Transcript Intermediate Microeconomic Theory

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.

However, in the end, it is this derived
demand function that tells us all we need to
know about consumer behavior.
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Demand Analysis

The first thing we will characterize is how
a consumer’s demand for a given good
changes with his or her income.

Normal Good - demand for good rises with
income, or
q1 ( p1 , p2 , m)
0
m

How would we show this graphically?

Examples of normal goods?
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Demand Analysis

Alternatively, consider a good where
demand decreases as income increases, or
q1 ( p1 , p2 , m)
0
m

Inferior Good

How would we show this graphically?

Examples of inferior goods?
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Demand Analysis

Would linear preferences (U(q1,q2) = q1 + q2) imply q1 is a
normal good?

How about quasi-linear preferences (U(q1,q2) = aq10.5 + q2) ?
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Income Expansion Paths and Engel Curves

We often want to describe how demand changes as income changes.
To do so, we use:


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Income Expansion Path - traces out optimal bundle as income
increases, holding prices constant.
Engel Curve – shows how demand for a given good changes as income
changes, holding prices constant.
How do we show these graphically?
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Deriving Engel Curve Analytically

Straightforward given a utility function and prices.

Example: Suppose prices are p1 = 5, p2 = 10 and
utility function given by U(q1,q2) = q10.5q20.5 .

What will be the equations for his Engel Curve for
good 1 and good 2?

Do these make sense?
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The Slope of the Engel Curve

The slope of the Engel Curve is
informative.

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?
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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?
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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?
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The Slope of the Engel Curve

What will be the shape of the Engel Curve
for an inferior good?
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Demand Curves

We also often want to describe how demand changes as prices
change. To do so, we use:



Price Offer Curve - traces out optimal bundle as price of one good
changes, holding other prices and income constant.
Demand Curve – shows how demand for a given good changes as its
price changes, holding other prices and income constant.
How do we show these graphically?
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Deriving a Demand Curve Analytically

Also straightforward given a utility function,
prices of other goods and income.

Example: Suppose prices are m = 24, p2 = 10 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?
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Demand Curves

Slope of demand curve indicates how
much demand 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?
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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
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Beer and pizza.
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

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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.



Clearly they aren’t perfect substitutes. Even if
pizza was more expensive, I still might order a
few chicken wings.
A raise in the price of one would definitely cause
me to consume less of it an more of the other.
Some degree of substitutability between them
but not perfect.
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Gross Substitutes and Complements



Gross substitutes - a rise in the
price of one increases the
demand 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?
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Gross Substitutes and Complements

Gross complements - a rise in
the price of one decreases the
demand 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?
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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?
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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?
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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 demand
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 demand
for that good changes as income changes, holding other prices
fixed.

Changes in prices may shift an Engel curve.
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Summary

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This means that:

The change in demand 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 demand 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 demand 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 demand 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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