1. DEMAND ANALYSIS Demand Relationships Demand Elasticities
Overview of Chapter 3
Demand Relationships
Demand Elasticities
Income Elasticities
Cross Elasticities of Demand
Combined Effects of Elasticities
2005 South-Western Publishing 1

2. Health Care & Cigarettes
Raising cigarette taxes reduces smoking
In Canada, $4 for a pack of cigarettes reduced smoking 38% in a decade
But cigarette taxes also helps fund health care initiatives
The issue then, should we find a tax rate that maximizes tax revenues?
Or a tax rate that reduces smoking?

3. Demand Analysis
An important contributor to firm risk arises from sudden shifts in demand for the product or service.
Demand analysis serves two managerial objectives:
(1) it provides the insights necessary for effective management of demand, and
(2) it aids in forecasting sales and revenues. 2

4. Demand Curves
Individual Demand Curve the greatest quantity of a good demanded at each price the consumers are willing to buy, holding other influences constant
$/Q $5 20
Q /time unit 3

5. Sam Diane = Market
The Market Demand Curve is the horizontal sum of the individual demand curves.
The Demand Function includes all variables that influence the quantity demanded
Q = f( P, Ps, Pc, Y, N W, PE)
? ? +
P is price of the good
PS is the price of substitute goods
PC is the price of complementary goods
Y is income, N is population, W is wealth, and
PE is the expected future price 4

6. Downward Slope to the Demand Curve
Reasons that price and quantity are negatively related include:
income effect -- as the price of a good declines, the consumer can purchase more of all goods since his or her real income increased.
substitution effect -- as the price declines, the good becomes relatively cheaper. A rational consumer maximizes satisfaction by reorganizing consumption until the marginal utility in each good per dollar is equal: 8

7. Elasticity as Sensitivity
Elasticity is measure of responsiveness or sensitivity
Beware of using Slopes
Slopes
change
with a
change in
units of
measure
price price
per per
bu bu.
bushels hundred tons 10

8. Price Elasticity ED = % change in Q / % change in P
Shortcut notation: ED = %Q / %P
A percentage change from 100 to 150 is 50%
A percentage change from 150 to 100 is -33%
For arc elasticities, we use the average as the base, as in 100 to 150 is +50/125 = 40%, and 150 to 100 is -40%
Arc Price Elasticity -- averages over the two points
Average quantity
arc price
elasticity
ED = DQ/ [(Q1 + Q2)/2]
DP/ [(P1 + P2)/2] D
Average price 11

9. Arc Price Elasticity Example
Q = 1000 when the price is $10
Q= 1200 when the price is reduced to $6
Find the arc price elasticity
Solution: ED = %Q/ %P = +200/1100
- 4 / 8 or
The answer is a number.
A 1% increase in price reduces quantity by .36 percent. 12

10. Point Price Elasticity Example
Need a demand curve or demand function to find the price elasticity at a point.
ED = %Q/ %P =(Q/P)(P/Q)
If Q = •P, find the point price elasticity at P = 30; P = 50; and P = 80
ED = (Q/P)(P/Q) = - 5(30/350) = - .43
ED = (Q/P)(P/Q) = - 5(50/250) = - 1.0
ED = (Q/P)(P/Q) = - 5(80/100) = - 4.0 13

11. Price Elasticity (both point price and arc elasticity )
If ED = -1, unit elastic
If ED > -1, inelastic, e.g.,
If ED < -1, elastic, e.g., -4.0
price
Straight line
demand curve
example
elastic region
unit elastic
inelastic region
quantity 14

12. Two Extreme Examples ( Figure 3.3)D D’
D D’
Perfectly Elastic | ED| = B and Perfectly Inelastic |ED | = 0

13. TR and Price Elasticities
If you raise price, does TR rise?
Suppose demand is elastic, and raise price. TR = P•Q, so, %TR = %P+ %Q
If elastic, P , but Q a lot
Hence TR FALLS !!!
Suppose demand is inelastic, and we decide to raise price. What happens to TR and TC and profit? 15

14. Another Way to Remember
( Figure 3.4 )
Another Way to Remember
Elastic
Unit Elastic
Inelastic
Linear demand curve
TR on other curve
Look at arrows to see movement in TR Q TR 16

15. MR and Elasticity Marginal revenue is DTR / DQ
To sell more, often price must decline, so MR is often less than the price.
MR = P ( 1 + 1/ED ) equation 3.7 on page 90
For a perfectly elastic demand, ED = -B. Hence, MR = P.
If ED = -2, then MR = .5•P, or is half of the price.

16. 1979 Deregulation of Airfares
Prices declined after deregulation
And passengers increased
Also total revenue increased
What does this imply about the price elasticity of air travel?
It must be that air travel was elastic, as a price decrease after deregulation led to greater total revenue for the airlines. 17

17. Determinants of the Price Elasticity
The availability and the closeness of substitutes
more substitutes, more elastic
The more durable is the product
Durable goods are more elastic than non-durables
The percentage of the budget
larger proportion of the budget, more elastic
The longer the time period permitted
more time, generally, more elastic
consider examples of business travel versus vacation travel for all three above. 18

18. Income Elasticity EY = %Q/ %Y = (Q/Y)( Y/Q) point income
arc income elasticity:
suppose dollar quantity of food expenditures of families of $20,000 is $5,200; and food expenditures rises to $6,760 for families earning $30,000.
Find the income elasticity of food
%Q/ %Y = (1560/5980)•(10,000/25,000) = .652
With a 1% increase in income, food purchases rise .652%
EY = DQ/ [(Q1 + Q2)/2] arc income
DY/ [(Y1 + Y2)/2] elasticity 19

19. Income Elasticity Definitions
If EY >0, then it is a normal or income superior good
some goods are Luxuries: EY > 1 with a high income elasticity
some goods are Necessities: EY < 1 with a low income elasticity
If EY is negative, then it’s an inferior good
Consider these examples:
Expenditures on new automobiles
Expenditures on new Chevrolets
Expenditures on 1996 Chevy Cavaliers with 150,000 miles
Which of the above is likely to have the largest income elasticity?
Which of the above might have a negative income elasticity? 20

20. Point Income Elasticity Problem
Suppose the demand function is:
Q = •P + 3•Y
find the income and price elasticities at a price of P = 2, and income Y = 10
So: Q = 10 -2(2) + 3(10) = 36
EY = (Q/Y)( Y/Q) = 3( 10/ 36) = .833
ED = (Q/P)(P/Q) = -2(2/ 36) = -.111
Characterize this demand curve, which means describe them using elasticity terms. 21

21. Cross Price Elasticities
EX = %QA / %PB = (QA/PB)(PB /QA)
Substitutes have positive cross price elasticities: Butter & Margarine
Complements have negative cross price elasticities: DVD machines and the rental price of DVDs at Blockbuster
When the cross price elasticity is zero or insignificant, the products are not related 22

22. PROBLEM:
Find the point price elasticity, the point income elasticity, and the point cross-price elasticity at P=10, Y=20, and Ps=9, if the demand function were estimated to be:
QD = ·P + 2·Y + 2·Ps
Is the demand for this product elastic or inelastic? Is it a luxury or a necessity? Does this product have a close substitute or complement? Find the point elasticities of demand. 23

23. Answer
First find the quantity at these prices and income: QD = ·P + 2·Y + 2·Ps = 90 -8·10 + 2·20 + 2·9 = = 68
ED = (Q/P)(P/Q) = (-8)(10/68)= which is elastic
EY = (Q/Y)(Y/Q) = (2)(20/68) = +.59 which is a normal good, but a necessity
EX = (QA/PB)(PB /QA) = (2)(9/68) = +.26 which is a mild substitute

24. Combined Effect of Demand Elasticities
Most managers find that prices and income change every year. The combined effect of several changes are additive.
%DQ = ED(% DP) + EY(% DY) + EX(% DPR)
where P is price, Y is income, and PR is the price of a related good.
If you knew the price, income, and cross price elasticities, then you can forecast the percentage changes in quantity.

25. Example: Combined Effects of Elasticities
Toro has a price elasticity of -2 for snow-throwers
Toro snow throwers have an income elasticity of 1.5
The cross price elasticity with professional snow removal for residential properties is +.50
What will happen to the quantity sold if you raise price 3%, income rises 2%, and professional snow removal companies raises its price 1%?
%DQ = EP • %DP +EY • %DY + EX • %DPx = -2 • 3% • 2% +.50 • 1% = -6% + 3% + .5%
%DQ = -2.5%. We expect sales to decline.
Q: Will Total Revenue for your product rise or fall?
A: Total revenue will rise slightly (about + .5%), as the price went up 3% and the quantity of snow-throwers sold will fall 2.5%.