Elasticities

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Elasticities
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Why Is This Important?

• 1982 Metropolitan Opera and NY Transit Authority
  raised revenues by choosing opposite pricing
  strategies (Lipsey and Steiner). How?
• How much tax revenue will sin taxes provide?
• Why do stores provide coupons?
• Why do airlines give discounts for advance
  bookings?
• Why do men and women often pay different prices
  for the same product?
• When is a monopoly a monopoly?

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Elasticities Measuring Responsiveness

• Elasticities show the extent to which one
  variable responds to another.
• Example. The price elasticity of demand shows how
  the quantity demanded of a product responds to a
  change in price.
• The algebraic definition
• General Change Y/ Change X
• Price Elasticity of Demand change Qd/ change
  P

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Examples of Price Elasticity of Demand

• If the price elasticity of demand (h) is equal to
  4 . . .
• Qd will change by four times the percentage
  change in P and Qd will move in the opposite
  direction from the change in P.
• A 10 increase in price will result in a 40
  decline in quantity demanded.
• If h 0.5 . . .
• A 10 decline in price will raise Qd by 5.

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Elastic Demand, Price, and Revenue (Expenditure)

• If elasticity gt 1 . . . elastic demand
• then percent change in q gt percent change in p
• price and revenue move in opposite direction
• Example Opera Tickets

R P x Q
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Inelastic Demand, Price, and Revenue (Expenditure)

• If elasticity lt 1 . . . inelastic demand
• then percent change in q lt percent chagne in p
• price and revenue move in same direction

R P x Q
10
Less than 10
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Unit Elastic Demand, Price, and Revenue

• If elasticity 1. . . unit elastic demand
• percent change in qpercent change in p
• revenue does NOT change when p changes

R P x Q
no change
10
Exactly 10
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Determinants of Price Elasticity Availability of
Good Substitutes

• more substitutes gt more elastic.
• elasticity of demand for Pepsi is higher than the
  elasticity of demand for colas, which is higher
  than the elasticity of demand for softdrinks.
• intensified competition in the marketplace raises
  the price elasticity of demand for a single
  sellers product, since consumers have more
  substitutes available to them.

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Necessities v. Luxuries

• luxuries gt more elastic
• the demand for opera tickets is more elastic than
  the demand for subway tokens.
• the demand for vacation air travel is more
  elastic than the demand for business air travel
• also related to availability of substitutes

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Share of Budget Devoted to Item

• larger share of budget gt more elastic
• Whats the price of a box of salt? It comprises
  a small fraction of a typical consumers budget,
  and its demand is probably quite inelastic since
  consumers will not respond greatly to a price
  increase.
• For example, among college students, gasoline
  probably has a greater price elasticity of demand.

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Time Frame

• longer time frame gt more elastic
• the oil shocks of the 1970s
• the response to higher oil prices was modest in
  the immediate period after the price increases,
  but as time passed, people found ways to consume
  less gas and oil
• better mileage from their cars
• insulation in their homes
• car pooling

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Segmenting the Market by Elasticity

• If consumers can be divided into groups according
  to elasticity of demand, higher prices can be
  charged to those with inelastic demands, and
  lower prices to those with elastic demands, thus
  increasing revenues received from both groups.

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Calculating Elasticities

• Point Formula
• Usual method of calculating percent changes is
  not appropriate in this case gives different
  answers depending on choice of point 1.

Q2-Q1 -------- x 100
Q1 --------------------- P2-P1 ------- x
100 P1
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Arc or Midpoint Formula

• provides same answer no matter which point is
  taken to be point 1.

Q2-Q1 Q2-Q1
P1P2 1 P1P2
------------- x 100 -------- x
--------- ---------- x --------
.5(Q1Q2) P2-P1 Q1Q2
slope Q1Q2 -------------------------
P2-P1 ------------ x 100 .5(P1P2)
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Other Useful Elasticities

• cross elasticity defines market competition
• income elasticity shows normal, inferior,
  luxury, necessity
• price elasticity of supply