### price elasticity - Gregory C. Mason

```Introduction to microeconomics
Demand relationships
Chapter 4
Learning Goals
• Understand the nature of demand
• Identify optimum spending for a good in the
face of a budget constraint
• Define the price elasticity of demand
• Describe the effects of a change in price and
income (substitution and income effects)
• Calculating market demand
• Define income and cross-price elasticity
The Law of Demand
• Demand curve is a relationship between the
quantity demanded and its price.
• The Law of Demand
– Other things remaining equal, price and quantity
demand will be inversely related.
– the cost of consuming good or service is the sum of all
the sacrifices needed to consume
– The price of good A is the amount of another good
(B)needed to gain the exclusive right to consume
– Most often use a common good B to measure price
(money)
LO3: Derive a Demand
Curve
Ch4 -3
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Utility
• Utility – the satisfaction derived from
consuming a good or service.
• Utility Maximization – economists assume
people try to allocate choose a set of goods to
maximize their satisfaction.
• Util – a fictional unit of pleasure or utility
obtained from an item.
LO1: Derive Rational
Spending Rule
Ch4 -4
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Marginal utility typically declines and then becomes negative
Total utility increases and then falls
Cone quantity
(cones/hour)
Total utility
(utils/hour)
0
0
1
100
2
150
3
175
4
187
5
184
Marginal utility switches from + to
– at the same point where total
utility starts to decline.
Total utility increases with each cone
eaten, up to the fourth cone/per hour.
The marginal utility of ice cream
consumption (cones/hour) declines
with number of cones eaten per hour
LO1: Derive Rational
Spending Rule
Ryerson Limited
Total Utility from Ice Cream Consumption
Marginal utility = change in utility/change in consumption
Cone quantity
(cones/hour)
Total utility
(utils/hour)
0
0
1
100
2
150
3
175
4
187
5
184
Marginal utility
(utils/cone)
100
50
25
150 utils - 100 utils
2 cones - 1 cone
 50 utils/cone
marginal utility 
12
-3
marginal utility 
Why do we need cones/hour and not just cones?
 Utility
 Cones
 d (U ) / d ( c )
What does the marginal marginal utility measure?
LO1: Derive Rational
Spending Rule
Ch4 -6
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Diminishing marginal utility
– As the consumption of a good or service
increases, the additional utility gained from an
extra unit of the commodity tends to decline.
– Based on the cost-benefit principle, you continue
to order cones as long as the marginal utility from
an additional cone is greater or equal to zero.
– This assumes no budget constraint or any other
good (substitute – chocolate cake) or
complement (apple pie)
You have an income of \$10 per week to spend on two types
of ice-cream. Cones costs \$1; Sundaes costs \$2
The Optimal combination of
goods is the Affordable
combination that delivers
maximum total utility
LO1: Derive Rational
Spending Rule
Cone/sundae
combinations
Total utility (utils/week)
10 cones, 0 sundaes
80 + 0 = 80
8 cones, 1 sundae
82 + 50 = 132
6 cones, 2 sundae
80 + 80 = 160
4 cones, 3 sundae
68 + 105 = 173
2 cones, 4 sundae
50 + 120 = 170
0 cones,
Ch4 -8 5 sundaes
2012
McGraw-Hill
130
= 130
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The Rational Spending Rule I
• The marginal utility for the 3rd sundae is 25 utils (105-80 = 25 utils), and
the marginal utility per dollar is 12.5 utils (25/\$2 = 12.5).
• If you spends \$2 for cones instead (buying the 5th and the 6th cone), it will
increase your total utility by 12 utils ( 5th cone: 75-68 = 7 utils; 6th cone: 8075 = 5 utils).
•You are is getting more utils per dollar from the last sundae you purchases
LO1: Derive
than Rational
from the last cone, then you willCh4
-9 more sundae.
Spending Rule
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The Rational Spending Rule II
• Allocate spending across goods so that the marginal
utility per dollar is the same for each good.
MUC MU S

PC
PS
MU
• The marginal utility per dollar =
P
• Follows directly from the cost /benefit (here the
benefit/cost)principle.
• To maximize benefit (utility), the ratio of marginal
utility to price must be the same for each good the
LO1: Derive Rational
Spending Rule
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A demand curve emerges from
constrained choices
• If income rises from \$10 to \$14 per week, then …?
– Extra income stimulates demand by enlarging the set of
affordable combinations.
• If the price of cones rises to \$2 rather than \$1, then …?
– At \$1 per cone, marginal utility per dollar is 8 utils/dollar
– At \$2 per cone, marginal utility per dollar is 4 utils/dollar,
By applying the rational spending rule to price changes,
a demand curve emerges
As price of the cone
increases from \$1 to
\$2, applying the
rational spending
rule to the utility
schedule, the
demand for cone
has decreased from
4 to 1.
Price (\$/cone)
Demand for Vanilla Cones
2.00
1.50
1.00
D
1
2 3 4
Quantity (cones/week)
LO3: Derive a Demand
Curve
Ch4 -12
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Income and Substitution Effect
• Income effect:
the change in quantity demanded of a good that occurs because a
change in the price of the good changes the effective income of the
purchaser.
– A cone at \$1, allows you to maximize total utility by spending \$10 to
purchase 4 cones and 3 sundaes per week.
– A cone at \$2, requires \$14 to buy the previous combination, therefore
effective income falls.
• Substitution effect:
the change in quantity demanded of a good whose relative price has
changed while a consumer’s real income is held constant.
– When the price of a cone increases, rational consumers substitute the
good that has the relatively lower price.
LO4: Income and
Substitution Effect
Ch4 -13
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Individual and Market Demand Curves - Tuna
Market
demand
curve
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Private good (consumption)
• Total market demand for a private good is the
“horizontal” sum of individual demand.
• Utility for the consumer is derived solely from
his/her personal consumption
• Private goods involve no sharing of utility (or
disutility) among consumers
– The smell of tuna on Smith’s breath does not repel Wong
– Wong is not overjoyed at finding a fellow tuna eater
– Singh does not worry that Smith and Wong are eating an
endangered species
Equation for a Straight Line Demand
Curve
QD  c  dPD
• PD is for the price of the good.
• QD is for the quantity demanded.
• c is the horizontal intercept of the demand curve
or….? ---------->
• Consumption when price (PD) is zero (free).
– -d represents the reciprocal of the slope.
LO3: Derive a Demand
Curve
Ch4 -16
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The Market Demand Curve for Canned Tuna
slope  rise / run  1 / 2
QD  12 2PD
LO3: Derive a Demand
Curve
Ch4 -17
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Total Expenditure
• Total Expenditure equals
– The number of units bought multiplied by the
price of the good.
• Total Expenditure of consumers = Total
Revenue of Producers
LO3: Derive
a Demand Curve
Ch4 -18
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FIGURE 4.7 The Demand Curve for Movie Tickets
An increase in price
from \$2 to \$4 per
ticket increases total
expenditure on tickets
Price (\$/ticket)
12
10
8
6
New area gained > old area lost
4
2
0
D
1 2 3
4
5 6
Quantity (100s of tickets/day)
Common area
LO3: Derive a Demand
Curve
Ch4 -19
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14
14
12
12
10
8
6
4
2
0
10
8
6
4
2
1
2
3
4
5
6
0
Quantity (100s of tickets/day)
(a)
Increase in total
expenditure
Losses in total
expenditure
Price (\$/ticket)
Price (\$/ticket)
FIGURE 4.8 The Demand Curve for Movie Tickets
1
2
3
4
5
6
Quantity (100s of tickets/day)
(b)
An Increase in price from \$8 to \$10 per ticket results in a fall in total
expenditure on tickets.
Ch4 -20
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Own Price Elasticity of Demand
Definition: The percentage change in the quantity of a good
demanded resulting from a one-percent change in its own
price.
• Elastic Demand
– price elasticity is greater than one.
– Price increases/decreases, quantity demanded falls/rises
• Inelastic Demand
– price elasticity is less than one.
– Price increases/decreases, quantity demanded rises/falls
• Unitary elastic demand
– price elasticity equals one
– A transition point on every demand
LO5: Interpret Elasticities
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Price Elasticity and Expenditures
• Price elastic products: Quantity demanded is highly
responsive to price changes.
• Price inelastic: Quantity demanded is not
responsive to price changes.
ε>1
P ↑ R↓
P↓ R↑
ε=1
P ↑ R→
P ↓ R→
ε<1
P ↑ R↑
P ↓ R↓
• Inelastic demand: Apple iPhone 5
• Elastic demand: Fast Food
LO5: Interpret Elasticities
Ch4 -22
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Will a higher tax on cigarettes curb
teenage smoking?
•
•
•
•
Peer influence is the most important determinants of teen
smoking.
Most teenagers have small disposable incomes, cigarettes are
usually large share of a teenage smoker’s budget.
The price elasticity of demand for teens is likely to be fairly high
Therefore: A higher tax should make smoking less affordable for
some teenagers.
How does this apply to hard drugs? Are these price elastic or inelastic?
What does a company do to reduce the elasticity of demand for its
products?
What does government do to increase the price elasticity of demand for
cigarettes?
View notes page
Some Representative Elasticity
Estimates
Good or service
Price elasticity
Green peas
2.80
Restaurant meals
1.63
Automobiles
1.35
Electricity
1.20
Beer
1.19
Movies
0.87
Air travel (foreign)
0.77
Shoes
0.70
Coffee
0.25
Theatre, opera
0.18
LO5: Interpret Elasticities
Ch4 -24
Why are green peas
elastic?
Why are theatre
tickets so inelastic?
Ryerson Limited
Price elasticity of demand is defined as:
– the percentage change in the quantity of a good
demanded resulting from a one-percent change in
its price.
• Price elasticity = % change in quantity demanded / %
change in price.
• ε = (ΔQ/Q)/(ΔP/P).
– Since the slope of the demand curve is ΔP/ΔQ,
another way to express it is:
• ε = (P/Q)(1/slope).
LO6: Calculate Elasticities
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Graphical Interpretation of Price Elasticity of Demand
LO6: Calculate Elasticities
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Calculating Price Elasticity of Demand





ε = (P/Q)(1/slope)
Slope is the ratio of its
vertical intercept to its
horizontal intercept.
Slope = 20/5 = 4
εA = (8/3)(1/4) = 2/3
εB = (12/2)(1/4) = 3/2
The elasticity of demand varies along the demand curve
It is lowest (less elastic or more inelastic) at higher than lower prices
Slope (“steepness” of the demand) is only part of the story.
LO6: Calculate Elasticities
Ch4 -27
Elasticity and Total
Expenditure
• The slope of a straight line
demand curve is constant.
• The price-quantity ratio declines
as we move down the demand
curve.
• Price elasticity declines as we
move down the demand curve.
• As price increases, quantity
demanded increases as does total
expenditures until it reaches a
maximum when elasticity equals
one.
• Total expenditure begins to
decreases as quantity continues
to increases, until it reaches zero.
LO6: Calculate Elasticities
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Price Elasticity of Demand and Total
Expenditure
As price declines, quantity demanded increases, total expenditure
increases until it reaches a maximum of \$18, then decreases until
price is zero.
LO6: Calculate Elasticities
Ch4 -29
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The Relationship between Slope and
Elasticity
• When Price and quantity are the same, price
elasticity of demand is always less for the
steeper of the two demand curves.
At point A, P/Q is the same for both
curved; but D2 is steeper, D2 is less
elastic than D1 at point A
LO6: Calculate Elasticities
Ch4 -31
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Three Special Cases
• Perfectly Elastic demand
– Price elasticity of demand is infinite.
– Even the slightest change in price leads consumers to find
substitutes. (All fast food is equally disgusting)
• Perfectly Inelastic demand
– Price elasticity of demand is zero.
– Consumers do not switch to substitutes even when price
increases dramatically (Often substitutes do not exist).
• Unit Elastic demand
– Regardless of the price selected, total expenditure is
unchanged.
LO5: Interpret Elasticities
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Perfectly Elastic, Perfectly Inelastic, and Unit Elastic
Demand Curves
QD = 1/PD
LO5: Interpret Elasticities
Ch4 -33
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Income Elasticity of Demand
The percentage amount by which the quantity demanded
changes in response to a one-percent change in income.
Incomeelast icit y
percent agechangein quant it ydemanded  Q   I 
 /
 

percent agechangein income
Q
I


 
– Normal good: a good with a positive income elasticity
of demand.
– Inferior good: a good with negative income elasticity
of demand.
– Luxury good: a good with an income elasticity of
demand greater than one; a subset of normal good.
Ch4
-34
LO6: Calculate
Elasticities
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The strange story of the Giffen good
• Giffen good: people consume more as the price rises, apparently
violating the law of demand.
• In most cases, substitution dominates demand – price rises lead to
reductions in quantity demanded
• For a Giffen good, income effects dominate – price rises reduce
effective income, and in certain cases where the good is a necessity
(staple foods for low income families)
• Example: If the price of Kraft dinner rises, a low income family
experiences a loss of effective income, and to maintain calories,
cuts back on the consumption more expensive goods.
As Mr. Giffen has pointed out, a rise in the price of bread makes so large a drain on the resources
of the poorer labouring families and raises so much the marginal utility of money to them, that
they are forced to curtail their consumption of meat and the more expensive farinaceous foods:
and, bread being still the cheapest food which they can get and will take, they consume more, and
not less of it. Source: A. Marshall, Principles of Economics, 3rd ed.
All Giffen goods are inferior goods but not all inferior goods are Giffen goods.
Why not?
Experience, credence, post-experience
and Veblen goods
• Experience good: A good whose value can only
be determined on consumption (Example:
restaurant meal)
• Search Good: A good whose value can be
determined in advance of consumption (Example:
computer)
• Credence goods: Goods that are hard to assess
even on consumption (repairs, medical
treatment, vitamin supplements…)
• Veblen goods: Goods consumed as status
symbols (a form of luxury good).
Cross Price Elasticity of Demand
– The percentage amount by which the quantity
demanded of one good changes in response to a
one-percent change in the price of another good
Cross - price elast icit y
percent agechangein quant it ygood X
percent agechangein price of good Y
 Q x
 
 Qx
  PY
 / 
  PY



– Substitutes: two goods whose cross-price
elasticity is positive
– Complements : two goods whose cross-price
elasticity is negative
LO6: Calculate
Elasticities
Ch4
-37
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Chapter Summary
•
Price increase will
–
–
•
•
•
Price elasticity varies with price and along the demand curve
Price change is the main independent variable
Price changes have two main effects
–
–
•
•
•
Conmsumers increase spending on a good as long as marginal utility is higher than price
Spending is allocated among goods to equate the ratios of respective marginal utilities to prices
Total expenditure on a good reaches a maximum when price elasticity of demand is
equal to one.
The price elasticity of demand at a point
–
•
Income effect (price increases/decreases lead of decreases/increases in effective income)
Substitution effects (price increases/decreases force the consumer to manage a fixed income by
decreases/increases) in consumption
Benefit/cost principle of consumer demand
–
–
•
increase total expenditure if demand is inelastic
but reduce it if demand is elastic.
ε = (ΔQ/Q)/(ΔP/P) or ε = (P/Q)(1/slope).
Income elasticity of demand is the percentage change in quantity demanded of good
that arises from a 1 percent change in income.
Cross-price elasticity of demand is the percentage change in quantity demanded of a
good that arises from a 1 percent change in the price of a different good.
Chapter Summary
Ch4 -38