1. Consumer Theory-1 Lecture 12
Dr. Jennifer P. Wissink
©2019 Jennifer P. Wissink, all rights reserved.
March 6, 2019

2. 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.

3. 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.

4. 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 = Price x Quantity = $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!

5. Own Price Elasticity of Demand & Total Expenditures (TE)
What happens to total expenditures (TE) made by buyers in a market when market price increases?
Remember: TE = PD x 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 when PD↑  TE ↓
Why?
If demand is price INELASTIC, then when PD↑  TE ↑
On you own: reverse this argument to determine the relationship between total expenditure and elasticity when you consider a price decrease!
Price D
Perfectly Inelastic Demand (elasticity = 0)
Quantity

6. 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.

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

8. 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

9. 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

10. Two More Elasticities Cross Price Elasticity of Demand
Income Elasticity of Demand

11. The Other Elasticities
Extremely similar formulas are used:
(Midpoint) Arc formula
With discrete data points
Point formula
When you use the slope of the function
Just need to substitute in…
…carefully!

12. The Other Elasticities You Need to Know
Cross Price Elasticity of Demand
(Midpoint) Arc Formula
Point Formula

13. The Other Elasticities You Need to Know
Income Elasticity of Demand
(Midpoint) Arc Formula
Point Formula

14. Example: Demand Function & Income 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… plug in values for everything BUT Income (I).
So suppose: T&P=7; Pop=1,000; PCD=9; PB=15; PX=$7
You get:
Now find income elasticity of demand at I=5,000

15. The 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

16. Next Up: Consumer Theory

17. i>clicker question
Prof. Wissink really thinks Saabs are cool cars and she prefers them to Hondas, yet she drives a Honda Fit. This is because
she is not a good shopper.
she does not know how to solve the consumer theory problem.
she does not have enough money to buy a Saab.
All of the above are correct
None of the above are correct