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## Saturday, February 16, 2008

### 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:
qd = 10 - 3P and qs = 2P
By definition, demand and supply must be equal (qd = qs) for the condition of equilibrium.
qd = 10 - 3P = qs = 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.
Figure 9
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.

### 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 where 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:

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

### 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 (qd) 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 qdFigure 2
(B) Demand Function: The price-demand relationship shown above can be expressed in the form of a demand function as follows:
qd = 10 - 3P
On substitution of any scheduled value of P we get the relevant value of the quantity demanded. Thus when P = 1 then qd =10 - 3 (1) = 7 or when P = 3, then qd = 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,
qd = f (P) [ Y, Ps, N, Z ]const.
This explains that qd, 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).