Consumer demand
From the optimal choice of a
consumer to overall market
demand
Consumer demand


Up until now, we’ve examined how a single
consumer chooses the best (most satisfying)
bundle out of the set of affordable ones
The next step is to derive the demand
function for each good:


What amount of each good is chosen for each
level of its price?
Then, we need to see how all the individual
demand functions add up to the market
demand for that good
Consumer demand
Deriving consumer demand
From individual to market demand
Elasticities
Deriving consumer demand

As we have seen, given a stable set of
preferences, the amount of a good chosen
in a bundle depends on :




The price of the good
The price of other goods
The income of the agent
The quantity demanded by the ith agent is
therefore a function of these three variables
x  f  p1 , pothers , I
i
1
i

Deriving consumer demand

The effects of a change of income on
demand:



The demand for normal goods increases when
income increases
Some goods are inferior : The demand for these
goods decreases when income increases
If one plots all the quantities demanded for each
level of income, one gets the Engel curve
Deriving consumer demand
Income expansion path
Good 1
C
B


A

Good 2
Deriving consumer demand
Other
goods
E2
E3
E1
DVD
Income
Engel curve
150
E’3
100
50
E’1
E’2
Demand for
DVDs
Deriving consumer demand
Engel curves
Demand
Demand
Income
Income
Normal good
Inferior good
Deriving consumer demand

The effects of a change of price on demand



Generally, because of the substitution effect, the
demand for a good varies inversely with its price
Some goods are Giffen goods : The demand for
these goods varies in the same direction as price
(income effect)
If one plots all the quantities demanded for each
level of price, one gets the Demand curve
Deriving consumer demand
Good 1
Price expansion path
A

B

C

Good 2
Deriving consumer demand
Other
goods
E1
E2
E3
DVD
Price of
DVDs
40
20
10
E’2
E’1
E’3
Demand curve
Demand for
DVDs
Deriving consumer demand
A typical demand curve:
Price1
If the price falls,
the individual
demands more of
the good
p1
x1i  p1 , pothers , I i 
p1
x1i
x1i
Demand
of agent i
Deriving consumer demand

IMPORTANT NOTE:


The demand function depends on
 The price of the good
i
 The price of other goods
x1
 The income of the agent
p ,p
1
others
,I
i

The demand curve only shows a relation between
demand and the price of the good
 So how do the other variables (income, the
price of other goods) affect the demand curve?
Deriving consumer demand
The effect of income changes on the demand curve
Price1
If the income increases, the
demand increases (at constant
price)
If the income falls, the demand
falls (at constant price)
p1
x1i  p1 , pothers , I i 
x1i
Demand
of agent i
Deriving consumer demand
The effect of a change in another price on
the demand curve...
Price1
... is ambiguous !!
It depends on the relative size of
the income and substitution effects
(Of opposite directions here)
This in turn depends on
whether the 2 goods are
substitutes or complements
p1
x1i  p1 , pothers , I i 
x1i
Demand
of agent i
Consumer demand
Deriving consumer demand
From individual to market demand
Elasticities
From individual to market demand



Market demand is the aggregate quantity
demanded at a given price level
It is not the demand of a single individual, but that
of all the agents in the economy
The market demand for a good depends on the
relative price of that good and the distribution of all
the incomes in the economy
X 1  p1 , pothers , I 1 , I 2 ,
i n
, I n    x1i  p1 , pothers , I i 
i 1
From individual to market demand
A simple 2-agent example
Price
Agent 1’s
demand
1
x
Agent 2’s
demand
x
2
Market
demand
X
From individual to market demand
A Market demand curve
Price1
If the price falls,
the market
demand for the
good increases
p1
X 1  p1 , pothers , I 1 , I 2 ,
p1
X1
X1
Market
Demand
,In
Consumer demand
Deriving consumer demand
From individual to market demand
Elasticities
Elasticities


The concept of an elasticity is central to
microeconomic theory :
Up until now, we have reasoned in
qualitative terms.



A demand curve is downward sloping
It moves upwards if income increases
If we want our theory to be useful in the real
world, we need to quantify these concepts.


How sensitive is demand to price /Income ?
Is this the same for all goods ?
Elasticities

An elasticity is a measure of this sensitivity


It gives the % change in one variable following a
% change in another variable
Example : The price elasticity of demand
%  Qd 
 
%  p 
D
p

A price elasticity of demand of -0.5:


An increase in price of 1 % ⇒ fall in demand of 0.5 %
An increase in price of 10 % ⇒ fall in demand of 5 %
Elasticities

The percentage change of a function is defined as:
Qd
%  Qd  
Qd

This means that we can express the elasticity as:
%  Qd 
 
%  p 
D
p
Qd p
D
p 
p Qd

Qd p

Qd p
Slope of the demand function
Price/Demand ratio
Elasticities
Price elasticity of a linear demand curve
Price
Qd p
D
p 
p Qd
Slope of the demand function
Price/Demand ratio
p
∂p
∂Qd
Demand
Qd
Quantity
Elasticities

The demand function has 3 variables:
x  p1 , pothers , I
i
1

i

We now have measure of sensitivity for all
these variables:

The price of the good
 Price elasticity of demand (which you already know)

The price of other goods
 Cross price elasticity of demand

The income of the agent
 Income elasticity of demand
Elasticities

The price elasticity of demand:

Is negative in general
 An increase in price reduces the quantity demanded


Is positive for Giffen goods
Demand is price-elastic if the price elasticity is
greater than 1 in magnitude
 10 % increase in price ⇒ >10% fall in demand

Demand is price-inelastic if the price elasticity is
smaller than 1 in magnitude
 10 % increase in price ⇒ <10% fall in demand
Elasticities

The cross price elasticity of demand



Measures the variation of the quantity demanded
following an increase in the price of another
good
This gives information on whether the goods are
substitutes or complements
Example : what is the effect of the increase in
fuel prices on the demand for Hummers ??
Elasticities

The cross price elasticity of demand

Is negative in for complement goods
 Example : ↑ price of fuel ⇒ ↓ demand for cars

Is positive for substitute goods
 Example : ↑ price of coffee ⇒ ↑ demand for tea

The magnitude of the elasticity gives information
on the strength of the link
 A large magnitude (>1) means a strong complement /
substitute link
 A small magnitude (<1) means a weak link
 A magnitude close to 0 means no link
Elasticities

The income elasticity of demand


measures the variation of the quantity demanded
following an increase in income of agents
Is negative in for inferior goods
 An increase in income reduces the quantity demanded

Is positive for normal goods
 An increase in income increases the quantity demanded

Is greater than one for “luxury” goods
 An increase in income increases the quantity demanded
more than proportionately