply curve shifts towards its left (i.e. S₁ S₁) then at the same price OP, the quantity supplied decreases to Oq₁. If we begin with S₁ S₁ as the original supply curve, OS would represent a shift of the supply curve towards the right. In this case, quantity supplied increases at a given price.

The supply curve undergoes a shift in it with a change in the technical conditions or the price and supply conditions of the inputs (resources). With improved techniques or methods of production, the degree of the efficiency with which some or all resources can be utilized will increase. This results in a favorable change in the cost of production. Similarly with improved supplies and reduced prices of the inputs, the cost of production tends to fall and an increased supply of a commodity becomes possible at a given market price.

Elasticity of Demand and Supply 

(A) Price Elasticity

 i) Elasticity of Demand: Elasticity of demand can be classified into two major divisions: one the highly elastic, unitary elastic and the highly inelastic type and two, the extreme cases of the perfectly elastic and the perfectly inelastic type.

a) Highly elastic, Unitary elastic and highly inelastic: The laws of demand and supply are no doubt an important part of economic analysis. But the knowledge about demand and supply relations serves only a limited purpose. This is in view of the fact that both demand and supply laws are applicable to all kinds of goods. However, an actual rise or fall in the quantity demanded or supplied with a small variation in the price may considerably differ for different goods such as food, automobiles, film shows, garments, hardware materials, machines, land etc. In other words it is important to know the extent of rise or fall in the demand with a given change in the price for each individual good. This is exactly the purpose served by the concept of price elasticity of demand; this concept is advanced and subtle in nature. It was first developed by Alfred Marshall; he has defined elasticity as follows:

Elasticity of demand is the degree of responsiveness with which quantity demanded changes for a given change in price.

In other words it is a proportional change in the quantity demanded to a proportional change in price.

Price Elasticity of demand is then the ratio of the proportional change in the quantity demanded to the proportional change in price.

Proportional change in quantity can be expressed as        where q₁ is the initial and q₂ is the new quantity demanded.

Proportional change in price is similarly  &nbspwhere P₁ is initial and P₂ is the new price.

Elasticity ratio e is therefore,    

If symbols q and P are used for small variations in quantity and price respectively then,

Note that Dq / Dp is in the limit derivative or marginal change and p/q is the reciprocal of average change, therefore

Let’s illustrate this. In our demand schedule example above, when price changes from 2 to 3 units, the quantity demanded changes from 4 to 1 units. Substituting these values we have:

Note that the elasticity ratio 3/2 is more than one and has a negative sign. Both these are important features. Numerical values explain the extent or degree of change in demand while the sign of the ratio explains the direction of change. Since the law of demand is based on the inverse relation between price and quantity, the elasticity of demand is always stated with a negative sign.

The numerical value of elasticity can be equal to 1 (that is called ‘unit’) more than one or less than one. In case of unit elastic demand (e = 1) both price and quantity (demanded) changes occur in the same proportion. If the value of elasticity exceeds one (e > 1) then the percentage or proportional change in quantity demanded is greater than that in price and the good is said to be price elastic or highly responsive to a change in price. If the value of elasticity is less than one (e < 1) then the proportional change in quantity is smaller than that in price and the demand for the good is said to be price inelastic or not very responsive to a change in price. The information about the value of elasticity therefore serves an important purpose in classification of various goods as elastic or inelastic in demand. This helps in several practical and policy applications such as taxation, foreign trade, monopoly, price determination etc. 

There are four methods of measurement of elasticity of demand. These are percentage, proportion, outlay and geometric or point elasticity methods. The one mentioned last (point elasticity method) is the most accurate and can be explained conveniently with a given demand curve:

Quantity demanded

Figure 6

In the figure, AB is the demand curve and at any point on this, the elasticity of demand can be measured. At points R₁, R and R₂ the values of elasticity are:

At the mid point R on the demand curve, the value of elasticity is unit or equal to one. But above point R such as at R₁, the value of elasticity is more than one and demand is highly elastic. On the other hand at a lower point such as R₂ demand becomes inelastic as the value of elasticity is less than one. In general as we move in the direction of the Y axis, demand becomes more and more elastic. But as we move in the direction of the X axis, demand becomes less and less elastic. In other words at every higher price demand is relatively more elastic and at every lower price demand is relatively less elastic. This also explains that elasticity of demand differs not only from commodity to commodity but also for the same commodity at varying prices.

b) Two extreme cases: Besides the three explained above, two more extreme values of price elasticity of demand can be included in the analysis. These are:

(i) Perfectly Price Elastic: At this extreme, for any small decrease in price, the increase in the quantity demanded is infinitely large. In such a case, demanders demand all the can. Here the demand is said to be perfectly price elastic (e = that is infinity). This is represented graphically as a horizontal demand curve (D₁ in the figure above).

(ii) Perfectly Price Inelastic: At this extreme, for any change in price there is no change in the quantity demanded. Therefore the demand is completely unresponsive to any change in price. In this case the demand is said to be perfectly price inelastic (e = 0). This is represented graphically by a vertical demand curve (D₂ in the figure above).

ii) Elasticity of Supply: Like demand, elasticity of supply can also be classified into two major divisions: one the highly elastic, unitary elastic and highly inelastic type and two, the extreme cases of the perfectly elastic and the perfectly inelastic type.

a) Highly elastic, unitary elastic and highly inelastic: Elasticity of supply can similarly be defined and computed at varying prices and quantities supplied.

Elasticity of supply is the degree of responsiveness with which quantity supplied changes with a given change in the price.

This can be expressed with a similar formula:

An important difference between the price elasticity of demand and that of supply is that the latter is positive in value (as against the negative value in case of elasticity of demand). This is obvious from the fact that supply is a direct function of price: and both quantity and price change in the same direction. This will be clear from the following example. The values of ‘q’ and ‘P’ have been selected from the supply schedule given above.

The elasticity of supply also shows variations in its value for different commodities. Accordingly supply elasticity for different goods can be unit, (e_s = 1) more than one (e_s > 1) or less than one (e_s < 1). The goods can then be categorized as relatively elastic or inelastic in supply. Elasticity of supply is also of considerable practical importance in its policy applications.

b) Two extreme cases: Besides the three explained above, two extreme values of price elasticity of supply can be included in the analysis:

i) Perfectly Price Elastic: At this extreme for any small decrease in price, the quantity supplied is infinitely large. In such a case, suppliers supply all they can. Here the supply is said to be perfectly price elastic (e = that is infinity). This is represented graphically by a horizontal supply curve (S₁ in the figure below).

ii) Perfectly Price Inelastic: At this extreme for any change in price there is no change in the quantity supplied. Therefore the supply is completely indifferent to any change in price (e = 0). Here the supply is said to be perfectly price inelastic. This is represented graphically by a vertical supply curve (S₂ in the figure below).

Income elasticity: Demand is a function, besides price (P) also of the income (Y) of an individual. However, income and demand hold a direct relationship, such that Y and Q rise or fall together. Hence the sign of elasticity ratio in this case is normally positive. Let’s illustrate this :

Assume that the values of Y and Q are as follows :

Y₁ = 100          Q₁ = 16
Y₂ = 120          Q₂ = 18

In this case the value of income elasticity e_y will be:

(C) Cross Elasticity: The price elasticity of demand that we have studied so far is also called the "own elasticity." This is because we have determined the elasticity for good A with the change in the price of the same good. However, various goods A, B, C etc. hold a mutual relationship. As such if we attempt to find the elasticity of demand for good B whenever the price of good A changes, then it is called a cross elasticity ratio. However, the goods A and B may hold either of the following relationships:

i) Substitutes : as in case of tea and coffee or different brands of toothpaste, television sets etc. These goods are symbolized as B_S which implies that B is a substitute of A. In this case, whenever the price of A rises the demand for A will fall but that of B will rise. Therefore the relation between P_A and Q_B is direct. Hence the sign of elasticity ratio will be positive. This can be illustrated as:

P_A         &nbspQ_A      &nbspQ_BS

10         &nbsp8           8

12         &nbsp6         &nbsp10

ii) Complementary goods: Consider two complementary, good A - a vehicle and B - gasoline. In this case, with a rise in the price of A the demand for A (Q_A) will fall and similarly, the demand for B(Q_BC) will also fall. The sign of elasticity ratio will then be negative in sign. This can be illustrated as follows:

P_A          &nbspQ_A         &nbspQ_BC

5000       &nbsp100          40

6000          80          35

The Concept of Equilibrium

Both demand and supply functions independently serve important functions. However, it is important to bring them together in an attempt to establish equilibrium. The concept of equilibrium, though analytical in nature, is quite simple in practice. It can be defined as a point of equality or agreement between buyers and sellers. Since both demand and supply quantities are shown in the scheduled forms these indicate mutual willingness of consumers and producers to purchase or sell respectively, varying quantities at varying prices. The schedules do not yet explain actual market price at which deals take place. This can be possible only when the quantities demanded and supplied are exactly equal at some uniform price. So long as this has not been achieved, some buyers or sellers are yet dissatisfied and may attempt to raise or lower the price. In this sense equilibrium is a point of complete satisfaction of the given behavior of buying and selling and hence an act of fulfillment of a given economic activity.

Let’s present and illustrate the establishment of equilibrium with the help of demand and supply functions in our earlier examples (in the sections given above). We begin with two equations:

q_d = 10 - 3P and q_s = 2P

By definition, demand and supply must be equal (q_d = q_s) for the condition of equilibrium.

q_d = 10 - 3P = q_s = 2 P or 10 - 3P = 2P

On solving this we find equilibrium price:

On substituting the value of price in demand and supply function we get,

qd = 10 - 3P qd = 10 - 3 (2) = 10 - 6 = 4

qs = 2P qs = 2 (2) = 4

Hence equilibrium price is 2, at which both quantity demanded and supplied are equal to 4. The algebraic proof (Figure 7) of the equilibrium can also be presented geometrically.

  

In the figure, AB and OS are the demand and supply curves respectively. The two curves intersect at point E which is an equilibrium point at which price P = 2 and quantity demanded and supplied are both equal (q = 4). At any other price higher than P such as P₁, the quantity supplied S₁ exceeds the quantity demanded d₁ (S₁ > d₁) and hence at this stage, some sellers remain dissatisfied. On the other hand at any lower price such as P₂, quantity demanded d₂ exceeds quantity supplied S₁ (d₂ > S₁) and this time some buyers remain dissatisfied. Therefore only at the point of intersection between demand and supply curves can equilibrium be attained. In other words, equilibrium price represents that price at which buyers are willing to buy the good and sellers are willing to sell it. This is the point of satisfaction for both the groups.

**********