1. Elasticity Measures Lecture 10
Dr. Jennifer P. Wissink
©2018 John M. Abowd and Jennifer P. Wissink, all rights reserved.
February, 2018

2. Announcements-micro Spring 2018
All Prelim 1 Testing Locations – Please Check Cornell's Web pages for Building Codes and Building Locations
Tuesday at 7:30 evening prelim (please arrive no latter than 7:15)
Last Names starting with A-P in STL185 (Statler Aud)
Last Names starting with Q-S in STL196
Last Names starting with T-Z in STL265
Tuesday people w/accommodation letters start at 5:00pm (1110 & 1120)
URH 202
Tuesday early sitters start at 5:00pm (1110 & 1120)
RCK 122
Wednesday regular makeup start at 3:00pm (1110 & 1120)
BKL 119
Wed-day people w/accommodation letters start at 2:00pm (1110 & 1120)
URH G22

3. i>clicker questions
Can I use a cell phone or a smart phone or graphing calculator or anything like that for the prelim?
Yes No
Should I buy a simple function calculator before Prelim 1?
Yes No
Can I use a help sheet during the prelim?
Yes No

4. Beauty of Unit-free Comparisons
Gasoline and jewelry
It doesn’t matter that gas is sold by the gallon for about $3.50 and gold is sold by the ounce for about $1500.
We compare the demand elasticities of -0.2 (gas) and -2.6 (gold jewelry).
Gold jewelry demand is more price sensitive.
Paintings and meat
It doesn’t matter that classical paintings are sold by the canvas for millions of dollars each while beef is sold by the pound for about $2.99.
We compare the supply elasticities of 0 (classical paintings) and 5 (beef).
Beef supply is more price sensitive.

5. Values for Own Price Elasticities and Terminology
If we “report” them as positive numbers…
Not a problem with supply (owing to law of supply).
Take absolute value with demand (owing to law of demand).
Terms work the same way for own price elasticity of demand and supply. 1 2 3 4 5 6
price inelastic
price elastic
unit elastic

6. Calculating Elasticities
LET’S STICK TO DEMAND ONLY FOR NOW!
How does one calculate an elasticity?
Depends on the accuracy you want and the information you’ve got.
(Midpoint) Arc Formula
an approximation using two sets of data points & discrete differences.
Point Formula
an exact measure at a point, used when we have the demand function and its slope.

7. Own Price Elasticity of Demand
Recall the definition…
The (Midpoint) Arc Formula
P = Own price of the good X at two points, P1 and P2
QD = Quantity demanded of X at those two prices, Q1 and Q2
ΔP = Change in PX
ΔQD = Change in quantity demanded of X
NOTE: Since we do not know if 1 is “new” or if 2 is “new”, we just take the change in the two values and divide by the midpoint of the interval.

8. (Midpoint) ARC Own Price Elasticity of Demand Calculation
Goal: approximate own price elasticity of demand between A and B (ignore C).
Percent change in QD is (11-12) / [(11+12)/2] = -1/ = -8.69%.
Percent change in P is (38-36) / [(38+36)/2] = 2/37 = 5.40%.
Elasticity is approx % / 5.40% = -1.6

9. i>clicker question
The own price elasticity of demand between points A and B on the graph below (and reported using absolute values) is If we calculate the own price elasticity of demand using points A and C we would expect that
the elasticity would be the same, that is 1.6, silly, since it’s a straight line!
the elasticity would now be smaller than 1.6.
the elasticity would now be larger than 1.6.

10. POINT Own Price Elasticity of Demand at A, when P=$36 and QD=30-1/2P
Recall the (midpoint) arc formula using points A and B.
Now let’s make B get closer and closer to A.
In the limit we would get the exact elasticity at point A.
Rearranging, you get:

11. Point Elasticity As We Move Down a Linear Demand Curve$P
QD = 30 – 1/2P
$60
Price
Own price elasticity of demand – using point formula
Demand A 36 12 30 Q

12. i>clicker question
At their respective market equilibriums, in which of the markets below would you expect market demand to be the most price elastic?
The market for fruit.
The market for fresh fruit.
The market for fresh fruit you do not have to peel.
The market for fresh apples.
The market for fresh Gala variety apples.

13. Determinants of Own Price Demand Elasticity
Availability of substitutes in consumption.
thumb drives versus Lexar thumb drives
The importance of the item in individual budgets.
baby food versus textbooks (for you guys)
The time frame in question.
over a day versus over a year
At their respective market equilibriums, in which of the markets below would you expect market demand to be the most price elastic?
The market for fruit.
The market for fresh fruit.
The market for fresh fruit you do not have to peel.
The market for fresh apples.
The market for fresh Gala variety apples.

14. Perfectly Elastic Demand
Demand is perfectly elastic when a 1% change in the price would result in an infinite change in quantity demanded.
Example:
Price
Perfectly Elastic Demand (elasticity = -¥)
Quantity

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

16. Real World Example 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%.
So, elasticity = 27.5 ÷ 6 = 4.5  pretty darn elastic!
Way off on expected revenue collected, 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.

17. i>clicker question
What went wrong with the Barry administration’s model concerning gas taxes in Washington D.C.?
People are too poor in D.C. so they can not pay taxes.
They should have collected the taxes directly from demanders and not the suppliers.
Gas station owners in D.C. are just not very good entrepreneurs.
Mayor Barry’s economic advisers were pretty mediocre.
Someone stole all the revenue before it got to the mayor.

18. Own Price Elasticity of Demand & Total Expenditures (TE)
Suppose: Current toll for the George Washington Bridge is $15/trip.
Suppose: The quantity demanded at $15/trip is 1,000 trips/hour.
TE on trips per hour = $15,000/hour
i>clicker question If the own price elasticity of demand for bridge trips is known to be equal to -2.0, then what is the effect on TE of a 10% toll increase?
A. TE increase
B. TE stay the same
C. TE decrease
A 10% toll increase means the price is now $16.50 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 trips, number of trips falls to 800 trips/hour.
TE are now only $13,200/hour (= 800 x $16.50), so TE decreased!

19. Own Price Elasticity of Demand & Total Expenditures
What happens to total expenditures (TE) made by buyers in a market when market price increases?
Note: TE = PD•QD
PD↑ tends to increase TE.
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!
Price
Perfectly Inelastic Demand (elasticity = 0)
Quantity

20. Own Price Elasticity of Demand & Total Expenditure with Linear Demand
$TE=P•Q
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.

21. Own Price Elasticity of Demand & Total Expenditure with Linear Demand
$TE=P•Q
Price
Price elastic
Demand
Price inelastic
Quantity
Quantity

22. Example: Demand Function, Demand Curve & Own Price Elasticity of Demand
Suppose you know the demand function for compact disc players (X) is:
QDX = (T&P)(Pop) + 3I – 2PCD + 3PB – (5,145/T&P)PX
Now… to go from the demand function to the demand curve, plug in values for everything BUT PX
So suppose: T&P=7; Pop=1,000; I=5,000; PCD=9; PB=15
You get:
Now find own price elasticity of demand at PX=$7