Download Intermediate Microeconomic Theory

Intermediate Microeconomic Theory
Market Demand
1
Market Demand

Given an individual i’s endowment and preferences, we’ve
seen how to calculate an individual’s demand curve for each
good,
q1i(p1)

We want to use our individual consumer theory as basis for
analyzing consumer behavior in the market (which is what we
really care about).

Market Demand - sum of all of the individual consumer’s
n
demand at each price, or
Q1 ( p1 )   q1i ( p1 , p2 , mi )
i 1
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Market Demand (Graphically)
Consider a market with two individuals.
p1
p1
p1
10
10
10
7
7
7
4
4
4
20
40
q1i
10
30
q1j
20
20+10=30
70
Q1d
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Market Demand (cont.)

Two margins for changes in demand:
*Intensive margin – the change in demand due to each individual
consumer already in the market at one price buying more/less as price
changes (due to the downward slope of each individual demand curve).
*Extensive margin – the change in demand arising from the change in
quantity bought due to changes in the number of individuals who buy a
good changes as price changes.

So even if each consumer only demands one unit at most of given good
(e.g., a washing machine), extensive margin will still mean that market
demand will be smooth and downward sloping.
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Market Demand (Graphically)

Individual and Market demands for Washing Machines


Suppose there are 100 individuals of each “type” (i.e. willingness
to pay for a washing machine)
Consider what happens if we allow for many different types.
pw
1000
800
600
1
qw,1
1
qw,2
1
qw,3
100 200 300
Qw
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Market Demand (Graphically)

Consider again the market with two individuals.

Increase in demand from fall in price from $9 to $7, how much
happens at intensive margin vs. extensive margin? How about for
fall in price form $7 to $5?
p1
p1
p1
10
10
10
9
9
9
7
7
7
5
5
5
10
20 30
40
q1i
10 20 30
q1j
10
20
30
50 Q1d
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Market Demand (cont.)

Market Demand curve for good 1 tells us how the demand for good 1
changes as its price changes -- holding all other prices and incomes
constant!

However, we developed market demand curve from our micro
foundations of behavior.

Therefore, we can understand how market demand curve for one good
will change given changes in prices of other goods or changes in the
income distribution.
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Market Demand (cont.)

Examples:

What would happen to the market demand curve for ski lift
tickets if the price of skis increased?

If organic food is a normal good for most people, how will an
increase in incomes affect the market demand curve for organic
food?
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Measuring the responsiveness of demand

Why are we interested in deriving and analyzing demand curves?
 One key reason is that we want to know the responsiveness of demand
to a change in its price.

This will relate to what characteristic of a demand curve?

What might I mean by the units problem?
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Elasticity of Demand

Economists generally describe responsiveness of demand via Elasticities
 Price elasticity of demand – percentage change in quantity demanded
divided by the percentage change in price.
Q1d
p1
Q1d ( p1 ) Q1d
 1 ( p1 ) 

d
p1
p1 Q1 ( p1 )
p1


“What is the percentage change in quantity demanded due to a
percentage change in price?”
So if we consider marginal or very small changes in price,
Q1d
p1
1 ( p1 ) 
p1 Q1d ( p1 )
slope of the demand curve
ratio of price to quantity demanded
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Calculating Market Demand and Price Elasticity of Demand

Suppose everyone has endowment of $m and Cobb-Douglas preferences of
form:
U = q1 a q 2 b


If each individual has $m, what is each individual’s demand curve for
good 1?
Market demand curve?
* with 3 people?
* with N people?
* For N people, what is Demand Elasticity for good 1 at any given p1?
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Elasticities

So implicit in Cobb-Douglas utility functions is the assumption of a
constant demand elasticity of -1
 How do we interpret this in words?

Do all demand curves have constant elasticity of demand?
 Consider a very simple linear demand curve QD1(p1) = 100 – p1.
 What does demand curve look like?

What is demand elasticity?
12
Elasticity (cont.)

Since demand curves have negative slope (∂Qd/ ∂p < 0), price elasticities are
negative.

However, we talk about elasticities in absolute magnitudes
(e.g. good with elasticity of -3 more elastic than good with elasticity of -2)

When ε(p) < -1 (i.e. further from zero than -1) at a given price, we say at good has
an elastic demand at that price.

Increase in price by 1% , demand decreases by more than 1%.

When ε(p) = -1 at a given price, we say good has a unitary elasticity of demand at
that price.

Increase in price by 1% , demand decreases by 1%.

When -1 < ε(p) < 0 (i.e. closer to zero than -1) at a given price, we say good has an
inelastic demand at that price.

Increase in price by 1% , demand decreases by less than 1%.
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Taxes and Demand Elasticity

One reason we care about elasticity of demand is with respect
to tax policy.

Suppose we want to raise some funds by taxing a certain good.
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Taxes and Demand Elasticity

Consider a percentage tax t on each unit sold (e.g. a sales tax of 10%).
 So consumers pay p(1+t) for each unit of good.

Will an increase in the tax necessarily lead to more revenue?
 Show analytically?

Show graphically?
15
Taxes and Demand Elasticity
Relatively elastic demand
$
Relatively inelastic demand
$
p(1+t)
p(1+t)
Tax Revenue (TR) w/ rate t
p
Tax Revenue (TR) w/ rate t
p
Q(p(1+t))
Q(p(1+t))
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Taxes and Demand Elasticity
Now consider an increase in the tax rate from t to t’
Relatively elastic demand
$
Relatively inelastic demand
$
p(1+t’)
p(1+t’)
increase
p(1+t) in TR
decrease in TR
p(1+t)
increase in TR
decrease in TR
p
Q(p(1+t’))
Q(p(1+t))
Q(p(1+t’)) Q(p(1+t))
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