


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
 Inelastic demand elasticity  quantity demanded is not sensitive to changes in market price
 Unitary elastic demand elasticity  if market price decreases by 1%, then quantity demanded increases by 1%
 Elastic demand elasticity  quantity demanded is sensitive to changes in market price
 Example:
 E_{D} = 0.25 for coffee
 If the price of coffee decreases by 1%, then quantity demanded increases by 0.25%, viceversa
 E_{D} = 1 for movies
 If the price of movies increases by 1%, then quantity demanded decreases by 1%, viceversa.
 E_{D} = 4.0 for air travel
 If the price of air travel decreases by 1%, then quantity demanded increases by 4%, viceversa.
 Note: Can multiply elasticities by a number
 E_{D} = 0.25 for coffee
 If the price of coffee decreases by 10%, then quantity demanded increases by 2.5% (viceversa).
 E_{D} = 4.0 for air travel
 If the price of air travel decreases by 10%, then quantity demanded increases by 40% (viceversa).
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
 Substitution Effect
 Elastic goods tend to have many substitutes
 Inelastic goods tend to have few substitutes
 Cigarettes, gasoline, and alcohol
 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.
 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
 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}
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
 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.
 If demand is inelastic, an increase in price will cause total revenue to increase (and viceversa).
 If demand is elastic, a decrease in price will cause total revenue to increase (and viceversa).
 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
 Shortrun, Honda can produce more cars by using more labor and resources
 Longrun, 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!
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 perunit 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 (shortrun)
 Beer / liquor
 Cigarettes

Terminology 
 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

 crossprice 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


