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APPLIED ECONOMICS FOR BUSINESS
MANAGEMENT Lecture 3

•  
• Review
• Go over Homework Set 3
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• Continue consumer behavior

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Derivation of the consumer demand function

• As in the previous example (i.e., changing
• the price of one commodity and finding the new
  consumer
• equilibrium point), if we continue to change
  , we can get
• the following

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• We see that as p1 changes, ceteris paribus, ?
  shift in the budget line
• ? new consumer equilibrium point

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Consumer Demand Function


Using these consumer equilibrium points, we can
derive the consumers demand for z1.
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Consumer Demand Function

• Demand illustrates the quantities of a good
  (commodity) consumer would be willing to purchase
  at alternative prices, ceteris paribus.

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Mathematical Derivation of Demand

• A consumers ordinary demand function
• (called the Marshallian demand function)
• is derived from utility maximization subject
• to a budget constraint.

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Mathematical Derivation of Demand
? constrained objective function
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Mathematical Derivation of Demand
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Mathematical Derivation of Demand
Likewise for z1 , we obtain
Note that these demand functions are a special
case since theyre functions of only own price
and income. Question Are these demand
functions downward sloping? How can you
tell? Downward sloping ? the slope is negative
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Mathematical Derivation of Demand

The demand for
(Using reciprocals or inverses)
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Mathematical Derivation of Demand
We can easily solve for from the demand
function namely

function is negative or demand is downward
sloping.
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Mathematical Derivation of Demand
Likewise we get the same result for the consumer
demand for z1 since
negative or demand is downward sloping.
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So we have the following graph
The law of demand states that price and
quantity that are demanded are negatively
related.
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Mathematical Derivation of Demand
Is income a positive shifter of demand?

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Mathematical Derivation of Demand
In the usual case for demand derived from utility
maximization, we have
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Mathematical Derivation of Demand
To derive this general form, we need to adjust
the form of the utility function. Suppose we
have
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Mathematical Derivation of Demand
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Mathematical Derivation of Demand

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Mathematical Derivation of Demand
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Mathematical Derivation of Demand
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Mathematical Derivation of Demand
we can rewrite the equation as
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Mathematical Derivation of Demand
Demand function is downward sloping
Is income a positive shifter of the demand
function?
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Demand vs. Quantity Demanded
Distinction between demand and quantity
demanded This distinction is usually heavily
emphasized in introductory and intermediate
microeconomics courses. Demand refers to the
entire schedule. Quantity demanded refers to the
quantity purchased by the consumer at a
particular price level.
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Demand Function
General form of the demand function where
our usual demand curve. If these other factors
change, then demand will shift.
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Factors Affecting Demand

1. Changes in income (for normal goods)
(vs inferior or Giffen goods)
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Factors Affecting Demand

1. Changes in income (for normal goods)
2. Changes in the price of substitutes
Take the case of beef and pork (substitutes)
If price of pork ? ? demand for beef ? Why?
Consumers substitute beef for pork when the
price of pork ? If the price of pork ??
demand for beef ?
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Factors Affecting Demand

1. Changes in income (for normal goods)
2. Changes in the price of substitutes
3. Changes in the price of complements.
Take the case of milk and cereal
(complements) If the price of milk ? ? demand
for cereal ?. Why? Milk is an input into
cereal consumption. Likewise, if the price of
milk ? ? demand for cereal ?.
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Factors Affecting Demand

1. Changes in income (for normal goods)
2. Changes in the price of substitutes
3. Changes in the price of complements.
4. Changes in tastes and preferences.
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Factors Affecting Demand

4. Changes in tastes and preferences.
No exact relationship, depends on the specific
changes. Example cholesterol scare ? demand for
eggs ?. Example Dietary information about the
benefits of fish consumption and the health
concerns over red meat consumption ? demand for
fish ? ? demand for red meats ? ? demand for
chicken and turkey ?
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Factors Affecting Demand

1. Changes in income (for normal goods)
2. Changes in the price of substitutes
3. Changes in the price of complements.
4. Changes in tastes and preferences.
5. Increase in population or the number of
consumers.
Generally, if population ? ? demand for most
commodities ?.
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Elasticity
The concept of elasticity is used as a measure of
consumption responsiveness to changes in a
particular variable (e.g., own price, income, or
cross prices i.e., prices of substitutes or
complements).
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Elasticity
We will concentrate on 3 elasticity concepts

• own price elasticity of demand

• income elasticity of demand

• cross price elasticity of demand

We will also evaluate point elasticity rather
than arc elasticity.
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Elasticity
Why do economists use elasticity and not slope to
measure responsiveness of demand? Because you
will get a different measure of responsiveness
if you simply change the units of measure on
either the vertical or horizontal axis.
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For example
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Now simply change the units of measure of
from /unit to /unit.
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Elasticity
Thus, the slope is not a good measure of
responsiveness. Economists prefer using
elasticity to measure responsiveness because
elasticity is in terms.
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Elasticity
Let the demand for good be
The own price elasticity of demand measures the
responsiveness of consumption of good to
changes in the price of good , ceteris
paribus.
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Elasticity
Why is the own price elasticity negative? To
reflect the downward sloping demand schedule.
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Elasticity
the elastic portion of the demand function.
the unitary elastic point on the demand function.
the inelastic portion of the demand function.
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Elasticity
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Example
Estimate the own price elasticity of demand at
the point
(this point lies on the elastic portion of the
demand function)
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Example
Suppose now you wanted to determine the price
elasticity at
(this point lies on the inelastic portion of the
demand function)
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Factors affecting the price elasticity of demand

• Availability of substitutes
• (and closeness of substitutes).

More substitutes and closer substitutes ? more
elastic demand.
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Factors affecting the price elasticity of demand

• Availability of substitutes
• (and closeness of substitutes).

2. Uses of the product.
More uses of the product or goods ? more elastic
demand.
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Factors affecting the price elasticity of demand

• Availability of substitutes
• (and closeness of substitutes).

2. Uses of the product.
3. Share in consumer budgets.
Commodities with larger shares tend to be more
elastic. Pencils are a small portion of
consumers budgets, so if the price of pencils
changes, one would not expect a large quantity
response. However, items such as automobiles,
appliances, etc. tend to be more elastic.
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Factors affecting the price elasticity of demand

• Availability of substitutes
• (and closeness of substitutes).

2. Uses of the product.
3. Share in consumer budgets.
4. Luxuries vs. necessities
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Factors affecting the price elasticity of demand
4. Luxuries vs. necessities
Demand for necessities tend to be more inelastic
than luxuries. Demand for gasoline, milk, salt,
etc. tend to be inelastic. Demand for large
screen TVs, vacations abroad, etc. tend to be
elastic.
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Factors affecting the price elasticity of demand

• Availability of substitutes
• (and closeness of substitutes).

2. Uses of the product.
3. Share in consumer budgets.
4. Luxuries vs. necessities
5. Time period for consumption.
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Factors affecting the price elasticity of demand
5. Time period for consumption.
Over a long period of time, consumers can either
adjust their budgets to a price change in a
particular commodity or find substitutes.
Consequently, the long run elasticity tends to be
more elastic than the short run price elasticity.
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Examples
Gasoline -0.40 -1.50 Housing
-0.30 -1.88
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Other Elasticities
a. Income elasticity
The income elasticity measures the responsiveness
of good to changes in income, ceteris
paribus.

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Plotting and (income), one traces out
the Engel curve.
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Other Elasticities
a. Income elasticity
b. Cross price elasticity
The cross price elasticity of demand measures
the responsiveness of to changes in the
price of other goods ceteris paribus.

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Cross Price Elasticity
? consumers switch to z, so the demand for z ?

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Cross Price Elasticity
As ?? quantity demanded of ?
Since and are complements , ? demand for
?
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Relationship Among Elasticities
There are 3 key relationships among elasticities

• homogeneity condition

• Slutsky or symmetry condition

• Engel condition

The theory behind these elasticity relationships
makes a certain assumption regarding individual
consumer behavior.
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Elasticity Matrix

Given n goods and income, we have the following
elasticity matrix
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Elasticity Matrix
Own price elasticities are located on the
diagonal. Cross price elasticities are on the
off-diagonal. Income elasticities are on the
last column.
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Homogeneity condition
The homogeneity condition states that the sum of
the own and cross price elasticities and income
elasticities for a particular commodity is zero.
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Homogeneity condition
The homogeneity condition stems from Eulers
Theorem which states that if a function
is homogeneous of degree k then
If then the function is
homogeneous of degree zero (HD0).
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Homogeneity condition
Since , we can rewrite this
as
Now divide through by
This is the homogeneity condition.
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Homogeneity condition
The meaning of the homogeneity condition is that
the magnitude of the own price elasticity must
be consistent with the cross price elasticities
and income elasticity of that commodity.
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Example
Demand for beef Own price elasticity
-0.62 Cross price with pork
0.11 Cross price with lamb 0.01 Cross
price with chicken 0.06 All other cross
elasticities -0.01 Income elasticity
0.45
? 0
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Slutsky or Symmetry Condition

This condition specifies a specific relationship
between and
The Hotelling-Jureen relationship states
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Hotelling-Jureen

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Engel Condition
The consumers budget can be written as
?assuming all income is spent on
commodities
The effects of changes in income on consumption
can be obtained by differentiating the above
equation with respect to I
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Engel Condition
Multiply each component by
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Engel Condition
Recall that
and
This states that the weighted sum of the income
elasticities for all items in the consumers
budget should sum to 1.
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Market Demand Conditions
How are market demand functions obtained from
consumer demand functions? Quantities demanded
or purchased by consumers are added together for
each price level.
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Market Demand Conditions
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Market Demand Conditions
Consumer 1 Consumer 2
Consumer 3
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Market Demand Conditions