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

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

and percent change in quantity demanded is:

We can use algebra to reduce the equation to:

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 (P ₁, Q ₁) or the final (P ₂, Q ₂), 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. E _D = -0.25 for coffee
     • If the price of coffee decreases by 1%, then quantity demanded increases by 0.25%, vice-versa
  2. E _D = -1 for movies
     • If the price of movies increases by 1%, then quantity demanded decreases by 1%, vice-versa.
  3. E _D = -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. E _D = -0.25 for coffee
     • If the price of coffee decreases by 10%, then quantity demanded increases by 2.5% (vice-versa).
  2. E _D = -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 Q ^a
  • E _D = a

Elastic Demand Curve	Inelastic Demand Curve
Price	Price
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 < E D < 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< E D < 0

Unitary Elastic
Price
Quantity
Unitary Elasticity - any movement along this demand curve always has an elasticity of -1. E D = -1

Linear demand functions - a straight line

• Have an elasticity that ranges from 0 to negative infinity
• P = b - a Q
  • E _D = 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
Quantity
Linear (Straight line) Demand Curve - ¥< E d < 0

Perfectly Elastic	Perfectly Inelastic
Price	Price
Quantity	Quantity
Slope: a = 0 and E D = - ¥	Slope: a= ¥ and E D = 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:

• 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.

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
	Quantity
	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 Q 2 If Q = 0, then TR = 0 If Q = b / a, then TR = 0 max. TR where Q = b / 2 a
	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).
• 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:

• 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 < E _I < 1
      • Food, E _I = 0.51
      • As income increases by 1%, then demand for food increases by 0.51 %.
    • Luxury E _I => 1
      • New cars, E _I = 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.

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.

• If E _XY> 0, then products X and Y are substitutes
  • Example: E _XY = 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 E _XY= 0, then products are not related
• If E _XY < 0, then products X and Y are complements
  • Example: E _XY = -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:

The price elasticity of supply will be positive because of the Law of Supply.

• Elasticity is similar to demand
  • If E _S < 1, then supply elasticity is inelastic
  • If E _S = 1, then supply is unitary elastic
  • If E _S > 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
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
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
Price
Quantity (in thousands)

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

Supply of Coffee
Price
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
Price
Quantity

• 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
Price
Quantity

• 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

Terminology