Elasticities and Welfare
Lesson 6


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 - The DQ over DP is the inverse of a slope; Elasticity does not equal a line's slope

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 a minus 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 elasticities 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. Calculations

  • Example 1 - a college raises its tuition from $20,000 to $25,000 and students enrollments falls from 10,000 to 8,000.
    • Compute the price elasticity of demand.
    • Is it elastic or inelastic
    • Answer
    • Average price = $22,500
    • Average quantity = 9,000
    • Elasticity = 1
    • Unitary elastic

3. 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. Luxury versus necessity
    • Luxury goods tend to be elastic
      • Consumers may be sensitive to price in buying expensive clothes, jewelry, etc.
    • Necessity goods tend to be inelastic
      • Person needs heart medication
  4. 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

4. 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
Unitary elastic demand function

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
Elasticity of a linear demand function
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 pay revenue to 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
Linear Demand Function

P = b - a Q


If Q = 0, then P = b

If P = 0, then Q = b / a

Elasticity for a linear demand function
  Total Revenue
Two Equations:

TR = P Q and 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


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).
  • Example 1
    • Demand for higher education is elastic. Oklahoma State University wants to maximize total revenue from the students.
    • If OSU increases tuition, total revenues will decrease.
    • If OSU decreases tuition, total revenues will increase.
      • Price decreases a little, but quantity demanded increases a lot.
  • Example 2
    • Cigarettes are inelastic. Firms want to maximize total revenue from sells.
    • If firms increase price, then total revenue increases.
      • Price increases a lot, but quantity demanded decreases a little.

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
        • New cars, EI = 2.45
        • As income increases by 1%, then demand for cars increases by 2.45 %.
  • 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.
Blue Arrow As a country becomes richer (higher income), then the production of normal goods will expand, while production for inferior goods will decrease!

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 and the products are steak and chicken; if the price of chicken increases by1%, then demand for steak 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 and the products are DVDs and DVD players; if the price of DVD players increase by 1%, then demand for DVDs fall by 0.9%
 Economists look at cross price elasticities to determine if products are in the same market or in different markets. Further, government officials can use these elasticities to determine if a monopolist has any substitutes for his product or service.

Price Elasticity of Supply

1. Analogous to the price elasticity of demand. Price elasticity of supply is:

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 < 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
    • Short Run - firms do not have enough time to change plant size
      • Supply tends to be inelastic
      • Inelastic - is not sensitive to price changes
    • Long Run - firms have enough time to change plant size
      • Supply tends to be more elastic
      • Elastic - is sensitive to price changes
  • Example: The price of a Honda Civics increases
    • Short-run, Honda can produce more cars by using more labor and resources
    • Long-run, Honda can build additional factories
Elastic Supply Curve Inelastic Supply Curve
Price Price
Elastic supply function Inelastic supply function
Quantity Supplied Quantity Supplied

Social Welfare

1. Consumer Surplus - the area below the demand curve but above the actual price paid.

  • Measure of social welfare.
  • An aggregate benefit to all consumers in the market.
    • The market price of coffee is $1.50 and consumers buy 15 (million) pounds of coffee.
    • I place a $2.50 value on this soda, but bought it for $1.50
    • I received a benefit of $1.00
  • If the market price of the soda decreases to $0.50, consumers' surplus increases!
    • Social welfare increases
Demand for Coffee Demand for Coffee
Price Price
Consumers' surplus Consumers' surplus
Quantity (in thousands) Quantity (in thousands)

2. Producer Surplus - the area above the supply curve but below the actual sales price.

  • Measure of social welfare
  • An aggregate benefit to all producers in the market
  • Producers' surplus is total fixed costs + profits
Supply of Coffee
Producers' surplus
Quantity (in thousands)

3. Social Welfare is the sum of consumer plus producers' surpluses

Supply of Coffee
Consumers plus producers' surpluses
Quantity (in thousands)

The Impact of a Tax

1. Tax incidence - how the "economic" burden of tax is shared between buyers and sellers.

  • Statutory incidence of tax - the legal assignment of who pays a tax; i.e. who sends the taxes to the government
  • Tax incidence and statutory incidences differ.

2. Example: Gov. places a $1 tax on each pizza sold on pizza producers.

  • Statutory incidence falls on producers.
  • Tax rate - the per-unit tax
    • $1 per pizza.
    • Do not use percent tax!
    • Percent tax changes the slope of the supply function
  • Supply curve shifts left by exactly $1.
  • Market price was at P*, $10 per pizza. New price, Pt, does not equal $11.
  • Price lies between $11 and $10.
    • The tax changes consumer's behavior.
    • New market price is higher (price + tax)
    • Consumers buy less, Qt.
  • Tax base - the total amount of goods, which are taxed.
    • The higher the tax rates, the smaller the tax base.
      • Tax rates change consumers' and producers' behavior and thus the size of the tax base
  • Tax revenue from pizza = Qt X $1.
    • (area of a rectangle width X height)
    • blue area + yellow area.
    • "Yellow area" - actual tax burden on sellers.
    • "Blue area"- actual tax burden on buyers.
  • Deadweight loss of taxation - the red area.
    • "Excess burden of taxation"
    • Nobody receives this revenue
    • A loss to society, because government interfered with the market
Pizza Market
Social welfare when tax is placed on a product
  • What if the $1 pizza tax was placed on the buyer.
    • (switching statutory incidence from sellers to buyers).
    • The buyers send the tax to the government
    • The demand curve will shift to the left by $1, but the end result is exactly the same!
    • Statutory incidence of tax changed, but the tax burden remained the same.
Pizza Market
Social welfare when gov. imposes a tax on buyers
  • Inelastic demand (relative to supply) - quantity demanded is not sensitive to price changes.
  • Tax burden falls more heavily on consumers
    • Gov. loves to tax inelastic goods
      • Gasoline (short-run)
      • Beer / liquor
      • Cigarettes


  • price elasticity of demand
  • elastic demand
  • inelastic demand
  • unitary elastic demand
  • nonlinear demand function
  • linear demand function
  • perfectly inelastic demand
  • perfectly elastic demand
  • total revenue test (TR)
  • income elasticity of demand
  • normal goods
  • inferior goods
  • cross-price elasticity of demand
  • price elasticity of supply
  • short run
  • long run
  • consumers' surplus
  • producers' surplus
  • social welfare
  • tax incidence
  • statutory incidence of tax
  • tax rate
  • tax base
  • deadweight loss of taxation