Introduction
It is generally observed that market aggregate demand curve for a commodity is downward
sloping, given other things. Our problem is to investigate economic rationality behind this for a
commodity of all individual consumers. The market demand basically depends on the
characteristics of demand for a commodity by individual consumers, and the demand for a
commodity of an individual consumer depends upon the behavior of the consumer. Clearly, to
investigate economic rationality behind the law of demand, we shall start with the analysis of
consumer behavior.
The Basic Themes
There are different approaches to analyses the consumer behaviour. But in all approaches, it is
assumed that the consumer is rational. This means that the consumer’s objective is to maximise
her utility by choosing one commodity bundle from among all the commodity bundles (money
income and the prices of the commodities are given to the consumer).
Consumer Choice Concerning Utility
Consumers can’t maximise her utility unless she can measure it. Hence, utility must be a
measurable concept. The measurement is undertaken differently in different approaches. In
traditional frame, we have two types of measurement of utility,
- Cardinal analysis
- Ordinal analysis
Cardinal Theory: An Introduction
In cardinal approach, utility is measured cardinally or numerically in terms of money. The
consumer not only knows which one is preferred but also by what amount. The assumptions of
this approach is given below: - Consumer is rational. Implication: The consumer’s objective is to maximise her utility by
choosing one of the commodity bundle from all other available commodity bundles at given
prices of commodities and money income. - If the taste and preferences are given, the total utility of the consumer depends on the
quantity of consumption. - Goods are good. Implication: Let ‘U’ denote utility level of the consumer and let ‘x’ be the
consumption bundle. As ‘x’ increases (decreases), ‘U’ increases (decreases). Therefore,
marginal utility is positive. - Marginal utility of ‘x’ is diminishing. Implication: As ‘x’ increases (decreases), MUx decreases
(increases). Therefore, MUx curve is downward sloping - Utility is measured cardinally or numerically in terms of money. Implication: Since it is
measured numerically consumer not only knows which commodity bundle is preferred but
also by how much amount.Marginal utility of money is constant. Implication: MUm =λ where λ is positive and constant.
That means as money income increases (decreases) by one unit, utility increases (decreases)
by λ unit.
Consumer Equilibrium
According to our assumption for ‘x’ units consumption of the commodity, gross utility obtained
by the consumer is U(x).But for this, the consumer must spend px.x units of money income if px
be the price of the commodity ‘x’, which is given to the consumer. Since from assumption 6, λ
represents fall in utility due to one unit fall in money income, the net utility of the consumer is
given by N(x) = U(x)-λ px.x, where λ and px are given to the consumer. So consumer’s objective
is to maximise N(x) by choosing ‘x’. For that we take the first derivative of N(x) and set that equal
to zero, we get From this first order condition, we can derive the
optimum value of ‘x’ which is (say) x* = x*(px,λ). The second order condition for utility
Maximization requires
Which is ensured by the assumption of falling MUx.
Codinal Theory: A Short Note
In ordinal approach, utility is measured ordinally i.e., qualitatively (not numerically or
quantitatively). Alternatively, consumer can rank her preferences according to the order she
wants to compare but not in terms of the different amount. It is a qualitative measure and
therefore more realistic measurement of utility or satisfaction.
There are two different approaches of ordinal theory, viz., - Indifference curve approach
- Revealed preference approach
Indifference Curve Approach
Indifference curve is constructed by taking utility level constant, so different indifference curves
imply different level of utility for same consumer. The equilibrium is achieved when indifference
curve become tangent to the budget line. - Revealed Preference Approach
- In revealed preference approach, consumer equilibrium can be found by ranking different
- bundle of goods in the commodity space. Given the budget constraint, consumer chooses the
- best bundle for which her utility will maximise. This theory was originally constructed by the
- famous economist Paul. A. Samuelson.
- Introduction to Demand Analysis
- It is generally seen that market demand curve is downward sloping. Market demand curve (or
- sometimes called Aggregate demand curve) is nothing but the aggregation of individual demand
- curves. Individual demand curve can be constructed by joining different consumer equilibrium
- for different prices (remember that consumer can’t alter the market prices, it is given to the
- consumer). In neo-classical consumer theory, price is exogenous variable, so demand curve can
- be obtain only if we change the price exogenously and join all the equilibrium points. From next
- on our objective is to find out the consumer demand curve, for which we will adopt ordinal
- theory and in that, we will take indifference curve approach.
- Ordinal Theory: Indifference Curve Approach
- In indifference curve approach consumer is assumed to be rational, so that consumer’s objective
- is to maximise her utility by choosing a commodity bundle among all other available commodity
- bundles (under budget constraint) where total utility (‘U’) depends on quantity consumption
- given Her taste and preferences. Therefore, in a two-commodity world (say x1 and x2) utility
- function is given by U = U (x1, x2) and it depends on taste and preferences of the consumer,
- which is specified by axioms given below:
- Axiom of Reflexiveness: Consumer’s choice is reflexive.
Implication: ‘R’ denotes weak preference relation. Suppose there are two goods x1 and x2
and suppose x1 is weakly preferred to x2 i.e., x1Rx2 which implies that either x1 is strictly
preferred over x2 (it is denoted by x1Px2) or x1 is indifference to x2 (it is denoted by x1Ix2),
where ‘P’ and ‘I’ implies strict preference relation and indifference respectively.
The set constituted by all commodity bundles or vector is known as commodity set (X). Any
one commodity bundle is denoted by ‘x’ is weakly preferred (i.e., either strictly preferred or
indifferent) over any other commodity bundle (i.e., in respect to ‘x’). Therefore, we have xRx.
Clearly, any one commodity bundle may be indifferent to another commodity bundle i.e.,
there is a possibility of indifference or same level of utility between the commodity bundles.
None of the commodity bundles are not preferred i.e., consumer can choose any commodity
bundle. So choice set of this consumer is specified by the commodity set ‘X’. - Axiom of completeness: Consumer’s choice is complete.
Implication: Since consumer is rational, she must have a unique preference relation. That
means the consumer choice is either x1Rx2 or x2Rx1. Alternatively, consumer’s choice is
consistent or comparable. For unique preference relation, consumer choice must be
transitive, where transitivity implies that if x1Rx2 and x2Rx3 then x1Rx3, where x3 is another
commodity.