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Chapter 15 MARKET
DEMAND
15.1 From Individual to Market
Demand
Consumer i’s demand for good 1: xi1(p1,p2,mi)
 Consumer i’s demand for good 2: xi2(p1,p2,mi)
 n consumers in the economy: i=1, …,n
 Market demand for good 1: the sum of these
individual demands over all consumers.

n
X 1 ( p1, p2 , m1 ,
mn )   xi1 ( p1, p2 , mi )
i 1
15.1 From Individual to Market
Demand

If we fix all the
monetary incomes and
the price of good 2, we
can illustrate the
relation between the
aggregate demand for
good 1 and its price.
15.1 From Individual to Market
Demand



Substitutes: increasing the price of good 2 will tend to
shift the aggregate demand curve for good 1 outward.
Complements: increasing the price of good 2 will
shift the aggregate demand curve for good 1 inward.
Normal good: increasing monetary income, holding
everything else fixed, will shift the aggregate demand
curve outward.
15.2 The Inverse Demand Function

Inverse demand function, P(X)
 It
measures what the market price for good 1
would have to be for X units of it to be demanded.
EXAMPLE: Adding Up “Linear”
Demand Curves

Since the demand curves are only linear for positive quantities,
there will be a kink in the market demand curve.
15.3 Discrete Goods
15.4 The Extensive and the Intensive
Margin
Adjustment on the intensive margin: when
the price changes, the consumer changes the
quantities demanded, but still ends up
consuming both goods.
 Adjustment on the extensive margin: when
the price changes, the consumers enter or exit
the market for one of the goods.

15.5 Elasticity
Elasticity: a measure of responsiveness.
 Price elasticity of demand: the percent
change in quantity divided by the percent
change in price.

q q
q p dq p
  lim
 lim

p 0 p p
p 0 q p
dp q
dq p dq q d ln q



dp q dp p d ln p
EXAMPLE: The Elasticity of a
Linear Demand Curve
Linear demand curve: q=a-bp.
 Elasticity:  =-bp/q=-bp/(a-bp)

 =0;
 p=a/b :  =-;
 p=a/2b:  =-1;
 p>a/2b:  <-1;
 p<a/2b:  >-1;
 p=0:
EXAMPLE: The Elasticity of a
Linear Demand Curve
15.6 Elasticity and Demand
Elastic Demand: elasticity of demand is
greater than 1 in absolute value.
 Inelastic Demand: elasticity of demand is less
than 1 in absolute value.
 Unit Elastic Demand: elasticity of demand is
exactly -1.

15.7 Elasticity and Revenue
Revenue: R=pq
 Price change: p+△p
 Quantity change: q+△q
 New revenue:
R=(p+△p)(q+△q)=pq+q△p+p△q+△p△q
 Change in revenue:
△R= q△p+p△q+△p△q

15.7 Elasticity and Revenue
15.7 Elasticity and Revenue





Small values of △p and △q: the last term can safely
be neglected.
△R= q△p+p△q or △R/△p=q+p△q/△p
△R/△p>0: p△q/q△p>-1 or |(p)|<1
Revenue increases when price increases if the
elasticity of demand is less than 1 in absolute value.
Revenue decreases when price increases if the
elasticity of demand is greater than 1 in absolute
value.
15.7 Elasticity and Revenue

Differential approach
R  pq

dR
dq
p dq 
q p
 q 1 
  q 1  
dp
dp
 q dp 
|  |>1: dR/dp<0;
 |  |<1: dR/dp>0.


15.8 Constant Elasticity Demands

A unit elastic
demand curve has
a constant
elasticity of -1. For
this demand curve,
price times
quantity is constant
at every point.
15.9 Elasticity and Marginal
Revenue
△R= q△p+p△q
 Marginal revenue:
MR=△R/△q = p+ q△p/△q
MR = p(1+ q△p/p△q)
=p(1+ 1/(p))
=p(1-1/|(p)|)

15.9 Elasticity and Marginal
Revenue

 =-1: MR=0
 Revenue
doesn’t change when the firm increases
output.

|  |<1: MR<0
 Revenue
will decrease when the firm increases
output.

|  |>1: MR>0
 Revenue
output.
will increase when the firm increases
15.10 Marginal Revenue Curves
Linear (inverse) demand curve: p(q)=a-bq
 Marginal revenue:
MR=△R/△q = p(q)+q△p(q)/△q
= p(q)-bq
=a-bq-bq
=a-2bq

15.10 Marginal Revenue Curves

The marginal revenue
curve has the same
vertical intercept as the
demand curve, but has
twice the slope.
15.11 Income Elasticity

Income elasticity of demand: it describes
how the quantity demanded responds to a
change in income.
q q
q m dq m
 m  lim
 lim

m 0 m m
m 0 q m
dm q
15.11 Income Elasticity
Normal good: an increase in income leads to
an increase in demand.
 Inferior good: an increase in income leads to
a decrease in demand.
 Luxury good: a one percent increase in
income leads to more than one percent
increase in demand.

15.11 Income Elasticity
Two different levels of income: m and m0
 Budget constraints:
p1x1+p2x2=m
p1x10+p2x20=m0
 Substraction:
p1△x1+ p2△x2=△m
 Further manipulation:
(p1x1/m)(△x1/x1)+ (p2x2/m)(△x2/x2)=△m/m

15.11 Income Elasticity

Finally:
s1(△x1/x1)/(△m/m)+ s2(△x2/x2)/(△m/m)=1

Expenditure share of good i: si= pixi/m

The weighted average of the income elasticity
is unity.
 The
weights are the expenditure shares.