1. Elasticity Measures Part 2
Dr. Jennifer P. Wissink
©2011 John M. Abowd and Jennifer P. Wissink, all rights reserved.

2. Recall: Own Price Supply Elasticities
When the price of DaVinci paintings increases by 1% the quantity supplied doesn’t change at all, so the quantity supplied of DaVinci paintings is completely insensitive to the price.
Own price elasticity of supply is 0.
When the price of beef increases by 1% the quantity supplied increases by 5%, so beef supply is very price sensitive.
Own price elasticity of supply is 5.
I am trying to give supply and demand about equal billing here. My text does elasticities before the detailed demand and supply discussions.

3. Supply Elasticity
Extremely similar formulas are used to calculate the own price elasticity of supply
Arc midpoint formula
Large delta style or small delta style
Point formula
Just need to substitute in
Quantity supplied and change in quantity supplied where appropriate

4. Supply Elasticity
Definition:
Arc Formula:
Point formula:

5. Example: Arc Calculation of Own Price Elasticity of Supply
Want supply elasticity at A
Use B: QS=9 and P=5
Use C: QS=16 and P=7
% change in QS = (16-9)/((16+9)/2)*100 = 56%
% change in P = (7-5)/((7+5)/2)*100 = 33.33%
Supply elasticity at A = 56/33.33 = 1.68
Nonlinear Supply Curve 12 10 8 C
Price 6 B A 4 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Quantity

6. Example: Point Calculation of Own Price Elasticity of Supply
Suppose you are given: QS = P
Note, that’s the same as: PS = Q
Suppose you want the exact own price elasticity of supply at P = $12
At P = $12, QS = = 38
Note: (dQS/dP) = 4
(Slope of drawn supply curve = .25, so.... 1/slope = 4)
So supply elasticity at P=$12 is... (4)•(12/38) = 48/38 = 1.26

7. Some Technical Definitions For Extreme Elasticity Values
Perfectly elastic means the quantity demanded or supplied is as price sensitive as possible.
a.k.a. completely elastic
a.k.a. infinitely elastic
Perfectly inelastic means that the quantity demanded or supplied has no price sensitivity at all.
a.k.a. completely inelastic

8. Perfectly Elastic Demand
Price
Quantity
Perfectly Elastic Demand (elasticity = -¥)
Demand is perfectly elastic when a 1% change in the price would result in an infinite change in quantity demanded.
Example:
Your discussion from your lecture 6

9. Perfectly Inelastic Demand
Price
Quantity
Perfectly Inelastic Demand (elasticity = 0)
Demand is perfectly inelastic when a 1% change in the price would result in no change in quantity demanded.
Example:
ditto.

10. Perfectly Inelastic Supply
Supply is perfectly inelastic when a 1% change in the price would result in no change in quantity supplied.
Example: wheat?
At harvest?
Yes.
Across planting seasons?
No.
Price
Quantity
Perfectly Inelastic Supply (elasticity = 0)
ditto.

11. Perfectly Elastic Supply
Supply is perfectly elastic when a 1% change in the price would result in an infinite change in quantity supplied.
Example: wheat?
Across planting seasons?
Yes.
Price
Quantity
Perfectly Elastic Supply (elasticity = ¥)
Your discussion from your lecture 6

12. Determinants of Elasticity
What is a major determinant of the own price elasticity of demand?
Availability of substitutes in consumption.
What is a major determinant of the own price elasticity of supply?
Availability of alternatives in production.

13. Real World Example – Getting It Wrong
Gas taxes in Washington DC, 1980
Extra 6% tax imposed Aug 16, 1980 to raise much needed revenue for D.C.
Increased price at pump by 8¢ (a nearly 6% increase).
By end of first month, QD down by 27.5%.
 elasticity = 27.5÷6 = 4.5  pretty darn elastic!
Way off on expected revenue, too.
By October, sales had dropped by 40% and 242 gas station workers were laid off.
Tax lifted by Mayor Marion Barry on November 24, 1980.
What went wrong? What didn’t they account for?

14. Real World Example – Getting It Wrong

15. Own Price Elasticity of Demand & Total Expenditures
Question: What happens to total expenditures made by buyers (TE) in a market when market price increases?
Note: TE = P•QD
P↑ tends to increase TE, but it also decreases QD.
QD↓ tends to decreases TE.
So what happens to TE?
Knowing own price elasticity will help!
If demand is price ELASTIC, then TE ↓
Why?
If demand is price INELASTIC, then TE ↑
On you own: reverse this argument to determine the relationship between total expenditure and elasticity when you consider a price decrease!
Set-up slide

16. Bridge Toll Example
Suppose: Current toll for the George Washington Bridge is $6.00/trip.
Suppose: The quantity demanded at $6.00/trip is 100,000 trips/hour.
So: TE on trips per hour = $600,000
If the own price elasticity of demand for bridge trips is known to be -2.0, then what is the effect of a 10% toll increase?
Note: since demand is price ELASTIC  TE↓
A 10% toll increase means the price is now $6.60 per trip.
If η=-2, a toll increase of 10% implies a 20% decline in the quantity demanded.
If there is a 20% decline in trip, number of trips falls to 80,000/hour.
Total expenditure falls to $528,000/hour (= 80,000 x $6.60).
$528,000 < $600,000
Your example.

17. Own Price Elasticity of Demand & Total Expenditure with Linear Demand
$TE
Price
Price elastic
Demand
Price inelastic
Quantity
Quantity
Starting at the “top” of the demand curve, where demand is price elastic, as price falls, and quantity demanded rises, total expenditures rise, but increase at a decreasing rate.
At the midpoint, where demand is unit elastic, total expenditures will be at their maximum value.
As you continue down the demand curve, where demand is now price inelastic, as price falls, and quantity demanded rises, total expenditures fall.
your graph

18. Cross-Price Elasticity of Demand
Elasticity of demand with respect to the price of a complementary good (cross-price elasticity)
This elasticity is negative because as the price of a complementary good rises, the quantity demanded of the good itself falls.
Example: software is complementary with computers. When the price of software rises the quantity demanded of computers falls.
Elasticity of demand with respect to the price of a substitute good (also a cross-price elasticity)
This elasticity is positive because as the price of a substitute good rises, the quantity demanded of the good itself rises.
Example: hockey is substitute for basketball. When the price of hockey tickets rises the quantity demanded of basketball tickets rises.
Cross-price elasticities quantify effects like these.
If you don’t like my example, which they have seen before, use your own.

19. Cross-Price Elasticity of Demand
Definition:
Arc Formula:
Point Formula:
If you don’t like my example, which they have seen before, use your own.

20. Income Elasticity of Demand
The elasticity of demand with respect to a consumer’s income is called the income elasticity.
When the income elasticity of demand is positive (normal good), consumers increase their purchases of the good as their incomes rise (e.g. automobiles, food).
When the income elasticity of demand is greater than 1 (luxury good), consumers increase their purchases of the good more than proportionate to the income increase (e.g. ski vacations, haute cuisine).
When the income elasticity of demand is positive but less than 1 (a necessity), consumers increase their purchases of the good less than proportionate to the income increase (e.g. socks, bread).
When the income elasticity of demand is negative (inferior good), consumers reduce their purchases of the good as their incomes rise (e.g. spam, potatoes).

21. Income Elasticity of Demand
Definition:
Arc Formula:
Point Formula:
If you don’t like my example, which they have seen before, use your own.

22. All Four Elasticities You Need to Know
Own Price Elasticity of Demand
Cross Price Elasticity of Demand
Income Elasticity of Demand
Own Price Elasticity of Supply