Quantitative Demand Analysis
Baye Chapter 3
• General concept that measures the
responsiveness of two variables to one
• Mechanism to characterize demand and
• Measure of how markets react to changing
• Allows for a more detailed understanding
and analysis of supply and demand
• ED = % change in Q / % change in P
• Shortcut notation: ED = %Q / %P
• A percentage change from 100 to 150 is 50%
• A percentage change from 150 to 100 is -33%
• For arc elasticities, we use the average as the base, as in
100 to 150 is +50/125 = 40%, and 150 to 100 is -40%
• Arc Price Elasticity -- averages over the two points
Average quantity arc price
ED = Q/ [(Q1 + Q2)/2]
P/ [(P1 + P2)/2] • D
Arc Price Elasticity Example
• Q = 1000 when the price is $10
• Q= 1200 when the price is reduced to $6
• Find the arc price elasticity
• Solution: ED = %Q/ %P = +200/1100
– A 1% increase in price reduces quantity by .36
Point Price Elasticity Example
• Need a demand curve or demand function to
find the price elasticity at a point.
ED = %Q/ %P =(Q / P)(P/Q)
If Q = 500 - 5•P, find the point price
elasticity at P = 30; P = 50; and P = 80
1. ED = (Q / P)(P/Q) = - 5(30/350) = - .43
2. ED = (Q / P)(P/Q) = - 5(50/250) = - 1.0
3. ED = (Q / P)(P/Q) = - 5(80/100) = - 4.0
(Both point price and arc elasticity )
• If ED = -1, unit elastic
• If ED > -1, inelastic, e.g., - 0.43
• If ED < -1, elastic, e.g., -4.0
price demand curve
Two Extreme Examples
Perfectly Elastic | ED| = and Perfectly Inelastic |ED | = 0
Use For Elasticity
• Elasticity is related to revenues
• Suppose demand is elastic, and you raise
• TR = P•Q, so, %TR = %P + % Q
• If elastic, P increases but Q falls a lot
• Hence TR FALLS
• Suppose demand is inelastic, and we decide
to raise price. What happens to TR? and
Another Way to Elastic
Remember Unit Elastic
• Linear demand
• TR on the other TR
• Look at arrows to TR
see movement in
1979 Deregulation of Airfares
• Prices declined after deregulation
• And passengers increased
• Also total revenue increased
• What does this imply about the price
elasticity of air travel?
Determinants of the Price Elasticity
• The availability and the closeness of substitutes
– more substitutes, more elastic
• The more durable is the product
– Durable goods are more elastic than non-durables
• The percentage of the budget
– larger proportion of the budget, more elastic
• The longer the time period permitted
– more time, generally, more elastic
– consider examples of business travel versus vacation travel
for all three above.
Time and Adjustment to an Reduction in Supply
• Consider the market for gasoline of
the late 1970s and early 1980s (and Price S2
now). ($ per gallon)
• The price of a gallon of gasoline in S1
1978 was $.70 (point A).
• When supply declined unexpectedly
in the late 1970s, prices increased
to $1.20 and consumption fell to 7.0
million barrels per day (from 7.4) as
consumers moved along their short A
run demand curve (to point B).
• Note how little quantity demanded .50
fell due to this shock. In the long .40
run, the demand for gasoline is more .30
responsive to price changes .20 DLR
• By 1982, the market equilibrated at Quantity
point C, with consumption of 6.6 6.6 7.0 7.4 (million
million barrels a day and a market barrels of
gas per day)
price of $1.00 a gallon).
Elasticity of Demand
Inelastic Approximately Unitary Elasticity
Salt 0.1 Movies owner occupied (long run) 0.9
Matches 0.1 Shellfish (consumed at home) 1.2
Toothpicks (short run)
Airline travel 0.1 Oysters (consumed at home) 0.9
Gasoline (short run) 0.1 1.1
Gasoline (long run) 0.2 Private education
Tires (short run 1.1
Natural gas, home (short run) 0.7 Tires (long run) 0.9
Natural gas, home (long run) 0.1 Radio and television receivers 1.2
Fish (cod), at home 0.3 Elastic
Tobacco products (short run) 0.5 Restaurant meals run) 2.3
0.5 Foreign travel (long
Legal services (short run) 4.0
0.4 Airline travel (long run)
Taxi (short run) 0.6
Fresh green peas run)
Automobiles (short 2.8
Automobiles (long run) 0.6
Chevrolet automobiles 4.0
Fresh tomatoes 4.6
• Can you explain why the demand for some goods
is highly inelastic while that for others is elastic.
EY = %Q/ %Y = ( Q/ Y)( Y/Q) point income
EY = Q/ [(Q1 + Q2)/2] arc income
Y/ [(Y1 + Y2)/2] elasticity
• Arc income elasticity:
– suppose dollar quantity of food expenditures for families earning
$20,000 is $5,200; and food expenditures rises to $6,760 for
families earning $30,000.
– Find the income elasticity of food
– %Q/ %Y = (1560/5980)•(10,000/25,000) = .652
– With a 1% increase in income, food purchases rise .652%
Income Elasticity Definitions
• If EY >0, then it is a normal good
– some goods are Luxuries: EY > 1 with a high income
– some goods are Necessities: EY < 1 with a low income
• If EY is negative, then it’s an inferior good
• Consider these examples:
1. Expenditures on new automobiles
2. Expenditures on new Chevrolets
3. Expenditures on 1996 Chevy Cavaliers with 150,000 miles
Which of the above is likely to have the largest income elasticity?
Which of the above might have a negative income elasticity?
Point Income Elasticity Problem
• Suppose the demand function is:
Q = 10 - 2•P + 3•Y
• find the income and price elasticities at a price of P =
2, and income Y = 10
• So: Q = 10 -2(2) + 3(10) = 36
• EY = (Q/Y)( Y/Q) = 3( 10/ 36) = .833
• ED = (Q/P)(P/Q) = -2(2/ 36) = -.111
• Characterize this demand curve, which means
describe them using elasticity terms.
Cross Price Elasticities
EAB = %QA / %PB = (QA/ PB)(PB /QA)
• Substitutes have positive cross price elasticities:
Butter & Margarine
• Complements have negative cross price
elasticities: DVD machines and the rental price of
DVDs at Blockbuster
• When the cross price elasticity is zero or insignificant, the
products are not related
Find the point price elasticity, the point income
elasticity, and the point cross-price elasticity at
P=10, Y=20, and PS=9, if the demand function
were estimated to be:
QD = 90 - 8·P + 2·Y + 2·Ps
Is the demand for this product elastic or inelastic?
Is it a luxury or a necessity? Does this product
have a close substitute or complement?
Combined Effect of
• Most managers find that prices and income change
every year. The combined effect of several
changes are additive.
%Q = ED(% P) + EY(% Y) + EX(% PR)
– where P is price, Y is income, and PR is the price of a related good.
• If you knew the price, income, and cross price
elasticities, then you can forecast the percentage
changes in quantity.
Example: Combined Effects of Elasticities
• Toro has a price elasticity of -2 for snow-throwers
• Toro snow throwers have an income elasticity of 1.5
• The cross price elasticity with professional snow
removal for residential properties is +.50
• What will happen to the quantity sold if you raise
price 3%, income rises 2%, and professional snow
removal companies raises its price 1%?
Q: Will Total Revenue for your product rise or fall?
Questions for Thought
• Studies indicate that the demand for Florida
oranges, Bayer aspirin, watermelons, and airfares
to Europe are elastic. Why?
– Why is the demand for salt, matches, and
gasoline (short-run) inelastic?
• Are the following statements true or false?
– A 10% reduction in price that leads to a 15% increase
in amount purchased indicates a price elasticity of more
– A 10% reduction in price that leads to a 2% increase in
total expenditures indicates a price elasticity of more
– Focus Groups
– Simulated Markets
• Price Experimentation
– Varying prices across different markets
• Statistical Analysis
– Estimate demand curves
– The problem of ceteris paribus and omitted variables
Price Elasticity of Supply
• The price elasticity of supply is the percent
change in quantity supplied divided by the
percent change of the price causing the
– Analogous to the price elasticity of demand.
– However, the price elasticity of supply will be
positive because the quantity producers are
willing to supply is directly related to price.
Determinants of Supply Elasticity
• Ability of sellers to change the amount of
the good they produce.
– Beach-front land is inelastic.
– Books, cars, or manufactured goods are elastic.
• Time period.
– Supply is more elastic in the long run.