Quantitative Demand Analysis

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• Quantitative Demand Analysis

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Headlines

• In 1989 Congress passed and president signed a
  minimum-wage bill. The purpose of this bill was
  to increase the purchasing power of unskilled
  workers.
• We know that the consequences of price floor is
  decrease in demand. Now lets quantify it.
• How many minimum-wage workers lost their jobs?
• What happened to the total wage bill of firms
  that hire unskilled workers?

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Elasticity

• Relative measure. Sign and magnitude show type
  of relationship and extent of demand response to
  a change in its determinant Z.
• EZ ?QX / ?Z
• Percentage ltgt proportion
• Units-free measure ? independent of the units
  of measurement
• Continuous variables (function, curve) gt precise
  point elasticity (derivative)
• Discrete variables (schedule, points) gt
  approximate arc elasticity (averages)

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Own Price Elasticity of Demand

• Negative according to the law of demand

Elastic
Inelastic
Unitary
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Example Quantifying the Change

• According to an FTC Report by Michael Ward,
  ATTs own price elasticity of demand for long
  distance services is -8.64.
• If ATT lowered price by 3 percent, what would
  happen to the volume of long distance telephone
  calls routed through ATT?
• Calls would increase by 25.92 percent!

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Perfectly Elastic Inelastic Demand
Price
Price
D
D
Quantity
Quantity
Perfectly Elastic
Perfectly Inelastic
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Factors Affecting Own Price Elasticity

• Available Substitutes
• The more substitutes available for the good, the
  more elastic the demand.
• Time
• Demand tends to be more inelastic in the short
  term than in the long term.
• Time allows consumers to seek out available
  substitutes.
• Expenditure Share
• Goods that comprise a small share of consumers
  budgets tend to be more inelastic than goods for
  which consumers spend a large portion of their
  incomes.

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Demand and Revenue

• Demand FunctionQ 70,000 100P
• Inverse Demand FunctionP 700 .01Q
• Total RevenueTR P Q 700Q .01Q2
• Average RevenueAR TR / Q 700 .01Q P
• Marginal RevenueMR dTR / dQ 700 .02Q
• For linear demand MR has the sameintercept and
  twice the slope of AR
• Arc MR ?TR / ?Q (TR2-TR1) / (Q2-Q1)
• Max TR dTR / dQ MR 0 Solve for Q

P or AR
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Own-Price Elasticity and Total Revenue

• Elastic
• An increase (a decrease) in price leads to a
  decrease (an increase) in total revenue.
• Inelastic
• An increase (a decrease) in price leads to an
  increase (a decrease) in total revenue.
• Unitary
• Total revenue is maximized at the point where
  demand is unitary elastic.

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Demand Curve orAverage Revenue
At high prices and small quantities, the
elasticity is large.
25.00
20.00
15.00
Price (dollars per pizza)
12.50
At low prices and large quantities, the
elasticity is small.
10.00
5.00
Marginal Revenue
0
25 50
350.00
312.50
300.00
250.00
Total Revenue (billions of dollars)
200.00
150.00
100.00
50.00
Quantity (pizza per hour)
0 25 50
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Cross Price Elasticity of Demand
Substitutes (EQx,Py gt 0)
Complements (EQx,Py lt 0)
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Example Impact of a change in a competitors
price

• According to an FTC Report by Michael Ward,
  ATTs cross price elasticity of demand for long
  distance services is 9.06.
• If MCI and other competitors reduced their prices
  by 4 percent, what would happen to the demand for
  ATT services?
• ATTs demand would fall by 36.24 percent!

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Income Elasticity
Inferior Good (EQx,I lt 0)
Normal Good (EQx,I gt 0)
Superior Good (EQx,I gt 1)
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Uses of Elasticities

• Pricing
• Managing cash flows
• Impact of changes in competitors prices
• Impact of economic booms and recessions
• Impact of advertising campaigns
• And lots more
• CDC study
• Du Pont antitrust law suit

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Glossary of Price Elasticityof Demand
Which means that
A relationship is described as
When its magnitude is
Infinity
Perfectly elastic or infinitely elastic
The smallest possible increase in price causes
an infinitely large decrease in quantity
demanded
Less than infinity but greater than 1
Elastic
decrease in quantity demanded exceeds
increase in price
Unit elastic
1
decrease in quantity demanded equals
increase in price
Inelastic
Greater than zero but less than 1
decrease in quantity demanded is less than
increase in price.
Perfectly inelastic or completely inelastic
Zero
The quantity demanded is the same at all prices
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Glossary of Cross Elasticityof Demand
A relationship is described as
When its magnitude is
Which means that
Perfect substitutes
Infinity
The smallest possible increase in price of one
good causes an infinitely large in the demand
of the other good.
Positive, less than infinity
Substitutes
If the price of one good increases, the
quantity demanded of the other good also
increases.
Independent
Zero
The demand for one good remains
constant, regardless of the price of the other
good.
Complements
Less than zero
The demand for one good decreases when the price
of the other good increases.
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Glossary of Income Elasticityof Demand
A relationship is described as
When its magnitude is
Which means that
Negative income elastic (inferior good)
Less than zero
When income increases, quantity demanded
decreases.
Greater than zero
Positive income elastic (normal good every
normal is not superior)
The percent increase in the quantity demanded is
less than the percentage increase in income.
Positive income elastic (superior good
everysuperior is normal)
Greater than 1
The percentage increase in the quantity demanded
is greater than the percentage increase in
income.