ELASTICITY

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CHAPTER 5 ELASTICITY Any elasticity is defined
as a ratio of percentage changes. E.g., the X
elasticity of Y is

• Measures the responsiveness of Y to changes in X.
• Changes are measured in percentage terms to yield
  pure numbers independent of units of
  measurement. Facilitates comparisons across
  products.

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Definition Price Elasticity of Demand The
percentage change in the quantity demanded
divided by the percentage change in price.

Measures how responsive the quantity demanded is
to a change in price. Midpoint (or Arc)
Formula
?d is a negative number due to the law of
demand. E.g. let Q0 200, Q1 220, P0 1, and
P1 0.98. Then,
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You need to be able to interpret what this number
means. ?d -4.7 means that a 1 reduction in
price will result in a 4.7 increase in quantity
demanded. Or, conversely, a 1 increase in price
will result in a 4.7 decrease in quantity
demanded. Elasticities vary substantially from
one product to another. E.g., - electricity
- local telephone service - gasoline - ATT
long distance service Elasticities are important
in formulating optimal decisions both in private
firms and public policy. E.g., Weyerhauser and
DOE.
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Elastic versus Inelastic Demand - If ?d gt
1, demand is elastic. ( ? Qd gt ?P). - If
?d lt 1, demand is inelastic. ( ? Qd lt
? P). - If ?d 1, demand is unitary
elastic ( ? Qd ? P). Extreme Cases
(Graphs) - Perfectly elastic, ?d - ? -
Perfectly inelastic, ?d 0 Examples -
Demand for a firms output under competition. -
Demand for human organs for transplantation.
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Figure 5.2b
Demand Curves May be Totally Inelastic or Totally
Elastic
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Figure 5.2a
Demand Curves May be Totally Inelastic or Totally
Elastic
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In general, price elasticity of demand varies as
we move along the demand curve.
(Graph) Generally, ?d increases (in absolute
value) as price rises (or as quantity demanded
falls). Explain. Variation in ?d along demand
curve makes comparisons between products somewhat
ambiguous.
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Figure 5.3
Differing Elasticities Along a Market Demand Curve
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Figure 5.1a
Price Elasticity of Demand
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Figure 5.1b
Price Elasticity of Demand
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Figure 5.1c
Price Elasticity of Demand
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Definition Total Revenue Total receipts from
the sale of a product. Equals price times
quantity. E.g. P 10, Q 1000 ? TR
10000. Because Total Revenue and ?d are both
functions of P and Q, they are related to each
other. Specifically, if ?d gt 1, TR ? as
Q? (P?) ?d lt 1, TR ? as Q? (P ?) ?d
1, TR constant as Q? (P ?) Graph.
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Relationship between TR and ED
TotalRevenue
TR
Price (/Q)
Elastic
Inelastic
Demand
Quantity
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Figure 5.5
Total Expenditures and Total Receipts Along a
Demand Curve
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Determinants of ?d - Number and availability
of substitutes. E.g., gasoline versus Exxon
gasoline. - Size of expenditures in consumers
budgets. E.g., salt versus housing. - Time
period. Longer period generally results in
increased ?d . Graph - Preferences. Strong
preference for a product leads to low ?d . -
Point on demand curve. Higher prices generally
lead to higher ?d .
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Figure 5.7
Elasticity of Demand over Time
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Definition Income Elasticity of Demand The
percentage change in quantity demanded divided by
the percentage change in income. Measures
how responsive demand is to a change in
income. Formula Example
Let Q0 20, Q1 18, y0 200, and y1 250.
Then, Interpret.
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If ?y gt 0, normal good. If ?y lt 0,
inferior good. E.g., boats versus Krystal
hamburgers. Relevant to diversification of
investments over business cycles.
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Definition Cross Price Elasticity of Demand
(?c ) - The percentage change in the quantity
demanded for one good divided by the percentage
change in the price of another good. Measures
the responsiveness of demand for one good (A) to
a change in the price of another good (B). If
?c gt 0, the goods are substitutes. If ?c lt
0, the goods are complements. If ?c 0, the
goods are unrelated. Example DuPont cellophane
case.
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Definition Price Elasticity of Supply The
percentage change in the quantity supplied
divided by the percentage change in
price. Measures the responsiveness of supply
to changes in price. Extreme Cases (?s gt
0) Perfectly Elastic
Also very important for public policy
decisions - - markets for organs. Effects of
time period.
S
P
P
S
Q
Q
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Figure 5.8
Time and Elasticity of Supply
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Elasticities of Demand and Supply and the Burden
of a Tax - As ?d ?, share of tax paid by
consumers ?, ceteris paribus. - As ?s ?, share
of tax paid by producers ?, ceteris
paribus. Graph. A tax on cigarettes.
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Figure 5.9
Effect of an Excise Tax on Cigarettes