Demand Analysis
Chapter 4
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part of Cengage Learning
Chapter 4
OVERVIEW
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Utility Theory
Indifference Curves
Budget Constraints
Individual Demand
Optimal Consumption
Demand Sensitivity Analysis: Elasticity
Price Elasticity of Demand
Price Elasticity and Marginal Revenue
Price Elasticity and Optimal Pricing Policy
Cross-price Elasticity of Demand
Income Elasticity of Demand
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Chapter 4
KEY CONCEPTS
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utility
nonsatiation principle
indifference
ordinal utility
cardinal utility
utility function
utils
market baskets
marginal utility
law of diminishing marginal
utility
indifference curves
substitutes
complements
perfect substitutes
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perfect complements
budget constraint
income effect
substitution effect
price-consumption curve
income-consumption curve
Engle curve
normal goods
inferior goods
optimal market basket
revealed preference
marginal rate of substitution
consumption path
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Utility Theory
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Assumptions About Consumer Preferences
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More is better.
Consumers rank-order desirability of products.
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Utility functions relate well-being to consumption.
 Marginal utility shows added benefit of a small
increase in consumption.
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Marginal utility is usually positive, MU>0.
Law of Diminishing Marginal Utility
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Marginal utility eventually declines for everything.
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Chapter 4: Demand Analysis
Where does the demand curve come from? The demand curve is based on
economics preferences for goods and services that bring them the most utility
per dollar.
U = f(Goods, Services)
Utility is a function of the goods and services consumed.
The more goods and services the higher the utility.
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Indifference Curves
A simple numerical example of indifference curves.
Marginal utility is the change in utility when goods or services change.
MU = ∆TU / ∆Q
Consumer base their purchasing decision on the marginal utility they receive per dollar spent. MU /
PRICE
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Mathematical proof of why the slope of the indifference curve is equal
to the marginal rate of substitution (MRS).
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Indifference Curves
 Basic
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Characteristics
Higher indifference curves are better.
Indifference curves do not intersect.
Indifference curves slope downward.
Indifference curves are concave to origin.
 Perfect
substitutes are products that
satisfy the same need, e.g., car models.
 Perfect complements are products
consumed together,
e.g.,
cars
and
tires.
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Budget Constraints
 Basic
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Characteristics
Show affordable combinations of X and Y.
Slope of –PX/PY reflects relative prices.
 Effects
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Budget increase (decrease) causes parallel
outward (inward) shift.
Relative price change alters budget slope.
 Income
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of Changing Income and Prices
and Substitution Effects
Income effect changes overall consumption.
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Learning
Substitution effect
alters
relative consumption.
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Optimal Consumption
 Marginal
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MRSXY = -MUX/MUY and equals indifference
curve slope.
MRSXY shows tradeoff between X and Y
consumption, holding utility constant.
MRSXY diminishes as substitution of X for Y
increases.
 Utility
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Rate of Substitution (MRS)
maximization requires
PX/PY = MUX/MUY, or
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/P
.
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Individual Demand
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Price-consumption curve shows consumption
impact of price changes.
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Income-consumption curve shows consumption
impact of income changes.
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Reflects movement along demand curve.
Reflects shift from one demand curve to another.
Engle curves plot income and consumption.
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Normal good consumption rises with income.
Inferior good consumption falls with income (rare).
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The Relationship between income and goods and
services consumed.
Consumption Path
When income increases, do you buy more of both goods?
What does this mean?
As I  demand for good X . X is an inferior good.
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Demand Sensitivity Analysis:
Elasticity
 Elasticity
measures sensitivity.
 Point elasticity shows sensitivity of Y
to small changes in X.
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εX = ∂Y/Y ÷ ∂X/X.
 Arc
elasticity shows sensitivity of Y to
big changes in X.
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EX = (Y2–Y1)/(Y2+Y1) ÷ (X2-X1)/(X2+X1).
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Price Elasticity of Demand
 Price
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Point price elasticity, εP = ∂Q/Q ÷ ∂P/P.
In all cases, εP < 0 .
 Price
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Elasticity Formula
Elasticity and Total Revenue
Price cut increases revenue if │εP│> 1.
Revenue constant if │εP│= 1.
Price cut decreases revenue if │εP│< 1.
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What makes demand more elastic?
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Products with close substitutes have elastic demand.
Demand for an individual brand is more elastic than
industry aggregate demand.
Products with many complements have less elastic
demand.
In the long run, demand curves become more elastic.
As price increases, demand becomes more elastic
The larger the percentage of income required to
purchase a good, the more elastic it’s demand.
Luxury goods tend to be more elastic
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Price Elasticity and Marginal
Revenue
 Elasticity
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As price rises, so too does │εP│.
As price falls, so too does│εP│.
 Price
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Varies along Demand Curve
Elasticity and Price Changes
MR > 0 if │εP│> 1.
MR = 0 if │εP│= 1.
MR < 0 if │εP│< 1.
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Price Elasticity and Optimal
Pricing Policy
 Optimal
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Price Formula
MR and εP are directly related.
MR = P/[1+(1/ εP)].
Optimal P* = MC/[1+(1/ εP)].
 Determinants
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of Price Elasticity
Essential goods have low│εP│.
Nonessential goods have high│εP│.
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Relationship Between Elasticity and Total Revenue
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Elasticity- numeric example
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Point Price Elasticity
-3000 x 2 =
3150
-6000
3150
= -6.19
= ep
Y = 5,000 – 3,000(2) + 200(2) + 75(10) + 60(50)
Y = 5,000 – 6,000 + 400 + 750 + 3000 = 3,150
y = 9150 – 3000PY
y = 9150 – 3,000
y = 6150
if PY = 1
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Solving for price elasticity
ePY = -3000 x
Interpreting
e < -1
-1 < e < 0
e = -1
1 = -3000 = -.488
6150 6150
elastic
inelastic
unit elastic
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Cross-price Elasticity of Demand
 Cross-price
elasticity shows demand
sensitivity to changes in other prices.
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εPX = ∂QY/QY ÷ ∂PX/PX.
 Substitutes
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have εPX > 0.
E.g., Coke demand and Pepsi prices.
 Complements
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E.g., Coke demand and Fritos prices.
 Independent
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have εPX < 0.
goods have εPX = 0.
E.g., Coke demand and car prices.
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Cross Price Elasticity
Cross Price Elasticity
If PX changes, what happens to the demand for Y?
Substitutes
coke, pepsi
Pc 
Complements
peanut butter, jelly
PPB 
dQy x PX = eYPx
dPx
QY
Y = 5000 – 3000PY + 200PX + 75I + 60A
PY = 2 PX = 2 I = 10 A = 50
eYPX = 200 x 2 = 400 = .127
3150 3150
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Dc 
DPB 
Bp  +
DJ  -
Income Elasticity of Demand
 Income
elasticity shows demand
sensitivity to changes in income.
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εI = ∂Q/Q ÷ ∂I/I.
 Normal
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Noncyclical normal goods have 0 < εI < 1,
e.g., candy.
Cyclical normal goods have εI > 1, e.g.,
housing.
 Inferior
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goods have εI > 0.
goods have εI < 0.
Very rare.
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Income Elasticity of Demand
If I change what happens to the demand for Y?
Normal/Luxury = As I  Y 
Inferior Goods = As I  Y 
EI = (dY/dI) x (I/Y) EI = 75 x (10/3150) = (750/3150) = .24
EI > 0
normal
EI > 0
luxury
0 < e < 0necessity
EI < 0
normal
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