Finance 30210: Managerial Economics

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Finance 30210 Managerial Economics

• Consumer Demand Analysis

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Suppose that you observed the following consumer
behavior
P(Bananas) 4/lb. P(Apples) 2/Lb.
Q(Bananas) 10lbs Q(Apples) 20lbs
Choice A
P(Bananas) 3/lb. P(Apples) 3/Lb.
Q(Bananas) 15lbs Q(Apples) 15lbs
Choice B
What can you say about this consumer?
Is strictly preferred to
Choice B
Choice A
How do we know this?
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Consumers reveal their preferences through their
observed choices!
Choice A
Choice B
Q(Bananas) 10lbs Q(Apples) 20lbs
Q(Bananas) 15lbs Q(Apples) 15lbs
P(Bananas) 4/lb. P(Apples) 2/Lb.
Cost 80
Cost 90
P(Bananas) 3/lb. P(Apples) 3/Lb.
Cost 90
Cost 90
B Was chosen even though A was the same price!
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What about this choice?
Choice C
Cost 90
P(Bananas) 2/lb. P(Apples) 4/Lb.
Q(Bananas) 25lbs Q(Apples) 10lbs
Q(Bananas) 15lbs Q(Apples) 15lbs
Cost 90
Choice B
Q(Bananas) 10lbs Q(Apples) 20lbs
Cost 100
Choice A
Is strictly preferred to
Is choice C preferred to choice A?
Choice C
Choice B
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Is strictly preferred to
Choice B
Choice A
Is strictly preferred to
Choice C
Choice B
C gt B gt A
Is strictly preferred to
Choice C
Choice A
Rational preferences exhibit transitivity
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Consumer theory begins with the assumption that
every consumer has preferences over various
combinations of consumer goods. Its usually
convenient to represent these preferences with a
utility function
Set of possible consumption choices
Utility Value
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Using the previous example (Recall, C gt B gt A)
Choice A
Q(Bananas) 10lbs Q(Apples) 20lbs
Choice B
Q(Bananas) 15lbs Q(Apples) 15lbs
Choice C
Q(Bananas) 25lbs Q(Apples) 10lbs
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We require that utility functions satisfy a few
basic properties
There is a definite ranking of all choices
A
C
B
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We require that utility functions satisfy a few
basic properties
More is always better!
C
A
B
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We require that utility functions satisfy a few
basic properties
People Prefer Moderation!
A
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C
10
5
B
5
15
10
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Suppose you are given a little extra of good X.
How much Y is needed to return to the original
indifference curve?
Marginal Utility of X
Marginal Utility of Y
The marginal rate of substitution (MRS) measures
the amount of Y you are willing to give up in
order to acquire a little more of X
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The marginal rate of substitution (MRS) measures
the amount of Y you are willing to give up in
order to acquire a little more of X
If you have a lot of X relative to Y, then X is
much less valuable than Y MRS is low!
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The elasticity of substitution measures the
curvature of the indifference curve
Elasticity of substitution measures the degree to
which your valuation of X depends on your
holdings of X
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The elasticity of substitution measures the
curvature of the indifference curve
If the elasticity of substitution is small, then
small changes in x and y cause large changes in
the MRS
If the elasticity of substitution is large, then
large changes in x and y cause small changes in
the MRS
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We often assume that the marginal rate of
substitution is dependant only on the ratio of X
and Y i.e. preferences are homogeneous
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Consumers solve a constrained maximization
maximize utility subject to an income constraint.
As before, set up the lagrangian
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First Order Necessary Conditions
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Demand Curves present the same information in a
different format therefore, all the properties
of preferences are present in the demand curve
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Demand relationships are based off of the theory
of consumer choice. We can characterize the
average consumer by their utility function.
Utility is a function of lemonade and hot dogs
Consumers make choices on what to buy that
satisfy two criteria
Their decision on what to buy generates maximum
utility
Their decision on what to buy generates is
affordable
These decisions can be represented by a demand
curve
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Example Suppose that you have 10 to spend. Hot
Dogs cost 4 apiece and glasses of lemonade cost
2 apiece.
This point satisfies both conditions and, hence,
is one point of the demand curve
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The marginal rate of substitution controls the
height of the demand curve
Willingness to pay is low
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Willingness to pay is high
10
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Now, suppose that the price of hot dogs rises to
6 (Lemonade still costs 2 and you still have
10 to spend)
You cant afford what you used to be able to
afford you need to buy less of something!
(Income effect)
Your decision at the margin has been affected.
You need to buy less hot dogs and more lemonade
(Substitution effect)
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Now, suppose that the price of hot dogs rises to
6 (Lemonade still costs 2 and you still have
10 to spend)
This point satisfies both conditions and, hence,
is one point of the demand curve
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Demand curves slope downwards this reflects the
negative relationship between price and quantity.
Elasticity of Demand measures this effect
quantitatively
Price
6.00
4.00
Quantity
2
1
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The elasticity of substitution will control the
slope of the demand curve
D
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Elasticity of Substitution vs. Price Elasticity
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Perfect Complements vs. Perfect Substitutes
(Almost)
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Now, suppose that the price of a hot dog is 4,
Lemonade costs 2, but you have 20 to spend.
Your decision at the margin is unaffected, but
you have some income left over (this is a pure
income effect)
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Now, suppose that the price of a hot dog is 4,
Lemonade costs 2, but you have 20 to spend.
This point satisfies both conditions and, hence,
is one point of the demand curve
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For any fixed price, demand (typically) responds
positively to increases in income. Income
Elasticity measures this effect quantitatively
Price
4.00
Quantity
2
4
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Income elasticity measures the response of
consumers to changes in income holding prices
constant the homogeneity of preferences will
effect this
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Cross price elasticity refers to the impact on
demand of another price changing
Note These numbers arent coming from the
previous example!!
Price
4.00
Quantity
2
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A positive cross price elasticity refers to a
substitute while a negative cross price
elasticity refers to a compliment
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Cross price elasticity measures consumer response
to changes in other prices this is influenced
by both homogeneity and elasticity of substitution
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An Example Cobb-Douglas Utility
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An Example Cobb-Douglas Utility
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An Example Cobb-Douglas Utility
With Cobb-Douglas Utility functions, your MRS is
directly proportional to your relative
consumption of the two goods.
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An Example Cobb-Douglas Utility
Cobb-Douglas Utility functions have constant
elasticity of substitution
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Cobb-Douglas demands are independent of other
prices!
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Consumer Surplus
Suppose that we have the following demand curve
100
A demand curve tells you the maximum a consumer
was willing to pay for every quantity purchased.
50
D
100
For the 100th sale of this product, the maximum
anyone was willing to pay was 50
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Consumer Surplus
Suppose that we have the following demand curve
100
75
50
D
100
For the 50th sale of this product, the maximum
anyone was willing to pay was 75
50
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Consumer Surplus
Consumer surplus measures the difference between
willingness to pay and actual price paid
100
75
Whoever purchased the 50th unit of this product
earned a consumer surplus of 25
50
D
100
For the 50th sale of this product, the maximum
anyone was willing to pay was 75
50
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Consumer Surplus
Consumer surplus measures the difference between
willingness to pay and actual price paid
100
If we add up that surplus over all consumers, we
get
CS (1/2)(100-50)(100-0)2500
2500
50
Total Willingness to Pay (7500)
5000
- Actual Amount Paid (5000)
D
Consumer Surplus (2500)
100