Download Lecture 3 - Trent University

Demand Theory
and Analysis
LECTURE 3
ECON 340
MANAGERIAL ECONOMICS
Christopher Michael
Trent University
Department of Economics
© 2006 by Nelson, a division of Thomson Canada Limited
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Topics
•
•
•
•
•
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Demand Relationships
Demand Elasticities
Income Elasticities
Cross Elasticities of Demand
Combined Effects of Elasticities
Indifference Curve Analysis
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Markets, Demand & Supply
and Equilibrium
Prices >
Equilibrium
lead to
surpluses
Prices <
Equilibrium
lead to
shortages
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Shifts and Movements in Demand
•
•
Movement along demand
curve?
»
If the price of a good
increases, or decreases
and everything else
remains the same there is
a movement along the
demand curve and a
change in the quantity
demanded.
Shift in the demand curve?
»
If the price of a good
remains constant but
some other influence on
buyers' plans changes,
there is a change in the
demand for that good and
the demand curve shifts.
•
•
•
•
•
Prices of related goods;
Expected future prices;
Income;
Population;
Preferences.
P
D
Q
P
D0
D1
Q
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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?
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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.
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Demand Curves
• Individual
Demand Curve
$/Q
$5
20 Q /time unit
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the greatest quantity
of a good demanded
at each price the
consumers are
willing to buy,
holding other
influences
constant
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• The Market
Demand Curve
Sam
+
Diane
=
Market
is the horizontal
sum of the
individual demand
curves.
4
• The Demand
Function
includes all
variables that
influence the
quantity demanded
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7
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
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Why is the Demand Curve
Downward Sloping????
• 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 one’s 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.
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Elasticity as Sensitivity
• Responsiveness in the QD of a
commodity to a change in its price
• Beware of using Slopes
price
per
bu.
price
per
bu.
bushels
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Slopes
change
with a
change in
units of
measure
hundred bushels
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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
ED = Q/ [(Q1 + Q2)/2]
P/ [(P1 + P2)/2]
arc price
elasticity
D
Average price
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Arc Price Elasticity Example
•
•
•
•
Q = 1000 when the price is $10
Q= 1200 when the price is reduced to $6
Find the arc price elasticity
Solution: ED = %Q/ %P = +200/1100
-4/8
or -0.3636.
The answer is a number.
A 1% increase in price reduces quantity by
0.36 percent.
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Price Point Elasticity Example
•
Need a demand curve or demand
function to find the price elasticity at a
point.
ED = %Q/ %P =(Q/P)(P/Q)
If Q = 500 - 5•P, find the point price
elasticity at P = 30; P = 50; and P = 80
1. ED = (Q/P)(P/Q) = - 5(30/350) = - 0.43
2. ED = (Q/P)(P/Q) = - 5(50/250) = - 1.00
3. ED = (Q/P)(P/Q) = - 5(80/100) = - 4.00
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Elasticity
• If ED = -1, unit elastic
• If ED > -1, inelastic, e.g., - 0.43
• If ED < -1, elastic, e.g., -4.00
price
elastic region
unit elastic
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Straight line
demand curve
example
inelastic region
quantity
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Price Elasticity
(both point price and arc elasticity )
| p | approaches – as the demand
curve approaches the Y-axis
Price per unit ($)
Elastic range: | p | > 1
| p | = 1 = Point of
unitary elasticity
Demand curve
Inelastic range: | p | < 1
Quantity demanded per time period
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| p | approaches 0 as the demand
curve approaches the X -axis
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Two Extreme Examples
D
D
D’
D’
Perfectly Elastic | ED| = ∞ and Perfectly Inelastic |ED | = 0
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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?
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• Elastic portion of
demand curve as price
increases TR
decreases, since small
changes in price has a
large impact on
quantity.
• Inelastic portion of the
demand curve, as price
increases, TR
increases, since a
small change in price
has a small impact on
quantity.
Elastic
Unit Elastic
Inelastic
Q
TR
Q
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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 = -∞.
Hence, MR = P.
• If ED = -2, then MR = 0.5•P, or is half of
the price.
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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.
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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) =0 .652
» With a 1% increase in income, food purchases rise
0.652%
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Income Elasticity Definitions
•
If EY >0, then it is a normal good
» some goods are Luxuries: EY > 1 with a high income
elasticity (luxuries are also called superior goods)
» 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 km
Which of the above is likely to have the largest income elasticity?
Which of the above might have a negative income elasticity?
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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) = 0.833
• ED = (Q/P)(P/Q) = -2(2/ 36) = -0.111
• Characterize this demand curve, which
means describe them using elasticity terms.
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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
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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.
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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)= -1.18 which
is elastic
• EY = (Q/Y)(Y/Q) = (2)(20/68) = +0.59
which is a normal good, but a necessity
• EX = (QA/PB)(PB /QA) = (2)(9/68) = +0.26
which is a mild substitute
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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.
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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 +0.50
• What will happen to the quantity sold if you raise
price 3%, income rises 2%, and professional snow
removal companies raise price 1%?
» %Q = EP • %P +EY • %Y + EX • %Px = -2 • 3% +
1.5 • 2% +0.50 • 1% = -6% + 3% + 0.5%
» %Q = -2.5%. We expect sales to decline.
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Example (concluded):
Combined Effects of Elasticities
Q:
Will Total Revenue for your product rise or fall?
A:
Total revenue will rise slightly (about + 0.5%), as
the price went up 3% and the quantity of snow
blowers sold will fall 2.5%.
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Indifference Curve Analysis of
Demand
• Consumers attempt to
maximize happiness,
or utility: U(F, E) over
food and entertainment
• Subject to an income
constraint:
Y = PF•F + PE•E
• Graph in 3-dimensions
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U
Uo
E
Uo
F
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Consumer Choice
• assume consumers can
rank preferences, that
more is better than less
(nonsatiation), that
preferences are transitive,
and that individuals have
diminishing marginal
rates of substitution.
Then indifference curves
slope down, never intersect,
and are convex to the
origin.
U2
U1
F
Uo
9
7
6
convex
567
E
give up 2F for one E
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Indifference Curves
Uo U1
F
c
a
b
E
PE
demand
• We can "derive" a
demand curve
graphically from
maximization of utility
subject to a budget
constraint.
• As price falls, we tend to
buy more due to (i) the
Income Effect and (ii)
the Substitution Effect.
E
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Optimal Consumption Point
• Optimality Condition:
MUF / PF = MUE / PE
“
the marginal utility per
dollar in each use is equal”
MU1 = 20, and MU2 = 50
and P1 = 5, and
P2 = 25
are you maximizing utility?
Suppose
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