Download Calculating the price elasticity of demand

Elasticity - elasticity of demand including Marginal revenue and the relationship with
elasticity of demand. Also, elasticity of supply, cross price elasticity, income elasticity
(Include coverage from chapters 2-6 of Science of Success)
Charles B. Koch, The Science of Success: How Market-Based Management Built the
World's Largest Private Company, Wiley, 2007.
Supply and Demand
Supply and demand form the backbone of economics and govern the laws of the
economic market. The inter relationship between them have long defined the allocation of
resources in the market. The quantity of demand and supply relate to the responsiveness of the
product in the market and in turn define its requirement. This change of demand/supply of
product leads to the concept of Elasticity. I would like to begin this paper by giving an example
of the relationship between demand, supply and price. (Investopedia, 2003)
Consider a new video game in the market and since the company’s previous research
determined that consumers would not buy games higher than for $300 only 30 were released
because the opportunity cost is too high for suppliers to produce more. If, however, the 30 games
are demanded by 50 people, the price will subsequently rise because, according to the demand
relationship. As the demand increases, so does the price. Consequently, the rise in price should
prompt more CDs to be supplied since the supply relationship shows that the higher the price, the
higher the quantity supplied.
However, if there are 30 video games console’s produced and demand is still at 20, the
price will not be pushed up because the supply more than accommodates demand. In fact after
the 20 consumers have been satisfied with their CD purchases, the price of the leftover consoles
might drop as the producers attempt to sell the remaining. The lower price will then make the CD
more available to people who had previously decided that the opportunity cost of buying the CD
was too high.
Elasticity:
The Economics glossary defines elasticity as:
"Elasticity is a measure of responsiveness to change. The responsiveness of behavior
measured by variable Z to a change in environment variable Y is the change in Z observed in
response to a change in Y. Specifically, this approximation is common:
Elasticity = (percentage change in Z) / (percentage change in Y)
The smaller the percentage change in Y is practical, the better the measure is and the closer it is
to the intended theoretically perfect measure." (Economics, 2009)
To put it in simple words elasticity is the degree of change in supply and demand curve
with respect to price. The degree of change varies with the product/service concerned. However,
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for commodities that are necessities price changes do not have much effect since consumers
would continue buying them irrespective of the increase in price. And similarly commodities that
are not much of a requirement will deter more consumers in case of a price increase.
Price Elasticity of Demand:
Where the Law of demand states that the decrease in price increases the demand of the product,
the price elasticity of demand determines how much of the quantity demanded responds to
change in price, i.e., it’s the proportionate change in demand given a change in price.
(Christensen, 2003)
Determinants of price elasticity of demand
The price elasticity of demand depends on many economic, social and physiological factors,
however some of the general rules include: (Bamford and Munday, 2002)
Substitute availability: There is a simple relationship here, greater the substitute greater is the
elasticity. For example if we consider butter and margarine, an increase in the price of margarine
while the butter remains same causes the sale of margarine to reduce drastically since its
substitutable. Whereas in case of eggs where there is no substitute its less elastic.
Necessarily Vs Luxury: Necessities tend to have a constant demand curve while luxury goods
tend to fluctuate. For example in case of increase in college tuition would not cause students to
stop classes in the middle of the semester, however when the real estate market faces a price
shoot up the number of buyers definitely dwindle.
Market definitions: Elasticity of demand also depends on how we define market boundaries.
Narrowly defined markets are more elastic than broadly defined ones. For example food in
general is broad and exhibits a constant demand, while if we narrow down to cookies, there are
many substitutes and depicts an inelastic relationship.
Income: Products requiring a larger portion of the consumer’s income tend to be more elastic.
Permanent or temporary price change: A one day sale would have different response than an
individual price decrease of the same magnitude.
Time Factor: Goods and services tend to have a more elastic effect over a longer period of time.
Calculating the price elasticity of demand
Since price elasticity of demand is change in price for quantity demanded,
mathematically it amounts to:
Price elasticity of demand = Percentage change in quantity demanded /Percentage change in
price
For example, a 10% increase in the price of a tread mill causes the amount of the equipment
bought to fall by 20 %. So the price elasticity of demand is
Price elasticity of demand = -20 % / 10% = - 2
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The value of elasticity, - 2, indicates that the change in the quantity demanded is
proportionately twice as large as the change in the price. The quantity demanded of a good is
negatively related to its price, i.e., the percentage change in quantity will always have the
opposite sign as the percentage change in price. (Baye, 2009)
Elastic, Inelastic and Unitary elastic
Demand is said to be elastic when the absolute value of the own price elasticity is greater
than 1, i.e., so the quantity demanded is more than the change in price. When the price of a good,
which has numerous substitutes, goes up, the consumers turn away to less expensive ones. This
means that the price is more elastic and will change with demand. (Baye, 2009)
Demand is said to be inelastic when the absolute value of the own price elasticity is lesser
than 1, i.e., percentage change in quantity decreases when there is a change in price. In certain
situations, the demand remains inelastic, in spite of prices being higher. This is in fact true for a
number of medications that are available to treat certain conditions, where there is no substitute.
Demand remains constant in spite of high prices. Also, take the case of fuel consumption, where
only few substitutes exist. During 2006, when the fuel prices were at its maximum, the demand
for gasoline was affected only slightly. Although there were very few alternatives like, hybrid
cars, they still continued to purchase gasoline and the demand was indeed considered inelastic.
Another typical example would be water, where there is no substitute. (Christensen, 2003)
Demand is said to be unitary elastic when the absolute value of the own price elasticity is
equal to 1. (Baye, 2009)
Below figure represents graphical representation of three types of elasticity.
The rule of thumb is that the price elasticity for most products is near to 1.0. For most consumer
goods and services price elasticity is in between 0.5 to 1.5. The table 1 below shows estimated
price elasticity’s of demand for a variety of consumer goods and services: (Anderson, 1997)
Estimated Price Elasticity’s of
Demand for Various Goods and Services
Source: (Anderson, 1997)
Goods
Estimated Elasticity
of Demand
Inelastic
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Salt
Matches
Toothpicks
Airline travel, short-run
Gasoline, short-run
Gasoline, long-run
Residential natural gas, short-run
Residential natural gas, long-run
Coffee
Fish (cod) consumed at home
Tobacco products, short-run
Legal services, short-run
Physician services
Taxi, short-run
Automobiles, long-run
0.1
0.1
0.1
0.1
0.2
0.7
0.1
0.5
0.25
0.5
0.45
0.4
0.6
0.6
0.2
Approximately Unitary Elasticity
Movies
Housing, owner occupied, long-run
Shellfish, consumed at home
Oysters, consumed at home
Private education
Tires, short-run
Tires, long-run
Radio and television receivers
0.9
1.2
0.9
1.1
1.1
0.9
1.2
1.2
Elastic
Restaurant meals
Foreign travel, long-run
Airline travel, long-run
Fresh green peas
Automobiles, short-run
Chevrolet automobiles
Fresh tomatoes
2.3
4.0
2.4
2.8
1.2 - 1.5
4.0
4.6
Marginal revenue – Relationship with elasticity of demand
In microeconomics, Marginal Revenue (MR) is the extra revenue that an additional unit of
product will bring. Marginal revenue (MR) is the change in total revenue per unit change in
output. Since MR measures the rate of change in total revenue as quantity changes, MR is the
slope of the total revenue (TR) curve.
The Total Revenue Test states that if demand is elastic, an increase (decrease) in price will lead
to a decrease (increase) in total revenue. And if demand is inelastic, an increase (decrease) in
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price will lead to an increase (decrease) in total revenue. Total revenue is maximized at the point
where demand is unitary elastic. (Baye, 2009)
The figure below represents the relationship between Marginal revenue and total revenue with
the elasticity of demand. The green curve indicates Total revenue, Yellow line indicates
Marginal revenue and Red line indicates demand curve.
(Source: Truett and Truett, 2006 )
From the above graph we can conclude that the Marginal revenue is positive only when demand
elasticity is greater than unity, i.e., a price fall causes proportionately larger increase in quantity
demanded. It also shows that when price falls, the total revenue increases and marginal revenue
is positive. Hence Marginal curve lies above the horizontal axis. Similarly, the Marginal revenue
is negative whenever elasticity of demand is lesser than unity, i.e., a price fall causes
proportionately smaller increase in quantity demanded. It also shows that when price falls, the
total revenue falls and marginal revenue becomes negative. This marginal curve lies below the
horizontal axis. (Truett and Truett, 2006)
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Moving from left to right on the bottom graph indicates what happens to total revenue as
price is lowered and the quantity sold increases. At lower quantities (higher prices) demand is
elastic. Quantity increases are relatively greater than price decreases and total revenue increases
as more units are sold. This means a company facing an elastic demand can increase revenue by
decreasing price.
When demand becomes inelastic, quantity increases are now relatively less than price
decreases, and total revenue falls. This means a company could increase total revenue by
increasing price and selling fewer units. This could mean a very high profit. Important questions
to be answered concern how competitors react to these higher prices, can the company produce
lower quantities at reasonably low costs, exactly how much profit will the company make, and
how will the government react to these higher profits. When demand is elastic, price and total
revenue move in the opposite direction. When demand is inelastic, price and total revenue move
in the same direction. (Truett and Truett, 2006)
The following table shows the consolidation of results obtained from the above graph:
Marginal
Revenue
Total Revenue
Price Elasticity of
Demand
MR > 0
TR increases as Quantity increases
Elastic
E>1
MR = 0
TR is maximized
Unit Elastic
E=1
MR < 0
TR decreases as Quantity increases
Inelastic
E<1
A firm maximizes its profits at the point where marginal revenue is equal to marginal
cost. Since marginal cost is predictably positive, marginal revenue should be positive too.
Therefore marginal revenue cannot be positive unless and until the elasticity of demand is
numerically greater than 1. (Spraos, 1956) I would cite the fuel costs set by OPEC as an
example. When the demand of fuel increases, OPEC tries to increase their production to meet the
demand and set their prices higher. When the demand of fuel decreases, they try to reduce
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production, cut their supplies so that there will be increase in demand for the fuel. Therefore in
both the cases, they earn revenues by changing the production rate.
Elasticity of Supply
Elasticity of supply is the ratio of relative change of the quantity supplied to the relative
change in the supply price. In other words, it is a measure of how much the quantity supplied of
a good responds to a change in the price of that good. This is important for the suppliers as they
indicate how much production will increase or decrease with a given price change. The price
elasticity of supply is used to see how sensitive the supply of a good is to a price change. The
higher the price elasticity, the more sensitive producers and sellers are to price changes. High
price elasticity suggests that when the price of a good goes up, sellers will supply a great deal
less of the good and when the price of that good goes down, sellers will supply a great deal more.
Low price elasticity implies just the opposite, that changes in price have little influence on
supply. (Bittermann, 1934)
Determinants of the Price Elasticity of Supply
a) Flexibility of sellers: goods that are somewhat fixed in supply have inelastic supplies.
b) Time horizon: supply is usually more inelastic in the short run than in the long run.
c) Production possibilities: Goods that can be produced at a constant (or very gently
rising) opportunity cost have an elastic supply. Goods that can be produced in only a
fixed quantity have a perfectly inelastic supply.
d) Storage possibilities: The supply of a storable good is highly elastic. The cost of storage
is the main influence on the elasticity of supply of a storable good. (Bittermann, 1934)
Supply is said to be elastic (inelastic) if the elasticity exceeds (is less than) 1. The more
elastic supply is, the more will a change in price increase production. Because firms often have a
maximum capacity for production, the elasticity of supply may be very high at low levels of
quantity supplied and very low at high levels of quantity supplied. (Bade and Parkin, 2002)
Perfectly Elastic Supply
An almost zero percentage change in price brings a very large percentage change in the quantity
supplied.
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A small rise in the price decreases the quantity supplied by a very large amount, i.e., supply is
perfectly elastic.
Elastic Supply
The percentage change in the quantity supplied exceeds the percentage change in price.
A 10% increase in the price of a book, increases the quantity supplied by 20%, i.e., the supply of
books is elastic.
Unit Elastic Supply
The percentage change in the quantity supplied equals the percentage change in price.
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A 10% increase in the price of fish, increases the quantity supplied of fish by 10%, i.e., the
supply of fish is unit elastic.
Inelastic Supply
The percentage change in the quantity supplied is less than the percentage change in price.
A 20% increase in the price of a hotel room, increases the quantity supplied of rooms by 10%,
i.e., the supply of hotel rooms is inelastic.
Price Inelastic Supply
The percentage change in the quantity supplied is zero when the price changes.
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A small rise in the price of a beachfront lot, increases the quantity supplied by 0%, i.e., the
supply of beachfront lots are perfectly inelastic. (Bade and Parkin, 2002)
Another application for elasticity of supply is the gold. Price of gold is volatile,
sometimes shooting upwards one moment and dramatically decreasing the next. This happens
because of shifts in demand and highly inelastic supply. Gold production is expensive and time
consuming to process
Cross Price Elasticity
Cross elasticity of demand is the % change in quantity demanded divided by the %
change in the price of a substitute or complement. It measures the responsiveness of quantity
demanded of good X to changes in the price of related good Y, holding the price of good X & all
other demand determinants for good X constant (Baye, 2009)
Cross elasticity is positive for goods that are substitutes. Cross elasticity of demand is
positive if the sales of product X move in the same direction as a change in the price of product
Y. Larger the positive cross-elasticity coefficient, greater the substitutability between the two
products. For example, when the price of hot dogs increases, the quantity of hamburgers
demanded increases.
Cross price elasticity is negative for goods that are complements. When cross elasticity is
negative: increase in price of product X decreases the demand for product Y. Larger the negative
cross-elasticity coefficient, greater the complimentarily between the two products. For example,
when the price of hot dogs increases, quantity of hot dog rolls demanded decreases.
A product's substitutability, measured by the cross-elasticity coefficient, is important in
businesses and government because the demand for their products is directly affected by the
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price of other products. The figure below shows the cross price elasticity of demand between
Pizza’s, soda and burgers. (Bade and Parkin, 2002)


Pizzas and burgers are substitutes, therefore Cross elasticity is positive.
Pizzas and soda are complements therefore Cross elasticity is negative.
Some of the cross price elasticity of goods is mentioned below:
Item
Consumer products
clothing/food
gasoline (competing stn)
Utilities
electricity/gas (residential)
electricity/oil (residential)
bus/subway
Market
Elasticity
U.S.
Boston, MA
0.1
1.2
Quebec
Quebec
London
0.1
0
0.25
Another application for cross price elasticity is the market for carbonated soft drinks industry.
The rivals coke and pepsi are typical examples. The sales of Coke will fall if the price of Pepsi
falls because some Coke drinkers will switch from Coke to Pepsi. The own and cross price
elasticities for regular carbonated soft drinks is given in below table: (Cotterill, 1994)
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Significant complements rather than substitute relationships is reflected in the above
table. Sprite, a clear soda, for example, has a negative (complementary) cross price elasticity of
(–0 .090) in the Coke demand equation and Coke is a complement in the Sprite equation. Since
these brands are both produced by the Coca Cola Company the results do provide some evidence
on the extent to which companies position and market products as complements rather than
substitutes. Mountain Dew, a Pepsico brand, however has a positive (substitute) cross price
elasticity in the Pepsi demand equation.
Complementary demand relationships were not expected among these competing regular
soft drink products. When Coke, for example, lowers its price, shoppers are attracted and pickup
some Sprite as a complementary product to provide “variety” or a clear soda for the non-coke
crowd. Other strong complementary relationships exist for the following two pairs: Seven-Up
and private label, and Mountain Dew and Dr. Pepper. (Cotterill, 1994)
Income Elasticity
Income elasticity of demand is the % change in quantity demanded divided by the %
change in income. Income elasticity (EM) measures the responsiveness of quantity demanded to
changes in income, holding the price of the good & all other demand determinants constant.
(Baye, 2009)
Income elasticity is positive for Normal (Superior) Goods such as steak and vacations more is purchased as income increases. A positive income-elasticity coefficient symbolizes a
normal good; income and quantity demanded move in same direction
Income elasticity is negative for Inferior Goods such as bread and hamburger - less is
purchased as income increases. A negative income-elasticity coefficient represents an inferior
good (Ex. retread tires, cabbage, used clothing). A negative coefficient means that the income
and quantity demanded move in opposite directions. i.e., as the income increases, the demand for
the good decreases meaning it is inferior.
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The below figure shows the demand curves for all the three types of income elasticity. (Bade and
Parkin, 2002)
The below table indicates the income elasticity for various products.
Item
Consumer
products
cigarettes
liquor
food
clothing
newspapers
Utilities
electricity
(residential)
telephone service
Market
Elasticity
U.S.
U.S.
U.S.
U.S.
U.S.
0.1
0.2
0.8
1
0.9
Quebec
Spain
0.1
0.5
The demand for necessities tends to be relatively less income elastic than the demand for
discretionary items. For example the demand for clothing is more sensitive to income than
demand for food.
The below table reflects the budget shares and income elasticites of various consumption
categories across the world. (Regmi et al., 2006)
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Based on the above table, low-income countries spend a greater portion (47 percent) of
their total expenditures on food compared with richer countries, which on average spend 13
percent of their total budget on food. In general, lower income countries spend a greater
proportion of their budget on necessities such as food, while richer countries spend a greater
proportion on luxuries. With income elasticity below one, food, beverages and tobacco, and
clothing and footwear appear to be necessities in all countries, while education, gross rent, fuel
and power, house operations, medical care, recreation, transport and other groups are all luxuries.
(Regmi et al., 2006)
Coverage from Science of Success:
Koch’s Market-Based Management system acts as a stepping stone between how individual
performance can be improved and how liberty can free societies to accomplish more. It is based
on five dimensions: vision, virtue and talents, knowledge processes, decision rights, and
incentives. (Koch, 2007)
Vision is about finding when and how an organization can create the greatest long-term value. It
uses experimentation to develop value delivered for customers based on what the finest
opportunities are and what the organization can most successfully accomplish.
Virtues and talents ensure that people with the right values, skills, and capabilities are hired,
retained, and developed. In short, it attracts and retains people who want to follow the right
principles with suitable talents for the tasks.
Knowledge processes involve creating, acquiring, sharing, and applying relevant knowledge, and
measuring and tracking profitability. In short, it analytically adds to, disseminates, and applies
knowledge related to profitability.
Decision rights ensure that the right people are in the right roles with the right authorities to
make decisions and holding them responsible. It encourages people to become better decision
makers after they have developed their skills and to be accountable for the decisions they make.
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Finally, incentives reward employees as much as possible by the long-term value they have
helped deliver for the organization. (Koch, 2007)
References:
Anderson, P.L., McLellan, R, Overton, J.P., & Wolfram, G. (1997, November). Estimated Price
Elasticities of Demand for Various. Mackinac Center Report, November, 67.
Bade, R., & Parkin, M. (2002). Foundations of Microeconomics. Retrieved March 20, 2009,
from
Elasticities
of
demand
and
Supply
Web
site:
http://www.unf.edu/~traynham/ch05lecture.pdf
Bamford, C.G., & Munday, S.C.R (2002). Markets – Studies in Economics and Business.
Heinemann Educational Publishers,[27-30].
Baye, M. R. (2009). Managerial Economics and Business Strategy, 6th Edition. St. Louis:
McGraw-Hill Irwin.
Bittermann, H.J (1934).Elasticity of Supply. The American Economic review. 24(3), [417-429].
Christensen, T.E. (2003). Wisegeek. Retrieved March 20, 2009, from Price elasticity of demand
Web site: http://www.wisegeek.com/what-is-price-elasticity-of-demand.htm
Cotterill, R.W (1994).Scanner Data: New Opportunities for Deman and Competitive Strategy
Analysis. Agricultural and Resource Economics Review. 23(2), 138.
Economics, (2009). About.com. Retrieved March 20, 2009, from Definition of Elasticity Web
site: http://economics.about.com/cs/economicsglossary/g/elasticity.htm
Investopedia, (2003). Investopedia. Retrieved March 20, 2009, from Economics basics - Demand
and Supply Web site: http://www.investopedia.com/university/economics/economics3.asp
Koch, C.G. (2007). The science of success: How market-based management built the world's
largest private company. John Wiley & Sons.
Regmi, A., Deepak, M.S., Seale, J.L., & Bernstein, J (2006). Cross-Country Analysis of Food
Consumption Patterns. Applied Economics, 38(13), 16.
Spraos, J (1956).Imperfect Competition and the Elasticity of Demand for Imports. The Economic
Journal. 66(261), [171-173].
Truett, L.J., & Truett, D.B. (2006). Managerial Economics - 8th edition.John Wiley & Sons.
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MULTIPLE CHOICE QUESTIONS:
1. In measuring the sensitivity of demand, the
a. price and income elasticities refer to movements along the demand curve; other
elasticities refer to shifts of the entire demand curve
b. price and cross-price elasticities analyze movements along the demand curve; other
elasticities refer to shifts of the entire demand curve
c. income and cross-price elasticities refer to movements along the demand curve; price
elasticity refers to shifts of the entire demand curve
d. price elasticity refers to movements along the demand curve; income and cross-price
elasticities refer to shifts of the entire demand curve
2. The value of price elasticity of demand:
a. Depends on the units that are used to measure quantities
b. Has the same value as the slope of the demand curve
c. Depends on the units that are used to measure prices
d. Do not depend on the units in which quantity and price are measured.
3. If the income elasticity of demand is 1, then
a. A 5 % increase in income will induce a 1% increase in purchases of good
b. A 5 % decrease in income will induce a 5% decrease in purchases of good
c. A 5 % increase in income will induce a 5% decrease in purchases of good
d. A 5 % increase in income will induce a 5% increase in purchases of good
4. Currently you purchase 4 packages of hot dogs a month. You will graduate from Ball
State University in May and you will start a new job in June. You have no plans to
purchase hot dogs in June. For you, hot dogs are
a. A substitute good.
b. A normal good.
c. An inferior good.
d. A law-of-demand good.
5. For a good that is a necessity,
a. Quantity demanded tends to respond significantly to a change in price.
b. Demand tends to be inelastic.
c. The law of demand often does not apply.
d. All of the above are correct.
ANSWERS TO MULTIPLE CHOICE QUESTIONS
1.
2.
3.
4.
5.
D
D
B
C
B
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