ELASTICITY: A GENERAL CONCEPT

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ELASTICITY A GENERAL CONCEPT

• Elasticity just measures responsiveness
• If I raise price by 10, how will my customers
  react?
• When peoples incomes go down by 15, how will
  sales be affected?
• We want to measure the responsiveness of
  cause-effect relationships.

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The more it responds, the more ELASTIC

• As this guys weight increases by 1,
• we measure the percentage
• change in the length of his undies.
• This would be the weight elasticity of undie
  length.
• Measures this!

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Elasticities in General

• The A elasticity of B is calculated by the
  formula
• ?B
• -------------- Elasticity
• ? A
• This measures the responsiveness of B to a change
  in A

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Price elasticity of demand

• When the PRICE of a good changes, other things
  equal, the QUANTITY DEMANDED will change.
• The price elasticity of demand measures the
  responsiveness of the change in quantity demanded
  to the change in price.
• Price elasticity is a number representing the
  percentage change in quantity demanded for a
  one-percent change in price.

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Simple Formula for price elasticity of demand
(PED), or EP

• Ep ? Qd/ ? P
• When price increases by 10, quantity demanded
  falls by 20. What is the elasticity
  coefficient?
• When P decreases by 30, Qd increases by 10.
  What is the elasticity coefficient?

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Interpretation of the elasitcity coefficient

• A. Ep -20/10 -2.
• B. Ep 10/-30 -1/3.
• What do these numbers mean?
• They tell us how many percentage points Qty
  demanded will change when price changes by 1.
• A is MORE ELASTIC(more responsive)

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When computing price elasticity of demand

• The sign will always be negative.
• Sometimes we just discuss the absolute value of
  p, and forget the minus sign.
• For price elasticity of demand we are interested
  only in the size of the coefficient, which gives
  us the responsiveness of quantity demanded to
  price changes.

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Elasticity formula (remember that ? means change
in)

• ? Qty Demanded
• -----------------------
  --
• ? Q (Q1 Q2)/2 (average
  q)
• Ep ------- -------------------------------
• ? P ? Price
• ------------------------
  -
• (P1 P2)/2
  (average p)

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Some examples
8 6
Demand
2 6

• When price increases from 6 to 8, qty demanded
  falls from 4 units to 2 units. What is the price
  elasticity?
• Ep (4)/(26)/2) / (2)/(68)2)
• (4/4)/(2/7)
• (1)(7/2)
• 3.5
• BIG change in Q, small change in P!

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One more

• When price falls from 4 to 2, Qd increases from
  10 to 14 units.
• Ep

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Elastic, inelastic, unitary elastic demand

• The demand for a product is said to be price
  elastic when the change in qty is ______ ______
  the change in price.
• Thus, when the elasticity coefficient is _______
  ________ ONE the relationship is said to be
  elastic.

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Elastic, inelastic, unitary elastic demand

• The demand for a product is said to be price
  elastic when the change in qty is greater than
  the change in price.
• Thus, when the elasticity coefficient is greater
  than one the relationship is said to be elastic.

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Elastic, inelastic, unitary elastic demand

• The demand for a product is said to be price
  inelastic when the change in qty is less than
  the change in price.
• Thus, when the elasticity coefficient is less
  than one the relationship is said to be
  inelastic.
• When they are the same, and EP1, we call it UNIT
  (or unitary) ELASTIC

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Perfectly inelastic demand, Ep0

• Change price, NO change in Q.

price
Almost perfectly inelastic demand
Perfectly inelastic demand
3 2 1

D
D
Qty/month
8 16
15
Perfectly elastic demand, Ep?!

• Change price a little, and Q0!

Price
Perfectly elastic demand
3 2 1
D
Almost perfectly elastic demand
Qty/mo
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What determines the degree of price elasticity?

• The existence of substitutes.
• The more substitutes there are, the more elastic
  is the relationship between changes in price
  and changes in Qty demanded.
• The share of budget (money available to spend).
• If a good is very expensive, a change in price
  will have a big effect on spending power.
• Compare a 20 increase in a 10 broom to a 20
  increase in a car. Big difference!

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What determines the degree of price elasticity?

• The length of time (after the price changes).
• The more time anyone has to make an adjustment to
  a price change, the greater the adjustment will
  be.
• If the price of gasoline were to increase by 25,
  (CP) the immediate decrease in qty demanded would
  be small, Eplt1.
• After a few years Ep would be much larger,
  perhaps gt 1 as people adjust to the higher gas
  prices (HOW?)

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Other Elasticities we measure

• A elasticity of B
• Price elasticity of Supply
• Income elasticity of Demand
• Cross Price elasticity of Demand
• ? B
• -------------- Elasticity
• ? A

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Properties of other elasticities

• Price Elasticity of Supply is positive
• Income Elasticity for normal goods -
  for inferior goods
• Cross Price for substitutes -
  for compliments

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Cross (price) elasticity of demand

• Cross elasticity tells us the responsiveness of
  the demand to prices in other goods (aCROSS
  goods)
• The formula is
• change in quantity of good X
• Exy -------------------------------------------
  
• change in the price of good Y

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When good Y is a substitute for good X

• If the the goods are substitutes, like burgers
  and pizza if the price of pizza rises (falls),
  more (fewer) burgers will be purchased.
• The sign on the coefficient will be positive.
• If price of pizza (Y) increases by 10 and the
  qty of burgers (X) increases 20 what is the
  cross elasticity?
• Exy

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When good Y is a complement to good X

• If the the goods are complements, like donuts and
  coffee if the price of coffee rises (falls),
  fewer (more) donuts will be purchased.
• The sign on the coefficient will be negative.
• If price of coffee (Y) increases by 20 and the
  qty of donuts (X) decreases 10 what is the cross
  elasticity?
• Exy

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Income elasticity of demand

• When income increases (decreases) the demand for
  normal goods will increase (decrease).
• The sign on the elasticity coefficient for normal
  goods will be positive for inferior goods
  negative.
• The formula is
• Percentage change in Qty
• Ei ---------------------------------------
• Percentage change in income

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Income elasticity

• Suppose income increases by 10 and quantity
  purchased of good A decreases by 20.
• What is the income elasticity coefficient?
• Is the relationship elastic?
• Is the good normal or inferior?

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Elasticity of supply

• Price elasticity of supply tells us the
  responsiveness of firms to an increase in the
  selling price of the product.
• change in Qty
• Es ----------------------
• change in selling price

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An example

• Suppose that the price of automobiles increased
  by 25 (CP) and qty sold increased by 7.5.
• What is the supply elasticity?
• Elastic? Inelastic? Interpretation?

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Why do we care?

• Government and businesses want to know these
  things.
• 1. Ep of gasoline
• 2. Eda for drugs and alcohol
• 3. Ep of tickets to a game
• 4. Ey of health care
• 5. Es of tanks and airplanes

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The relationship between price elasticity of
demand and total revenues for cell phone service
Elastic (Epgt1) Unit-elastic (Ep1)
Inelastic (Ep lt 1)
1.1 1.0 .9 .8 .7 .6 .5 .4 .3 .2 .1 0
3.0 2.5 2.0 1.5 1.0 .5 0
T o t a l R e v e n u e
P r i c e
Demand, or average revenue, curve
Total revenue curve
1 2 3 4 5 6 7 8 9 10 11
1 2 3 4 5 6 7 8 9 10 11
Quantity per Period
Quantity per Period
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If demand is INELASTIC,we can raise prices and
increase revenue

• For example, price is 10 and we sell 100 units.
  TR is 1,000.
• If Ep is 0.5, then if we raise prices by 10 to
  11, then we sell ____ units.
• So Total revenue goes up to _______.
• Price changes a lot, quantity changes a little.

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Short-run and long-run price elasticity of demand
D1
D2
P r i c e P e r U n i t
P1
E
Pe
Q2 Q1 Qe
Quantity Demanded per Period