Transcript Arc Price Elasticity

DEMAND ANALYSIS
 Demand Relationships
 The Price Elasticity of Demand
 Arc and point price elasticity
 Elasticity and revenue relationships
 Why some products are inelastic and others are
elastic
 Income Elasticities
 Cross Elasticities of Demand
 Combined Effects of Elasticities
Health Care & Cigarettes
 Raising cigarette taxes reduces smoking
 In
Canada, over $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?
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.
FIGURE 3.1 Demand for SUV (Ford
Explorer) as Gasoline Price Doubled
Downward Slope to the Demand Curve
 Economists presume consumers are maximizing their utility
 This is used to derive a demand curve from utility
maximization
income effect -- as the price of a good declines,
the consumer can purchase more of all goods since
his or her real income increased. So as the price
falls, we typically buy more.
Downward Slope to the Demand Curve
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. We buy more.
FIGURE 3.2 Consumption Choice on a
Business Trip
Downward Slope to the Demand Curve
targeting, switching, and positioning –
marketing efforts such as loyalty programs affect
demand.
Uo
Foo
d
PE
Indifference Curves to
U1
derive demand
• We can "derive" a demand
curve graphically from
maximization of utility
a
c
b
subject to a budget
2
constraint. Suppose the
price of entertainment
1
Entertainment
falls from line 1 to line 2
• We tend to buy more from
(i) the Income Effect and
(ii) the Substitution Effect.
demand
From a to b, is the
Entertainment
substitution effect. From b
to c is the income effect.
The Price Elasticity of Demand
 Elasticity is measure of responsiveness or
sensitivity
 Beware of using Slopes
price
per
bu.
price
per
bu.
bushels
Slopes
change
with a
change in
units of
measure
hundred tons
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 price 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
ED = Q/ [(Q1 + Q2)/2]
P/ [(P1 + P2)/2]
Average price
arc price
elasticity
D
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 -.3636.
The answer is a number.
A 1% increase in price reduces quantity by
.36 percent.
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 = 500 - 5•P, find the point price elasticity
at P = 30; P = 50; and P = 80
1. ED = (Q/P)(P/Q) = - 5(30/350) = - .43
2. ED = (Q/P)(P/Q) = - 5(50/250) = - 1.0
3. ED = (Q/P)(P/Q) = - 5(80/100) = - 4.0
Price Elasticity
(both point price and arc elasticity )
 If ED = -1, unit elastic
 If ED > -1, inelastic, e.g., - 0.43
 If ED < -1, elastic, e.g., -4.0
price
elastic region
unit elastic
Straight line
demand curve
example
inelastic region
quantity
FIGURE 3.4 Perfectly Elastic and
Inelastic Demand Curves
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?
( Figure 3.2)
Another Way to
Remember
Elastic
Unit Elastic
A
 Linear demand curve
 TR on other curve
 Look at arrows to
see movement in TR
A.
B.
Increasing price in the
inelastic region raises
revenue
Increasing price in the
elastic region lowers
revenue
Inelastic
B
Q
TR
Q
FIGURE 3.5 Price Elasticity over
Demand Function
FIGURE 3.5 Price Elasticity over
Demand Function
MR and Elasticity
 Marginal revenue is TR /Q
 To sell more, often price must decline,
so MR is often less than the price.
 MR = P ( 1 + 1/ED )
 For a perfectly elastic demand, ED = -B.
Hence, MR = P.
 If ED = -2, then MR = .5•P, or is half of
the price.
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.
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.
Empirical Price Elasticities
 Apparel (whole market) 







1.1
Apparel (one firm) -4.1
Beer -.84
Wine -.55
Liquor -.50
Regular coffee -.16
Instant coffee -.36
Adult visits to dentist
 men -.65
 Women -.78
Children visit to dentist -1.4
 Furniture -3.04
 Glassware & China -1.2
 School lunches -.47
 Flights to Europe -1.25
 Shoes -.73
 Soybean meal -1.65
 Telephones -.10
 Tires -.60
 Tobacco -.46
 Tomatoes -2.22
 Wool -1.32
Free Trade and
Price Elasticities
 NAFTA (North American Free Trade
Agreement) and Europe having a common
currency in the Euro are examples of
greater freedom in trade
 What does that do to price elasticities?
 With more substitutes, we expect that
products become More Elastic
 Consumers gain as firms are less able to
raise their prices, but firm face stiffer
competition
Income Elasticity
EY =
%Q/ %Y = (Q/Y)( Y/Q) point income
EY = Q/ [(Q1 + Q2)/2] arc income
Y/ [(Y1 + Y2)/2] elasticity
 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%
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:
1. Expenditures on new automobiles
2. Expenditures on new Chevrolets
3. 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?
Point Income Elasticity Problem
 Suppose the demand function is:
Q = 10 - 2•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.
Advertising Elasticity
EA =
%Q/ %ADV = (Q/ADV)( ADV/Q)
 If the Advertising elasticity is .60, then a 1%
increase in Advertising Expenditures increases
the quantity of goods sold by .60%.
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
Antitrust & Cross Price Elasticities
 Whether a product is a monopoly or in a
larger industry is dependent on the closeness
of the substitutes
 DuPont’s cellophane was at first viewed as a
monopoly. Economists showed that the cross
price elasticity with other products such as
aluminum foil, waxed paper, and other
flexible wrapping paper was Positive, the
large, DuPont showed its cellophane was not
a monopoly in this larger market.
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 = 90 - 8·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.
Answer
 First find the quantity at these prices and income:
QD = 90 - 8·P + 2·Y + 2·Ps = 90 -8·10 + 2·20 + 2·9
=90 -80 +40 +18 = 68
 ED = (Q/P)(P/Q) = (-8)(10/68)= -1.17 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
Combined Effect of
Demand Elasticities
 Most managers find that prices and income change
every year. The combined effect of several changes
are additive.
%Q = ED(% P) + EY(% Y) + EX(% PR)

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.
Example: Combined Effects of Elasticities
 Toro has a price elasticity of -2 for snow blowers
 Toro snow blowers 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%?


Q:
%Q = EP • %P +EY • %Y + Ecross • %PR = -2 • 3% + 1.5
• 2% +.50 • 1% = -6% + 3% + .5%
%Q = -2.5%. We expect sales to decline 2.5%.
Will Total Revenue for your product rise or
fall?
Example: Combined Effects of Elasticities
A: Total revenue will rise slightly (about +
.5%), as the price rises 3% and the quantity
of snow-blowers sold falls 2.5%.
Optimization
Techniques
Economic Optimization Process
 Optimal Decisions

Best decision helps achieve objectives most
efficiently.
 Maximizing the Value of the Firm

Value maximization requires serving
customers efficiently.


What do customers want?
How can customers best be served?
Expressing Economic Relations
 Tables and Equations


Simple graphs and tables are useful.
Complex relations require equations.
 Total, Average, and Marginal Relations

Total increases when marginal is positive.
Revenue per time period ($)
$9 8 7 6 5 4
3 Total revenue = $1.50 ´
output 2 1
0
123456789
Output per time period
(units)
Maximization Occurs when Marginal Switches from
Positive to Negative.
 If marginal is above average, average is
rising.
 If marginal is below average, average is
falling.
 Graphing Total, Marginal, and Average
Relations


Deriving Totals from Marginal and Average
Curves
Total is sum of marginal.
Marginal Analysis in Decision
Making
 Use of Marginals in Resource Allocation
 Maximum and minimum points occur where
marginal is zero.
 Distinguishing Maximums from Minimums
 Total and Marginal Relations
 Maximizing the Difference Between Two
Functions
 Maximum profit requires MR = MC.
 When profits are maximized, total profit decreases
with a change in output.
Practical Applications of Marginal
Analysis
 Profit maximization requires Mπ = MR-MC = 0
and MR=MC and that π is falling as output
expands.
 Revenue maximization requires MR=0.

Firms sometimes grab market share when
maximizing long-run profitability.
 Average cost minimization requires MC=AC
and that AC is rising as output expands.
Incremental Concept in Economic
Analysis
 Marginal v. Incremental Concept


Marginal relates to one unit of output.
Incremental relates to one managerial
decision.

Multiple units of output is possible.
 Incremental Profits

Profits tied to a managerial decision.
 Incremental Concept Example