Intermediate Microeconomic Theory
Demand
1
Demand Analysis

In analyzing individual’s behavior
regarding a given good, we start with a
consumer’s demand function for that good.
q1(p1,p2,m)

Recall that a demand function was derived
from “first principles”, or the explicit model
of preferences and choice given a budget
constraint (remember our underlying
assumptions?).

However, in the end, it is this derived
demand function that tells us all we need to
know about consumer behavior.
2
Engel Curves

We often want to describe how demand for a good changes as
income changes. To do so, we use:


Engel Curve – shows how quantity demanded for a given good changes
as income changes, holding prices constant.
How do we derive this graphically for good 1 given some set
preferences and prices (e.g. p1=5 and p2=10)?
3
Deriving Engel Curve Analytically

Straightforward given a utility function and prices.

Example: Suppose again p1 = 5, p2 = 10 and utility
function given by U(q1,q2) = q10.5q20.5 .

What will be the equation for his Engel Curve for
good 1?

Do these make sense?
4
Engel Curves

What would happen to the Engel Curve for a given good if prices changed?

Taking previous example, what if price of good 1 rose to $10/unit?
5
Engel Curves

How about Engel curve given linear preferences
(U(q1,q2) = q1 + q2)?

How about Engel curve given quasi-linear preferences
(U(q1,q2) = q10.5 + q2) ?
6
Further Characterizing Relationship between Demand and Income

Normal Good – quantity demanded of
good rises with income, or
q1 ( p1 , p2 , m)
0
m

How would we show this graphically in a
choice framework?

What does it imply about slope of Engel
Curve?

Examples of normal goods?
7
Further Characterizing Relationship between Demand and Income

Inferior Good - quantity demanded
decreases as income increases, or
q1 ( p1 , p2 , m)
0
m

Is this possible? How would we show this
graphically in a choice framework?

What does it imply about slope of Engel
Curve?

Examples of inferior goods?
8
The Slope of the Engel Curve

The slope of the Engel Curve is informative
beyond just being positive or negative.

Consider the Engel Curve shown below.
m
q1

What does linearity imply (sometimes referred
to as homothesticity)?

Do Cobb-Douglas preferences imply such a
linear Engel curve?
9
The Slope of the Engel Curve

The slope of the Engel Curve don’t have to
be constant.

Consider the Engel Curve shown below.
m
q1

What does concave shape imply?

What might be examples of goods with such
an Engel curve? What is a good term to
describe such goods?
10
The Slope of the Engel Curve

Consider the Engel Curve with convex shape.
m
q1

What does convex shape imply (hint: consider
Engel curve for quasi-linear preferences)?

What might be examples of goods with such an
Engel curve? What is a good term to describe
such goods?
11
Relevance of Engel Curve?

Why might understanding what Engel Curves are,
and estimating their shape for different goods be
important?
12
Demand Curves

We also often want to describe how demand changes as price
changes. To do so, we use:


Demand Curve – shows how quantity demanded for a given good
changes as its price changes, holding other prices and income constant.
How do we derive this graphically for good 1 given some set
preferences given p2=4 and m=24?
13
Deriving a Demand Curve Analytically

Also straightforward given a utility function,
prices of other goods, and income.

Example: Suppose prices are m = 24, p2 = 4 and an
individual has a utility function U(q1,q2) = q10.5q20.5
.

What will be the equation for his Demand Curve for
good 1?

Does this make sense? What will it look like?
14
Demand Curves

Slope of demand curve indicates how
much quantity demanded reacts to price.

Generally, demand curves will be downward
sloping, meaning as price rises demand falls,
or
q1 ( p1 , p2 , m)
0
p1

We saw this will be the case with CobbDouglas specification of preferences. How
about with linear utility function?

Given our assumptions, is it possible for a
demand curve to slope upward?
15
Demand Curves

A good with an upward sloping demand curve is called a
Giffen good (i.e. demand increases as price goes up and
vice versa)



Essentially, a Giffen good is an extremely inferior good.
“As Mr. Giffen has pointed out, a rise in the price of bread
makes so large a drain on the resources of the poor labouring
families and raises so much the marginal utility of money to
them, that they are forced to curtail their consumption of meat
and the more expensive foods: and, bread being still the
cheapest food which they can get and will take, they consume
more, and not less of it.”
-Alfred Marshall (1895)
While Giffen goods were known to be theoretically
possible, no one had proven the existence of one, until…
16
Demand Curves

Jensen and Miller (2008), “Giffen Behavior and Subsistence
Consumption” American Economic Review

Argue that Giffen behavior is most likely to occur when:




Households are poor enough that they face subsistence nutrition
concerns.
Households consume a very simple diet, including a basic staple and a
“fancy” good.
the basic good is cheapest source of calories available, comprises a
large part of diet/budget, and has no ready substitutes.
Households cannot be so impoverished that they consume only the
staple good.
17
Demand Curves

Conducted a field experiment

Randomly chose households given vouchers that subsidized primary staple
(rice or wheat), which lowered the effective price of that good.

Looked at consumption behavior between those given voucher and those
who weren’t.

Find an inverted U-shape pattern of consumption of staples for poor
populations.
18
Gross Substitutes and Complements

We have already discussed perfect substitutes
and perfect complements.

We can now consider more nuanced definitions
of substitutes and complements, with perfect
versions being subsets.
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Gross Substitutes and Complements

Beer and pizza.




Generally, I like to consume them together, one
beer with every slice.
However, if the price of a slice went to $10, I
might behave a little differently.
Some degree of complementarity, but not
perfect.
Pizza and Chicken Wings.



A raise in the price of one would definitely cause
me to consume less of it and more of the other.
However, they aren’t perfect substitutes. Even if
pizza was cheaper, I still might order a few
chicken wings.
Some degree of substitutability between them
but not perfect.
20
Gross Substitutes and Complements

Gross substitutes - a rise in the
price of one increases the quantity
demanded for the other, or if
q1 ( p1 , p2 , m)
0
p2

How would we show this
graphically?

Consider skiing and golf. Suppose
the price of lift tickets increased.


How will the demand for golf course
time be affected?
How about the demand curve for
golf course time?
21
Gross Substitutes and Complements

Gross complements - a rise in the
price of one decreases the quantity
demanded for the other, or if
q1 ( p1 , p2 , m)
0
p2

How would we show this
graphically?

Consider skiing and plane tickets.
Suppose the price of lift tickets
increased.


How will the demand for a plane
ticket to SLC be affected?
How about the demand curve?
22
Gross Substitutes and Complements

If someone’s preferences over two goods
are captured by a Cobb-Douglas Utility
function, will the two goods be gross
substitutes, gross compliments, or neither?

How about if someone’s preferences are
modeled using a quasi-linear utility
function?
23
Demand Curve and changes in income

Consider the Demand Curve for good 1 for
an individual with Cobb-Douglas Utility
U(q1,q2) = q10.6q20.4 , who has m = 20 and
p2 = 4.


How would this Demand Curve be affected
by a change in endowment from m = 20 to
m = 30?
What if preferences were such that good 1
was an inferior good?
24
Summary

Engel curves and Demand curves are derived from demand
function (which is in turn derived from underlying
preferences).

A Demand curve for a given good describes how the quantity
demanded for that good changes as its own price changes,
holding other prices and endowment fixed.


Changes in prices of other goods or endowment may shift a
Demand curve.
An Engel curve for a given good describes how the quantity
demanded for that good changes as income changes, holding
other prices fixed.

Changes in prices may shift an Engel curve.
25
Summary


This means that:

The change in quantity demanded for good i in
reaction to a change in the price of good i is
captured by a movement along the demand curve
for good i.

The change in quantity demanded for good i in
reaction to change in price of some other good j
or change in income is captured by a shift in the
demand curve for good i.
Similarly,

The change in quantity demanded for good i in
reaction to a change in income is captured by a
movement along the Engel curve for good i.

The change in quantity demanded for good i in
reaction to change in price of good i or another
good j is captured by a shift in the Engel curve
for good i.
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