ECO 3104

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ECO 3104

• Lecture 7

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Price Elasticity

• Rationale
• given law of demand, know price and quantity
  demanded are inversely related
• know supply shifts cause changes in equilibrium
  quantity demanded
• want to know by how much does quantity demanded
  change when price changes
• business decisions and revenues
• public policy decisions affecting price

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Price Elasticity

• Price elasticity of demand
• measures the sensitivity of quantity demanded to
  price changes
• measures the percentage change in the quantity
  demanded for a good or service that results from
  a one percent change in the price
• why use percentages?

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Price Elasticity

• The price elasticity of demand is

• Because of the inverse relationship between P and
  Q, EP is negative

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Price Elasticity

• Calculating Price Elasticity
• the percentage change in a variable is the
  absolute change in the variable divided by the
  level of the variable
• must choose what level of price and quantity to
  use as base to calculate percentages

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Price Elasticity

• Point Elasticity of Demand
• point elasticity measures elasticity using the
  initial price and quantity as a base
• Its formula is

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Price Elasticity

• relationship to demand curve
• measures consumer response to price change at a
  single point on demand curve
• depends on position on demand curve and slope of
  demand curve

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Price Elasticity

• problems using point elasticity
• we may need to calculate price elasticity over
  portion of the demand curve rather than at a
  single point
• the price and quantity used as the base will
  alter the price elasticity of demand

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Price Elasticity

• Arc elasticity of demand
• arc elasticity calculates elasticity over a range
  of prices
• Its formula is

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Price Elasticity

• An example
• Price increases from 8 to 10 quantity demanded
  falls from 6 to 4
• Point elasticity
• percent change in price 2/8 25.0
• percent change in quantity -2/6 -33.3
• elasticity -33.33/25.0 -1.33
• Arc elasticity
• percent change in price 2/9 22.2
• percent change in quantity -2/5 -40.0
• elasticity -40.0/22.2 -1.80
• Note that if changes are small, choice of base
  makes little difference

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Price Elasticity

• Elasticity and the shape of the demand curve
• for two demand curves that cross, at the point of
  intersection the one with the steeper slope has
  the smaller (in absolute value) elasticity
• steeper demand curve is less elastic

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Price Elasticity
Price
The steeper curve is less elastic at the point
of intersection.
P1 and P2 are the same for each curve. DB has a
flatter slope so (1/slope) is a larger number in
absolute value.
P1
DB
DA
Quantity
Q1
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Price Elasticity

• for two parallel demand curves, the one further
  from the origin is less elastic

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Price Elasticity
Price
The curve that is further from the origin is
less elastic.
P1 and the slopes of the two curves are the same.
Q1 is greater for DB, making P1/Q1 smaller.
P1
DB
DA
Quantity
Q1A
Q1B
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Price Elasticity

• for a straight-line (linear) demand curve, as
  move down along demand curve it becomes less
  elastic

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Price Elasticity
Price
The lower portion of a downward sloping demand
curve is less elastic than the upper portion.
A
P1A
The slope (and 1/slope) is constant along the
curve. However, as move from A to B, P1 gets
smaller and Q1 gets larger, making P1/Q1 smaller.
B
P1B
Q
Q1B
Q1A
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Price Elasticity

• a constant elasticity demand curve will have a
  curved shape
• change in position just offset by change in slope
• rectangular hyperbola

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Price Elasticity
Price
As the slope flattens out between A and B,
(1/slope) increases. At the same time P/Q
decreases, leaving the price elasticity constant.
P1A
A
B
P1B
Q
Q1A
Q1B
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Price Elasticity

• Categorizing price elasticities
• if EP gt 1, the percent change in quantity is
  greater than the percent change in price
• demand is elastic
• if EP lt 1, the percent change in quantity is
  less than the percent change in price
• demand is inelastic
• if EP 1, the percent change in quantity
  equals the percent change in price
• demand is unit elastic

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Price Elasticity

• Elasticity and total revenue
• TR PQ
• ?TR ? ?P ?Q
• ? means percentage change
• note can show by taking logs and
  differentiating
• whether total revenue goes up or down depends on
  magnitudes of price and quantity changes

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Price Elasticity

• Demand If Price Increases, If Price Decreases,
• Expenditures Expenditures

Inelastic (Ep lt1) Increase Decrease Unit Elastic
(Ep 1) Are unchanged Are unchanged Elastic (Ep
gt1) Decrease Increase
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Price Elasticity

• Determinants of price elasticity of demand
• availability of substitutes
• the better the substitutes available the more
  elastic the demand
• the more narrowly defined the good, the more
  substitutes and the more elastic the demand

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Price Elasticity

• Determinants of price elasticity of demand
• time period of adjustment
• the longer the time to adjust to a price change,
  the more elastic the demand
• more time to learn of price change
• more time to find substitutes
• short-run demand curve is less elastic than
  long-run demand curve

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Gasoline Short-Run andLong-Run Demand Curves
Gasoline
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Price Elasticity

• Determinants of price elasticity of demand
• share of budget spent on good
• if spend a lot on a good, more to be saved from
  finding a cheaper alternative

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Price Elasticity

• Questions
• Would a business firm prefer a relatively elastic
  or relatively inelastic demand for their product?
• What does this imply about the incentive of
  existing firms to attempt to keep out new
  entrants to a market?
• What would you predict about the elasticity of
  demand for air travel from Tallahassee to Orlando
  versus Tallahassee to Miami?

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Other Elasticities

• Income elasticity
• measures responsiveness of quantity to changes in
  income

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Other Elasticities

• Income elasticity
• if good is normal, income elasticity is positive
• if good is inferior, income elasticity is
  negative

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Other Elasticities

• Cross-price elasticity
• measures responsiveness of quantity of one good
  to changes in price of another

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Other Elasticities

• Cross-price elasticity
• if two goods are substitutes, cross-price
  elasticity is positive
• note that cross-price elasticity (and hence
  substitutability) depends on price level
• if two goods are complements, cross-price
  elasticity is negative

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End of Lecture 7