Price Elasticity of Demand Paper Elasticity of demand:For this question, please find an article from a mainstream news source that covers the topic of elas

Price Elasticity of Demand Paper Elasticity of demand:For this question, please find an article from a mainstream news source that
covers the topic of elasticity of demand, which highlights the importance of
elasticity of demand, prices, and revenues as it affects the determination of prices
in the market of a particular product and use graphs to support your answer. Elasticity of Demand
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Downward Slope and the Demand Curve
Suppose that the price of some product increased by 10%.
What would happen to the quantity demanded for that
product?
By the law of demand, we know that prices and quantity
demanded are inversely related, and so an increase in price
would cause the demand to fall.
It would be useful to a manager to know by how much the
quantity would fall.
This primary tool used to determine such a change is
elasticity analysis.
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Overview of Elasticity of Demand
Elasticity of Demand
➢Price elasticity
➢What is it ?
➢How do we compute it?
➢Understanding factors that determine price
elasticity.
➢Relating price changes to changes in sales revenue
Pricing strategy
➢Using price elasticity to form pricing strategy
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Price Elasticity of Demand
Also known as “own price elasticity of
demand” or “price elasticity”
Measures the responsiveness of a good’s
sales to changes in its price
Equal to the percent change in quantity
demanded divided by the percent change in
price
E = |%DQ / %DP|, ceteris paribus
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Price Elasticity of Demand, cont.
Elastic -> |%ΔQ|>|%ΔP|->|E|>1
Unit Elastic -> |%ΔQ|=|%ΔP|=1
Inelastic -> |%ΔQ| 0 -> X and Y are substitutes
» Exy X and Y are complements
Cross-price elasticities play an important role in the pricing decisions
of firms that sell multiple products.
➢ E.g. selling a hamburger with a soda. These products are
complements-when a consumer purchases a burger, he or she will
typically purchase a soda with it.
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Other elasticities
Assume that firm’s revenues are derived from sales of two products, X
and Y, then we can use the following formula to approximate changes
in revenues that obtain from changes in the price of product X:
ΔR = [Rx (1+EQx,Px) + RYEQY,Px ] x %ΔPx
Suppose that a restaurant earns $4,000 per week in revenues from
hamburger sales (Product X) and $2,000 per week from soda sales
(Product Y). Own price elasticity of demand for burgers is -1.5 and
cross price elasticity of demand between soda and burgers is -4.0.
What would happen to total revenues if it reduced the price of
hamburgers by 1%?
Homework set 3, Problem #6 will help you learn more about how
firms can take advantage of this idea and boost their revenues!
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Concept Check
A positive income elasticity tells us that that
good is:
➢a. a normal good
➢b. a substitute good
➢c. an inferior good
➢d. an inelastic good
The cross-price elasticity of demand
between bread and crackers is 4.
➢What can we conclude about bread and
crackers ?
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Elasticities from demand functions
Q = 6748 – 3P + 2.72Y + 1.68Po
Price
P = $15,000
Income
Y = $17,500
Related Price Po = $14,500
Q = 6748 – 3(15,000) + 2.72(17,500) + 1.68(14,500)
Q = 33,708
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Elasticities from demand functions
EP = -3 ( 15,000 / 33,708) = -1.335
EY = 2.72 ( 17,500 / 33,708 ) = 1.412
EPo = 1.68 ( 14,500 / 33,708 ) = 0.723
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TR and Price Elasticities
If you raise price, does TR rise?
Suppose demand is elastic, and raise price.
TR = P•Q, so, %DTR = %DP+ %DQ
If elastic, P , but Q a lot
Hence TR FALLS !!!
Suppose demand is inelastic, and we decide
to raise price. What happens to TR?
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Relating TR to price elasticity
d TR
dP
= P + Q
dQ
dQ
Q dP
MR = P 1 +
P dQ
MR = P [ 1 + 1 / Ep ]
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Relating TR to price elasticity
MR = P [ 1 + 1 / Ep ]
E = -1
MR = 0
Implication: Revenues are maximized when E=-1.
|E| > 1
MR > 0
|E| inelastic demand
North County Transit District (NCTD) had been losing
ridership in 2010, and so it gambled on reducing fares to
increase ridership.
http://www.signonsandiego.com/news/2010/sep/15/nctdgamble-lower-fares-build-ridership/
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Appendix B: Constant elasticity demand
functions
Q = kPb
dQ / dP = bkPb-1
Ep =
dQ P
dP Q
= bkPb-1
P
kPb
E=b
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Constant elasticity demand functions
Q = P -2.5 Y 1.7 A 0.4
Ep = -2.5
EY = 1.7
EA = 0.4
Log-linear transformation
Log Q = -2.5(Log P) + 1.7(Log Y) + 0.4(Log A)
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Appendix C: Computing elasticity
without a demand function.
It turns out that if we are just given a range
of prices and quantities, we can do a
reasonable job computing elasticity using a
formula called Arc elasticity.
This can be useful for a manager who wants
to introduce a new product, but does not
have much data on sales or quantity
demanded.
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ARC Elasticities
%DQ
Q2 – Q1
(Q1 + Q2)/2
P2 – P1
(P1 + P2)/2
%DP
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Arc elasticity
20
19
12
14
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Arc elasticity
%DQ = 2 / 13 = 15.38%
%DP = -1 / 19.5 = -5.13%
20
E = -3.0
19
12
14
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