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Sunday, July 24, 2011

Theory of Demand

Theory of Demand

There are three theories of demand or there are three theories of measuring demand:

(a)    Marginal utility analysis;
(b)   Indifference curve techniques; and
(c)    Revealed preference theory.

Marginal Utility Analysis:
Also known as ‘Utility analysis of demand’.

Basic Assumptions:
(i)                  Cardinal measurement of utility,
(ii)                Utilities are independent,
(iii)               Constant marginal utility of money,
(iv)              Introspection – drawing reference about a person from one’s own experience.

(a)   Law of Diminishing Marginal Utility:
It refers to the additional benefit, which a persons derives from a given increase of his stock, diminishes with every increase in his stock.

(i)                  The marginal utility diminishes which every increase in stock,
(ii)                The total utility is maximum when the marginal utility is zero,
(iii)               Each particular want is stable,
(iv)              Goods are imperfect substitutes and consumed in appropriate portions.


(i)                  Consumption is continuous,
(ii)                The commodity is taken in suitable quantity,
(iii)               The commodity is taken at certain time interval,
(iv)              The greater the quantity of commodity is taken, the greater the utility,
(v)                Rational behaviour of consumer,
(vi)              Constant income of consumer,
(vii)             Change in other people’s stock,
(viii)           Possession of other related commodity,
(ix)              Trends in fashion not changed,
(x)                No change in the price of commodity,
(xi)              The marginal utility of rare collections does not diminished,
(xii)             The units of commodity taken are of same quality,
(xiii)           This law is not applied to the utility of money.

Definition of Marginal Utility:
It refers to the addition in total utility resulting from a one-unit change in the quantity consumed.  The consumer stops purchasing at a point where the princes and the marginal utility are just equal.  Above this point, the marginal utility will be negative.

Marginal Utility of Money:
The marginal utility of money increases with the increase in quantity of money.  But the law of diminishing marginal utility also applies to money.  As the amount of money increases it brings lesser and lesser pleasure to the recipient of money.

Marginal Utility and Price:
(i)                  The consume stops purchasing when the marginal utility and price are equal,
(ii)                The marginal utility indicates the prices.  For example, it is the marginal utility not the total utility that determines prices; otherwise the price of water should have been high, and that of gold low.

Marginal Utility and Supply:
The greater the marginal utility, the lesser the supply, and vice versa.  The marginal utility is equal to zero when the supply is super-abundant.

Marginal Utility of Related Goods:
(a)   Imperfect Substitutes:
The marginal utility increases with the decrease in quantity of substitute goods, and vice versa.
(b)   Complementary Goods:
The marginal utility increases with the increase in the quantity of complementary goods, and vice versa.

Importance of Law of Diminishing Marginal Utility:
(a)   Taxation:
It provides the basis of the laws and practices of taxation.  Since the marginal utility of money to a richer person is lower than poor person, therefore, higher tax rates are levied on him, and vice versa.

(b)   Price Determination:
It refers to a decrease in the value of a commodity with an increase in its supply, and vice versa.

(c)    Household Expenditure:
Larger the purchase, lower the marginal utility, and vice versa.

(d)   Downward Sloping Demand Curve:
This law also provides the reason for downward sloping demand curve.

(e)   Value-in-Use and Value-in-Exchange:
It also study the divergence between value-in-use and value-in-exchange.  For example, air has a higher value-in-use (utility) but a very little value-in-exchange.

(b) Law of Equi-Marginal Utility:
The law of equi-marginal utility or the law of equilibrium utility is known by various names.  It is also known as ‘law of substitution’, ‘law of maximum satisfaction’, ‘law of indifference’, ‘the proportionate rule’, and ‘Gossen’s second law’.

The consumer compares the satisfaction which he obtains from the purchased commodity and the price he pays.  If the utility of commodity is greater or at least equal to the loss of utility of money price, the consumer buys that commodity.  As he buys more and more of that commodity, the utility of successive units begins to diminish.  He stops further purchases at a point where the marginal utility of the commodity and the money he paid is just equal.  Beyond this point the marginal utility is negative.  And this can be stated as the point of equilibrium, where the consumer derives maximum satisfaction from a given commodity.  If the consumer finds that a particular expenditure in one use is yielding less utility than that of other, he will try to transfer a part of his purchase from the previous commodity to the new one yielding higher utility.  With two commodities, the consumer is in equilibrium at a point where the marginal utility of each commodity is in proportion to the price, and the ratio of the prices of all goods is equal to the ratio of their marginal utilities.  It can be mathematically expressed as follows:

Units of
Utility of
Utility of
Total Utility

Expenditure (Rs.)
Rate of
Marginal Utility
On Tea
On Cigar
On Tea
On Cigar

(a)    This law becomes inoperative when the consumer demand is influenced by fashions and customs;
(b)   Consumers do not usually measure the utility of the purchased commodity;
(c)    This law becomes inoperative when the unit of expenditure is not divisible;
(d)   Again the law is inoperative when the people have no freedom of choice to choose between various alternatives.

Practical Application of Law:
(a)   Consumption:
Substitution of two commodities’ utilities in order to achieve maximum marginal utility;
(b)   Production:
Substitution of two factors of production in order to maximise total profit;
(c)    Exchange:
Substitution of any two things in order to achieve the desired things;
(d)   Price Determination:
Substitution of less scarce good for the more scarce good in order to minimise the scarcity of more scarce goods.
(e)   Distribution:
The use of each factor of production is pushed by the entrepreneur to the margin of profitableness till the marginal product in each case is equal;
(f)     Public Finance:
Substitution of various public expenditures in order to maximise the benefit.

Demand Curve:
A fall in price has the following effects:

(i)                 Income Effect:
The real income of a consumer increases when the prices are decreased.  Now the consumer can afford more purchases within the unchanged income.
(ii)               Substitution Effect:
When the price of a product decreases, it tends to be substituted for other commodities.
(iii)             Cumulative Effect:
A commodity with decreased price is put to more uses before; and therefore, it has a cumulative effect when the commodity is more purchased and used by the consumer.

The Law of Diminishing Marginal Utility (LDMU) is the basis of the Law of Demand (LD).  The consumer will buy more only if the price falls because more he buys the lower is the marginal utility.

Demand is the function of price:

D = f (P)

In constructing the demand curve, we only consider the factor of price, and we ignore other factors, i.e., changes in fashion, wealth distribution, changes in real income, etc.

Assumptions of Law of Demand:
(a)    The consumer’s tastes, habits, income, etc are remain unchanged;
(b)   Prices of substitutes and complementary goods are remain unchanged;
(c)    No expectations for further changes in commodity’s price;
(d)   No new substitute commodity has entered into the market.

Relationship between LDMU and LD:
(a)    Law of diminishing marginal utility states that larger the quantity, less is the utility;
(b)   Law of demand states that larger the quantity, lower is the price, because the utility of the successive units is less;
(c)    This means that each addition to the quantity demanded, marginal utility of the consumer will be diminished;
(d)   Each additional unit of a good consumed within a given time period yields diminishing utility;

Theory of Benham – Relationship between LDMU and LD:
(a)    According to Benham, when the price of a commodity falls a divergence is created between the marginal utility and price, and it must be rectified;
(b)   According to Benham, it must be rectified, so as to equalise the marginal utility from the last paisa that the consumer spends in different ways.  And it can be done by purchasing more of the commodity, thus bringing the marginal utility to the level of price.

Exceptional Demand Curve – Giffen Paradox:
Sometimes the demand curve instead of sloping downward may tend to rise upwards from left to right.  This situation is represented by more purchases at a rise in price.  In other words, people buy more when the price rises.  This situation is imaginary and was first observed by Sir Robert Giffen.  His theory is commonly known as ‘Giffen Paradox’.  Benham has mentioned four seasons/cases for this imaginary situation:

(a)    In case of war, hyper-inflation, draught, a serious shortage is feared and people may be panicked to buy more even if the prices are rising;
(b)   When the use of a commodity confers distinction, then the wealthy people will buy more when the price rises, to be included among the distinguished personages.  Conversely, people tend to cut their purchases, if they believe the commodity to be inferior;
(c)    People may buy more, when the price rises, in sheer ignorance;
(d)   If the prices of necessary commodities go up, the consumer will ready just his expenditure, in order to maintain his previous quantity of purchases by reducing the purchases of other unnecessary commodities.

Difference between Movement and Shift of Demand Curve:
(i)                  Movement along demand curve refers to extension and contraction of demand.  It means that the change in demand is the result of a change in price instead of a change in other factors.
(ii)                Shifting in demand curve refers to the increase or decrease of demand.  It means that the change in demand is the result of a change in the factors other than price.

Elasticity of Demand
Kinds of Elasticities of Demand:
(a)    Price Elasticity,
(b)   Income Elasticity,
(c)    Cross Elasticity, and
(d)   Substitution Elasticity.

(a)   Price Elasticity:
It is the price elasticity, which is commonly referred to as elasticity of demand.  The law of demand indicates the direction of demand, however, it does not tell us the amount of quantity demand in response to a change in price.  Price elasticity of demand, particularly, tells us the responsiveness of demand in reaction to the change in price of a commodity.  It tells us the amount or the extent by which the demand will change in response to a change in the price.

Degrees of Price Elasticity of Demand:

(i)                  Perfectly Elastic Demand (e = ∞)
(ii)                Perfectly Inelastic Demand (e = 0)
(iii)               Unitary Elasticity of Demand (e = 1)
(iv)              Relatively Inelastic Demand (e < 1)
(v)                Relatively Elastic Demand (e > 1)

Measurement of Price Elasticity:

(i)                  Total Outlay Method
(ii)                Proportional Method
(iii)               Geometrical Method

(i)                 Total Outlay Method:
This method analyses the relationship between the price of commodity and total revenue earned by the seller.  Under this method, the elasticity of demand can be expressed in three ways, i.e., unitary elasticity, greater than unity elasticity, and less than unity elasticity.

a.      Unitary Elasticity:
Under the total outlay method, the unitary elasticity of demand is represented by the situation when, even though the price has changed the total amount spent or total revenue (from seller’s point of view) remains the same.  This situation is represented by a ‘rectangular hyperbola’, where the elasticity is unity throughout the demand curve at different price stages.

(e = 1) P ↑ O ↕, P ↓ O ↕

b.      Greater-than-unity Elasticity:
Under the total outlay method, greater than unity elasticity of demand refers to the situation when with the fall in price, the total amount spent by the consumer increases, and with the rise in price, the total amount spent by the consumer decreases.

(e > 1) P ↑ O↓, P ↓ O ↑

c.       Less-than-unity Elasticity:
Under the total outlay method, less than unity elasticity of demand refers to the situation when the total amount spent or total revenue increases with the rise in price and the decreases with the fall in price.

(e < 1) P ↑ O ↑, P ↓ O↓

Outlay /
e < 1
e < 1, e = 1
e = 1, e >1
e > 1
e > 1

(ii)               Proportional Method:
Under this method, elasticity of demand is measured in terms of a ratio of the percentage change in the quantity demanded to the percentage change in price.  It can be mathematically expressed as follows:

Under this method, the elasticity of demand is always negative, although by convention, it is taken to be positive.  It is negative because the fall in price is followed by a rise in demand.  Again, the elasticity is stated in three forms, i.e., greater than unity elasticity, unitary elasticity and less than unity elasticity of demand.

(iii)             Geometrical Method:
Geometrical method of measuring elasticity of demand can measure elasticity of demand at any point on the demand curve.  Elasticity is stated in terms of fraction and in three forms, i.e., greater than unity, unitary and less than unity elasticity of demand.  The middle of the curve represent unitary elasticity, below to which, elasticity is less than unity, and above to which, elasticity is greater than unity:


Point and Arc Elasticity:
1.      The point elasticity refers to elasticity of demand at any point on a demand curve.  Point elasticity considers small changes in demand and price.  The elasticity of demand on a particular point of demand curve can be mathematically calculated as below:

2.      According to Baumol, arc elasticity of demand is a measure of the average responsiveness to price changes.  This could be measured through finite stretch of a demand curve.  Therefore, any two points on a demand curve forms an arc, and between these two points, the arc provides measurement of elasticity of demand over a certain range of price and quantities.  This can be simply plotted into the following mathematically formula:

(b)   Income Elasticity of Demand:
It is generally observed that there is an inverse relationship between the quantity demanded and price of a commodity.  Therefore, the demand curve slopes downward from left to right.  Whereas, this is not in the case of the relationship of income and quantity demanded.  The higher the income of the consumer, the more units of commodity will be bought by him.  Thus, the demand curve in the income elasticity slopes from right to left.  Income elasticity of demand refers to the degree of responsiveness of quantity demanded to a change in the income of the consumer.  It can be mathematically expressed as follows:

Measurement of Income Elasticity:
The income elasticity can be measured through the above mathematical formula.  The resulting figure can be classified into the following:

(i)                 Greater-than-unity:
The elastic demand of a commodity is expressed in the figure greater than 1.  (e > 1)
(ii)               Unitary elasticity:
The unitary elasticity of demand means that the change in consumer’s income is followed by proportionate change in quantity demanded. (e=1)
(iii)             Less-than-unity:
The less than unity means inelastic demand of a commodity and expressed in the figure less than 1.  It means that the degree of change in quantity demanded is less than to the change in consumer’s income.  (e < 1)

(c)    Cross Elasticity of Demand:
When the quantity demanded of a commodity changes in response to the change in price of another commodity, it refers to cross demand elasticity.  These two commodities may either be substitutes of each other, or one may be a complementary good for another.  Therefore, the cross elasticity of demand is measured in accordance with these two types of inter-related goods, i.e., the substitutes, and complementary goods.  Cross elasticity of demand is expressed as the percentage change in quantity demanded of good X to the percentage change in the price of a related good Y.  Mathematically it can be measured as below:

The cross elasticity of demand can be further bifurcated into:

(i)                  Cross elasticity of substitute goods, and
(ii)                Cross elasticity of complementary goods.

(i)                 Cross elasticity of substitute goods: The examples of substitute goods are: tea and coffee, motor car and motor cycle, cigarette and pipe, pen and pencil, telephone and mobile phone, business and service or investments in marketable securities, lease hold property and free hold property, etc.  Suppose the prices of motor cars significantly rise, there will be a shift of demand from motor car to a cheaper substitute, i.e., motor cycle.  It should be remembered that the elasticity of demand of substitutes will always positive.  The cross elasticity of substitute goods can be in three forms:

a.      Greater-than-unity: Greater than unity elasticity means that the change in price of a good, say, motor cycle leads to more proportionate change in the quantity demanded of the substitute, say, motor cycle. (e > 1)
b.      Unitary elasticity: of demand refers to the proportionate change in price of a good followed by equal proportionate change in quantity demanded of the substitute.  (e = 1)
c.       Less-than-unity: elasticity of demand refers to less proportionate change in quantity demanded of the substitute good leaded by the change in price of a good.  (e < 1)

(ii)               Cross elasticity of complementary goods: The examples of complementary goods are: pen and ink, motor vehicle and petrol/gas, house and paint, fertiliser and seeds, aeroplane and internal equipment, computer and internet products, mobile phones and charging adopter, etc.  Complementary goods are jointly demanded by a consumer.  Therefore, with a rise in the price of a commodity will lead to a fall in demand for its complementary goods.  In this case the elasticity of demand is negative.

(d)   Substitution Elasticity of Demand:
The substitution elasticity of demand refers to the fact that to what extent one commodity can be substituted for another without making any change in the total satisfaction of the consumer.  The underlying concept is the ‘marginal rate of substitution’ as studied in ‘Indifference Curve’.  From the definition of substitution elasticity, it can be concluded that the consumer is to remain on the same indifference curve at various combinations of substitution commodities.  It is the substitution effect that measures the substitution elasticity of demand, just as in the price elasticity of demand, measured by price effect.

Following are the forms of substitution elasticity of demand:

(i)                  Elasticity of substitution is infinite,
(ii)                Elasticity is equal to zero,
(iii)               Greater-than-unity,
(iv)              Lower-than-unity, and
(v)                Unitary elasticity.

(i)                 Elasticity of substitution is infinite: means that the substitution of one good for another is extremely difficult, that even a small change could bring huge instead infinite variations in the marginal rate of substitution (MRS). (e = ∞)
(ii)               Elasticity of substitution is zero: refers to the perfectly inelastic demand substitution.  It means that any variation in the proportions of commodities will not bring much change or no change.  This situation leads the elasticity of substitution is zero. (e = 0)
(iii)             Elasticity of substitution equals to/not equals to unity: There are two extremes discussed above, i.e., infinite and zero elasticities.  Between these two extremes, there are number of variations.

The elasticity of substitution can be measured with the help of following formula:

Where qx/qy is original proportion between quantities of X and Y;
∆(qx/qy) is change in the proportion of X and Y;
∆y/∆x is initial MRS of X and Y;
∆(∆y/∆x) is change in MRS of X and Y.

Relationship between Price Elasticity, and Substitution Elasticity and Income Elasticity:
  1. The price effect consists of two components, viz., the income effect and substitution effect;
  2. Therefore, the price elasticity depends on income elasticity and substitution elasticity;
  3. The relationship between price elasticity, and income and substitution elasticities is expressed in the following formula:

Where, ep = Price elasticity;
ei = Income elasticity;
es = Substitution elasticity;
KX = Proportion of consumer’s income spent on X.

  1. Thus, the price elasticity of demand depends on:

(i)                  Income elasticity (ei)
(ii)                Substitution elasticity (es)
(iii)               Proportion of income spent on the goods other than X

Indifference Curve Analysis
Properties of Indifference Curve:
  1. Indifference curve slopes downward from left to right telling us that a consumer is having the same level of satisfaction at any point on the indifference curve.
  2. Indifference curve cannot be a straight line and sloping upwards from left to right.
  3. Two indifference curves cannot intersect each other.  How can one combination of two commodities yield two different levels of satisfaction?
  4. Indifference curve is normally convex to the origin.
  5. Indifference curve cannot be a straight line sloping downward and a concave line.
  6. Convexity to the origin means that more of one unit of a commodity is consumed, the consumer is prepared to forego a smaller number of other commodity.

Marginal Rate of Substitution:
MRS is the ratio of prices of two substitutes.  According to J.R. Hicks, MRS of x for y is the quantity of y which would compensate the consumer for the loss of marginal unit of x.  This concept is parallel to the concept of marginal utility.

Price Line:
Price line has several names, viz., price opportunity line, price-income line and budget line.  It depicts the highest level or the maximum limit of the consumer’s income that can be spent on two commodities (in fact).  It may also show the prices of the goods in the market.

Consumer’s Equilibrium:
For consumer’s equilibrium is necessary that indifference curve must be:

(i)                  Concave to the origin, and
(ii)                Tangent to the price-line.

Following assumptions are made for consumer’s equilibrium:

  1. There must be scale of preferences for various combinations of two goods.
  2. There must be a given and constant amount of money to be spent on two goods.
  3. Prices of goods in the market are given and constant.
  4. Goods are homogeneous and divisible.
  5. The purpose is to maximise satisfaction at any cost.

Income Effect:
Income effect refers to the situation that with every change in consumer’s income, there is either increase or decrease in his satisfaction attained from the consumption of purchased goods.

Substitution Effect:
As we know that when there is a change in the price of a commodity, the real income of the consumer automatically changes in contrast.  Whereas in substitution effect, in such a case, the real income is to be adjusted, in order to maintain the same level of real income as it was before the price changes.  As a result, the quantity demanded increases or decreases in contrast to the price changes.  Or in other words, there should be a change in the combination of the two commodities.  This shift from one point to another point on the same indifference curve is to be mentioned here as ‘substitution effect’.

Price Effect:
Price effect refers to the change in consumer’s equilibrium as a result of a change in the price of a commodity, while his income and price of other commodities remaining the same.  The price effect is depicted with the help of price consumption line.

Price Effect = Income Effect + Substitution Effect

Giffen Goods:
Sir Robert Giffen, in the middle 19th century, had observed that when the price of bread rose, the poor bought more bread and less meat and less of some other more expensive food stuff.  Giffen goods are inferior goods.  Their quantity demanded falls with every decrease in the price.  The income effect of Giffen Goods are negative.  Whereas in case of ordinary inferior goods, the income effect is not as powerful as substitution effect, as a result, when the price falls, the quantity demanded increases.  The demand curve of Giffen Goods slopes upward from left to right.

Analysis of Price Effect:
Indifference curve analysis enables us to analyse the price effect, income effect and substitution.  When the price of a commodity falls, besides price effect, these are two reasons for an increase in demand:

(i)                 Income effect – the real income rises which also tend to increase the quantity demanded.
(ii)               Substitution effect – more consumers will shift their demand from expensive substitutes to a cheaper substitute.

This is also known as the technique of compensating variation in income.

Exception Cases of Consumer’s Equilibrium:
For consumer’s equilibrium on indifference curve, it is usual that the indifference curve must be convex to the origin and tangent to the price line.  But here are some exceptional cases, where the consumer is still in equilibrium:

Figure (a): gives concave indifference curves.  The consumer is in equilibrium at point P, where the consumer is buying only good y; or at point L where he is buying only good x.  He is not in equilibrium at point Q.

Figure (b): is not convex to the origin and tangent to the price line.  The equilibrium point is P.

Figure (c): is similar to figure (b).  The indifference curve has lower slope than price line PL.  The equilibrium point is L.

Figure (d): represents the case of complementary goods.  The indifference curve 2 is tangent is price line PL.  Therefore, the consumer is in equilibrium at point C.


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