Elasticities and Welfare Measures
Lecture 3

 

Price Elasticity of Demand

1. Price elasticity of demand - the sensitivity of quantity demanded to a change in price. Price elasticity is

Price elasticity of demand formula

The symbol delta, D.means change, percent change in price is:

Percent change in price

and percent change in quantity demanded is:

Percent change in quantity demanded

We can use algebra to reduce the equation to:

Price elasticity of demand

Note - Economists change frequently the denominator of the fractions for percent change. What number should you divide with? Should you divide by the initial point (P1, Q1) or the final (P2, Q2), or an average of these two points.

  • Elasticity has no units!
    • Can compare apples to oranges
    • Also called elasticity coefficient
    • The elasticity of demand has aminus sign; it shows the Law of Demand, where price and quantity have an inverse relationship.
      • Some economists drop the minus sign
      • Exam questions drop the minus sign
    • Three categories
      1. Inelastic demand elasticity - quantity demanded is not sensitive to changes in market price
      2. Unitary elastic demand elasticity - if market price decreases by 1%, then quantity demanded increases by 1%
      3. Elastic demand elasticity - quantity demanded is sensitive to changes in market price
  • Example:
    1. ED = -0.25 for coffee
      • If the price of coffee decreases by 1%, then quantity demanded increases by 0.25% (vice-versa).
    2. ED = -1 for movies
      • If the price of movies increases by 1%, then quantity demanded decreases by 1% (vice-versa).
    3. ED = -4.0 for air travel
      • If the price of air travel decreases by 1%, then quantity demanded increases by 4% (vice-versa).
  • Note: Can multiply elasticites by a number
    1. ED = -0.25 for coffee
      • If the price of coffee decreases by 10%, then quantity demanded increases by 2.5% (vice-versa).
    2. ED = -4.0 for air travel
      • If the price of air travel decreases by 10%, then quantity demanded increases by 40% (vice-versa).

2. Determinants of price elasticity of demand.

  1. Substitution Effect
    • Elastic goods tend to have many substitutes
    • Inelastic goods tend to have few substitutes.
      • Cigarettes, gasoline, and alcohol
  2. Income Effect
    • Elastic goods tend to take a large portion of income.
      • Cars, computers, an houses.
    • Inelastic goods tend to take a small portion of income.
      • Matches, toothpicks, and salt.
  3. Time
    • Second Law of Demand
    • Goods are more elastic in the long run than the short run
    • More time to adjust to price changes
    • Example - During 1970's, OPEC cut back on production of oil (supply curve shifted left)
      • Petroleum and gasoline prices increased
      • Short run:
        • Quantity demanded dropped very little (inelastic)
      • Long run:
        • Americans made fewer trips
        • Bought fuel efficient Japanese cars
        • Moved closer to work
        • Quantity demanded dropped significantly (more elastic)
      • U.S. car manufacturers were hurt in the 1980s, because they could not make small cars

3. Demand function has two forms

  • Nonlinear demand functions - have a slight curvature to them
    • Nonlinear - not a straight line
    • Have constant elasticity at any point along function
    • P = b Qa
      • ED = a
Elastic Demand Curve Inelastic Demand Curve
Price Price
An elastic demand function An inelastic demand function
Quantity Quantity
  • Relatively Elastic - any movement along this line has a constant elasticity
    • Tend to be flat
    • A small change in price leads to a large change in quantity demanded

-µ < ED < 1

  • Relativity Inelastic - any movement along this curve has a constant elasticity:
    • Tend to be steep
    • A large change in price leads to a small change in quantity demanded

- 1< ED < 0

   
Unitary Elastic
Price
Unitary elastic demand function
Quantity

Unitary Elasticity- any movement along this demand curve always has an elasticity of -1

ED = -1

  • Linear demand functions- a straight line
    • Have an elasticity that ranges from 0 to negative infinity
    • P = b - a Q
      • ED = 1 - b / (a*Q)
    • Has two exceptions
      • Perfectly inelastic - vertical demand function
        • Quantity demanded does not respond to changes in price\
      • Perfectly elastic - horizontal demand function
        • Quantity is perfectly sensitive to a change in market price
Linear Demand Function
Price
Elasticity of a linear demand function
Quantity

Linear (Straight line) Demand Curve

-¥< Ed < 0


Perfectly Elastic Perfectly Inelastic
Price Price
Perfectly elastic demand function Perfectly inelastic demand function
Quantity Quantity

Slope: a = 0 and ED = -¥

Slope: a= ¥ and ED = 0

Total Revenue and Price Elasticity

1. Total revenue (TR) - consumers payrevenueto a business for a product or service.

Total Expenditures = Total Revenue (TR) = Q P

  • Example: Consumers buy 1 million pizzas for $10 each, so total expenditures = $10 million.
    • The firms collect this money so total revenue is $10 million.
    • Total revenue is an area under the demand function.
    • Shown below:

Total Revenue

  • If the the market price decreases to $5 per pizza, then pizza producers collect a new rectangle for total revenue, which is light blue and yellow rectangles.
  • Because the light blue rectangle is common to both revenues for both prices, we can ignore it.
  • The lower price causes a loss of the green rectangle and a gain in the yellow rectangle, causing revenue to decrease. We are assuming pizza is an inelastic good.

Gains and losses in revenue

Linear Demand Function
  Price
Linear Demand Function

P = b - a Q

Intercepts

If Q = 0, then P = b

If P = 0, then Q = b / a

Elasticity for a linear demand function
  Quantity
  Total Revenue
Two Equations:

TR = P Qand P = b - a Q

Substitute demand function into total revenue function

TR = (b - a Q) Q

TR = b Q - a Q2

If Q = 0, then TR = 0

If Q = b / a, then TR = 0

max. TR where Q = b / 2 a

Total revenue function
  Quantity

2. Conclusion:

  • When price, P, increases, quantity demanded, Q, decreases.
  • Change in total revenue is an interaction between P and Q.
  • How TR changes depends on elasticity.
    1. If demand is inelastic, an increase in price will cause total revenue to increase (and vice-versa).
    2. If demand is elastic, a decrease in price will cause total revenue to increase (and vice-versa).
    3. If demand is unitary elastic, an increase in price will cause no change in total revenue. (The price increase exactly offsets the decreases in quantity demanded).

Estimate an equation for changes in revenue. Equation is below:

Relating price changes to revenue changes

  • Example 1
    • Tourists have a price elasticity of demand to travel to north Europe of -1.73
    • If the price increases by 10%, then quantity demanded falls by 17.3%
    • Revenue fron the tourists would fall approximately 7.3%
  • Example 2
    • Tourists fron North America have a price elasticity of demand for international travel of -0.58
    • If the price increases by 5%, then quantity demanded for international travel falls by 2.9%
    • However, revenue from these tourists increase approximately by 2.1%

Also can relate changes to quantity demand to changes in revenue, the equation is below:

Changes in revenue related to chagnes in quantity demanded

  • Example
    • Tourists travelling to Latin America have a price elasticity of demand of -0.58
    • If 10% more tourists are travelling to Latin American, then revenue they spend decreases by 7.24%
    • Remember - price decreased, which attracted more travellers

 

Demand Elasticities

1. Income elasticity - indicates the responsiveness of the demand for a product to a change in income. Income elasticity is:

Income elasticity of demand

  • Normal goods - goods with income elasticity of demand > 0 (i.e. positive).
    • As income increases, the demand for normal goods will rise.
    • Demand curve shifts right!
      • Necessity 0 < EI < 1
        • Food, EI = 0.51
        • As income increases by 1%, then demand for food increases by 0.51 %.
      • Luxury EI => 1
        • Travel to southern Europe, EI = 2.34
        • As income increases by 1% for tourists, then demand to souther Europe increases by 2.34 %111.
  • Inferior goods- goods with a income elasticity < 0 (i.e. negative).
    • As income increases, the demand for inferior goods will decrease.
    • Demand curve shifts left!
      • Margarine is -0.20
      • As income increases by 1%, then demand for margarine decreases by 0.20%
      • Rice, bus travel, etc.

2. Cross Price Elasticity - can determine if demands for two products are related. Products are defined as X and Y.

Cross price elastcity

  • If EXY> 0, then products X and Y are substitutes
    • Example: EXY = 0.5
    • The products are travel to Italy or travel to Greece
    • If the price of a trip to Greece increases by1%, then demand for a trip to Italy increases by 0.5 percent.
  • If EXY= 0, then products are not related
  • If EXY < 0, then products X and Y are complements
    • Example: EXY = -0.9
    • The products are airline tickets and hotel room prices
    • If the price of increase airline tickets increase by 1%, then demand for hotel rooms fall by 0.9%

3. Transport elasticity - important for tourism economics. Tourists need a means to get to the tourist destination

  • Example: Transport elasticity for tourists travelling to North America is -1.89%
  • If transportation prices increase by 1%, then travel to North America decreases by 1.89%
  • Travellers are sensitive to transport prices

4. Foreign exchange elasticity - international tourists are impacted by exchange rates

  • Example: Tourists from developed Asian countries have a -0.51 elasticity to exchange rates
  • If the exchange rate increases by 1% (place going to), then demand for tourism falls by 0.51%
    • Vacation is more expensive, when tourists converts their home currency into foreign country's currency

5. Marketing elasticity - how effective marketing is for a tourist destination

  • Example: Tourists from North Europe have a marketing elasticity of 0.31
  • If marketing increased by 1%, then North Europeans will increase their demand for international travel by 0.31%
  • Marketing elasticities tend to be inelastic

6. Example of elasticities

  • Of Origin - the region where the tourists are coming fron
  • Of Destination - the region where the tourists are travelling to
Region Income Price Exchange Rates Transport Costs Marketing
Of Origin
North Europe 2.06 -0.37 -1.57 -0.86 0.31
South Europe 1.67 -0.54 -1.41 -1.30 0.23
North America 174 -0.58 -1.51 -1.52 0.59
Oceania 2.55 -0.73 - -1.46 0.20
Latin America 0.28 -0.84 - -1.26 0.61
Asia (Developed) 4.45 -0.74 -0.51 -0.62 0.28
Of Destination
North Europe 1.79 -1.73 -0.44 -1.54 -
South Europe 2.34 -0.64 -1.34 0.11 0.39
North America 2.06 -1.42 -1.54 -1.89 -
Oceania 3.35 -0.74 - -0.98 0.23
Latin America 1.76 -0.58 - -1.28 0.67
Asia (Developed) 1.17 -1.18 - -1.61 -

Source: Mak, James. Tourism and the economy - understanding the economics of tourism.

Price Elasticity of Supply

1. Tourism supply - has two definitions

  • Definition 1 - an increase in demand requires an increase in facilities and infrastructure
  • Definition 2 - tourism may be stimulated by providing more facilities
    • Say's Law - supply creates its own demand
  • Encourages demand for tourism
    • Nature, forests, sea
    • History, culture, and tradition
    • Sun
    • Artistic
    • Monuments, ruins, etc.
    • Holy places
  • May require large scale investments from government and private markets
    • Could expand existing infrastruture if a population already lives there
  • Establish infrastructure for tourism
    • Places to stay - hotels, hostels, motels, etc.
    • Places to eat - restraurants, cafes, bakeries, cart stands, etc.
    • Banking facilities - tourists need access to cash
    • Shopping
    • Transportation - airports, ship ports, bus/train stations
    • Activities - things for the tourists to do
      • Museums
      • Outdoor activities

2. Price elasticity of supply - the senstitivity of a change of quantity supplied to the market price

Price elasticity of supply

Blue Arrow The price elasticity of supply will be positive because of the Law of Supply.
  • Elasticity is similar to demand
    • If ES = 0, then supply elasticity is perfectly inelastic
    • If ES < 1, then supply elasticity is inelastic
    • If ES = 1, then supply is unitary elastic
    • If ES > 1, then supply is elastic
  • Elasticity is related how fast producers can expand production
    • Very Short-Run Supply Curve - firms do not have enough time to change production level
    • ES = 0
      • Restraurants - can help a maximum number of consumers
      • Hotel - maximum number of rooms
      • Historic site - maximum number of admissions
      • Examples - Sistine Chapel, Mao's Tomb, etc.

A very short run supply curve

  • Short-Run Supply Curve - at least one factor of production is fixed, usually machines and equipment
    • Supply tends to be inelastic
    • Restraurants can hire more chefs, waiters, staff, etc.
    • Historic site can hire more tour guides

A short run supply curve

  • Long-Run Supply Curve - firms have enough time to change all factors of production
    • Supply is more elastic
    • Restraurants can expand dining space
    • Hotel can add new rooms
    • Gov. could build a new museum

A long run supply curve

Terminology

  • price elasticity of demand
  • inelastic demand
  • unitary elastic demand
  • elastic demand
  • substitution effect
  • income effect
  • nonlinear demand functions
  • relatively elastic
  • relativity inelastic
  • unitary elasticity
  • linear demand functions
  • perfectly inelastic
  • perfectly elastic
  • total revenue
  • income elasticity
  • normal goods
  • necessity
  • luxury
  • inferior goods
  • cross price elasticity
  • transport elasticity
  • foreign exchange elasticity
  • marketing elasticity
  • tourism supply
  • price elasticity of supply
  • very short-run supply curve
  • short-run supply curve
  • long-run supply curve
 

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