ECON 563 Market Equilibrium, Demand and Supply Analysis

.. ECON 563Managerial Economics
Module 2: Market Equilibrium,
Demand and Supply Model
Copyright 2017 Montclair State University
Module 2a: Brief Overview
Learning Objectives
(1) Explain the laws of demand and supply, and identify fac-
tors that cause shift in demand and supply.
(2) Define and calculate consumer surplus and producer
surplus.
(3) Explain price determination in a competitivemarket, and
show how equilibrium changes in response to changes
in determinants of demand and supply.
Learning Objectives
(4) Explain and illustrate how excise taxes, ad valorem taxes,

price floors, and price ceilings impact the functioning of
a market.
(5) Apply supply and demand analysis as a qualitative fore-
casting tool to see the big picture in competitive mar-
kets.
Module 2b: Demand
Demand
Market demand curve
• Describes the relationship between the total quantity
and price per unit of a good all consumers are willing
and able to purchase, holding other variables constant.
Law of demand
• The quantity of a good consumers are willing and able to
purchase increases (decreases) as the price falls (rises).
• Price and quantity demanded are inversely related.
Price
$/lb
$6
$4

$2
Quantity (lbs)742
D
0
Market demand curve
Movement Along Demand Curve
Change in quantity demanded
• Changing only price leads to changes in quantity de-
manded.
• Graphically represented by a movement along a given
demand curve, holding other factors that impact demand
constant.
Shift in Demand Curve
Shift in demand
• Changing factors other than price lead to changes in
demand.
• Graphically represented by a shift of the entire demand
curve.

Price
Quantity
Shift to the right
Shift to the left
Changes in Demand
Demand Shifters
Income
• Normal good
• Inferior good
Prices of related goods
• Substitute goods
• Complement goods
Advertising and consumer tastes
• Informative advertising
• Persuasive advertising
Population, Consumer expectations, Other factors
Price
Quantity
D

D′
0
Figure : Advertising and Increase in Market Demand Curve
Module 2c: Demand Function
The Demand Function
The demand function for good X (say, apples) is a mathe-
matical representation describing how many units (pounds,
lbs) will be purchased at different prices for X ($ per lb), the
price of a related good Y (say, orange), income and other
factors that affect the demand for good X.
The Linear Demand Function
One simple, but useful, representation of a demand function
is the linear demand function.
QdX = α0 + αXPX + αY PY + αMM + αHH
where
QdX is the number of units of good X demanded ;
PX is the price of good X ;
PY is the price of a related good Y ;
M is income ; and
H is the value of any other variable affecting demand.

Understanding the Linear Demand Function
The signs and magnitude of the α coefficients determine
the impact of each variable on the number of units of X
demanded
QdX = α0 + αXPX + αY PY + αMM + αHH.
For example
αX < 0 by the law of demand ;
αY > 0 if good Y is a substitute for good X ;
αM < 0 if good X is an inferior good.
Example
Suppose demand function for a firm's product X is :
QdX = 12000− 3PX + 4PY −M + 2AX .
Question
How many of good X will consumers purchase when
PX = $200 per unit, PY = $15 per unit, M = $10, 000 and
AX = 2, 000? Are goods X and Y substitutes or
complements ? Is good X a normal or an inferior good ?
Answer
QdX = 12000− 3(200) + 4(15)− 10000 + 2(2000)

QdX = 12000− 600 + 60− 10000 + 4000 = 5460.
X and Y are substitutes. X is an inferior good.
Inverse Demand Function
In the example, if we set PY = $15 per unit, M = $10, 000
and AX = 2, 000, the demand function is
QdX = 12000− 3PX +4(15)− 10000+ 2(2000) = 6060− 3PX .
We can solve for PX in terms of QdX to obtain
PX =
6060
3
− Q
d
X
3
= 2020− Q
d
X
3
.
It is called inverse demand function and is used to construct
market demand curve.

Price
$2020
Quantity6060
PX = 2020− Q
d
X
3
0
Graphing Inverse Demand Function
Module 2d: Supply
Supply
Market supply curve
• A curve indicating the total quantity of a good that all
producers in a competitivemarket would produce at each
price, holding input prices, technology, and other va-
riables affecting supply constant.
Law of supply
• As the price of a good rises (falls), the quantity supplied
of the good rises (falls), holding other factors affecting

supply constant.
Movement Along Supply Curve
Change in quantity supplied
• Changing only price leads to changes in quantity sup-
plied.
• Graphically represented by a movement along a given
supply curve, holding other factors that impact supply
constant.
Shift in Supply Curve
Shift in supply
• Changing factors other than price lead to changes in
supply.
• Graphically represented by a shift of the entire supply
curve.
Price
Quantity
Increase in supply
Decrease in supply
Changes in Supply

Supply Shifters
• Input prices
• Technology or government regulation
• Number of firms
• Entry
• Exit
• Substitutes in production
• Taxes
• Excise tax : a tax on each unit of output sold, where tax reve-
nue is collected from the supplier
• Ad valorem tax : percentage tax
• Producer expectations
Price
1.10
1.00
Quantity
t = $0.1
Excise tax = $0.10 per unit
A per unit (Excise) Tax

Price
1.10
1.00
Quantity
Ad Valorem tax = 10%
An Ad Valorem Tax
Module 2e: Supply Function
The Supply Function
The supply function for goodX is a mathematical represen-
tation describing how many units will be produced at alter-
native prices for X, alternative input pricesW , and alterna-
tive values of other variables that affect the supply for good
X.
The Linear Supply Function
A simple representation of a supply function is the linear
supply function.

QsX = β0 + βXPX + βWW + βrPr + βHH
where
QsX is the number of units of good X supplied ;
PX is the price of good X ;
W is the price of an input ;
Pr is price of technologically related goods ; and
H is the value of any other variable affecting supply.
Understanding the Linear Supply Function
The signs and magnitude of the β coefficients determine
the impact of each variable on the number of units of X
supplied
QsX = β0 + βXPX + βWW + βrPr + βHH
For example
βX > 0 by the law of supply ;
βW < 0 increasing input prices ;
βr > 0 technology lowers the cost of producing good X.
Example
Suppose supply function for a firm's product X is :
QsX = 2000 + 3PX − 4Pr − PW .
Question
How many units of good X will be produced when

PX = $400 per unit, Pr = $100 per unit and PW = 2, 050?
Answer
QsX = 2000 + 3(400)− 4(100)− 1(2050)
QsX = 2000 + 1200− 400− 2050 = 750.
Inverse Supply Function
In the example, if we set PW = $2050 per unit and Pr = 100,
the supply function is
QsX = 2000 + 3PX − 4(100)− 1(2050) = 3PX − 450.
We can solve for PX in terms of QsX to obtain
PX =
450
3
+
QdX
3
= 150 +
QdX
3
.
It is called inverse supply function and is used to construct
market supply curve.

Price
Quantity
150
PX = 150 +
QsX
3
0
Graphing Inverse Supply Function
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ECON 563
Managerial Economics
Module 2f: Consumer and Producer
Surplus
Consumer Surplus
Marketing strategies - like value pricing and price discrimi-
nation - rely on the concept of consumer value for the pro-
ducts.
• Total consumer value is the sumof themaximumamount
a consumer is willing to pay at different quantities.
• Total expenditure is the per-unit market price times the

number of units consumed.
• Consumer surplus is the extra value that consumers
derive from a good but do not pay extra for.
Priceper litre
$8
$4
8 Quantity in litres40
Market Demand and Consumer Surplus
Consumer Surplus
Total Consumer Value =
1
2
(8 + 4) · 4 = 24,
Total Expenditure = 4 · 4 = 16,
Consumer Surplus =
1
2
(4 · 4) = 8.

Producer Surplus
The amount producers receive in excess of the amount ne-
cessary to induce them to produce the good.
Price
Quantity900
150
450
0
Producer Surplus
Producer Surplus
Producer Surplus =
1
2
(450− 150) · (900) = 135000.
Module 2g: Market Equilibrium

Market Equilibrium
Competitive Market Equilibrium
• Determined by the intersection of the market demand
and market supply curves.
• A price and quantity such that there is no shortage or
surplus in the market.
• Forces that drivemarket demand andmarket supply are
balanced, and there is no pressure on prices or quanti-
ties to change.
• The equilibrium price is the price that equates quantity
demanded with quantity supplied.
Price
QuantityQ∗
15
P ∗
60
0
Market Equilibrium
Example
Consider a market with demand and supply functions for

good X given as :
QdX = 100− PX , QsX = 20 + PX .
A competitive market equilibrium exists at a price P ∗ such
that
QdX(P
∗ ) = QsX(P
∗ ), or .100− PX = 20 + PX ,
2PX = 80, or PX = 40, , and QX = 100− 40 = 60.
Equilibrium is PX = 40 and QX = 60.
Module 2h: Market Interventions
Price Restrictions and Market Equilibrium
• In a competitive market equilibrium, price and quantity
freely adjust to the forces of demand and supply.
• Sometime government restricts how much prices are
permitted to rise or fall,
• Price ceiling,
• Price floor.

Price
QuantityQ∗
20
P ∗
P c
100
0 Price ceiling
A Price Ceiling
Price Ceiling in Action
Consider the market with demand and supply functions for
good X given as :
QdX = 100− PX , QsX = 20 + PX .
Suppose a price ceiling of $30 is imposed in this market.
QdX = 100−30 = 70, QsX = 20+30 = 50, shortage = 70−50 = 20.
Full economic price of the 50th unit is PX = 100 − 50 = 50
where $30 is the dollar price and $30 is the non-pecuniary
price.
Price

QuantityQ∗
15
P ∗
60
0
Price Floor
Price Floor in Action
Consider the market with demand and supply functions for
good X given as :
QdX = 100 − PX , QsX = 20 + PX . Suppose
a price floor of $50 is imposed in this market.
QdX = 100−50 = 50, QsX = 20+50 = 70, surplus = 70−50 = 20.
Module 2i: Comparative Statics
Comparative Static Analysis
• The study of the movement from one equilibrium to ano-
ther.

• Competitivemarket equilibrium outcome, operating free
of price restraints, could change when
• Demand changes
• Supply changes
• Demand and supply simultaneously change.
Change in Demand
• Increase in demand only
• Increase equilibrium price
• Increase equilibrium quantity
• Decrease in demand only
• Decrease equilibrium price
• Decrease equilibrium quantity
Example of Change in Demand
• Suppose that consumer incomes are projected to in-
crease 2.5% and
• the number of individuals over 25 years of age will reach
an all time high by the end of next year.
• What is the impact on the rental car market ?
Price

Quantity0
Effect of change in demand
Both price and quantity increase
Change in Supply
• Increase in supply only
• Decrease equilibrium price
• Increase equilibrium quantity
• Decrease in supply only
• Increase equilibrium price
• Decrease equilibrium quantity
Example of Change in Supply
• Suppose that a bill before Congress would require all
employers to provide health care to their workers.
• What is the impact on retail markets ?
Price
Quantity0
Effect of increase in supply
Price goes down and quantity goes up

Module 4: Production and
Cost Theory
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Learning Objectives
(1) Explain ways of measuring the productivity of inputs and
the role of the manager in the production process.
(2) Calculate input demand and the cost-minimizing com-
bination of inputs and use isoquant analysis to illustrate
optimal input substitution.
(3) Calculate a cost function from a production function.
Learning Objectives
(4) Explain how economic costs differ from accounting costs.

(5) Explain the difference between and the economic re-
levance of fixed costs, sunk costs, variable costs, and
marginal costs.
(6) Calculate average and marginal costs from algebraic or
tabular cost data and illustrate the relationship between
average and marginal costs.
Learning Objectives
(7) Distinguish between short-run and long-run production
decisions and illustrate their impact on costs and eco-
nomies of scale.
(8) Conclude whether a multiple-output production process
exhibits economies of scope or cost complementarities
and explain their significance for managerial decisions.
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Module 4b: Production Technology
Production Function
Mathematical function that defines the maximum amount of
output that can be produced with a given set of inputs.
Q = F (K,L),

• Q is the level of the output,
• K is the level of the capital input,
• L is the level of the labor input.
Short-run and Long-run Decisions
Short-run
• Period of timewhere some factors of production (inputs)
are fixed, and constrain a manager's decisions.
Long-run
• Period of time over which all factors of production (in-
puts) are variable, and can be adjusted by a manager.
Productivity Measures
Total product (TP)
• Maximum level of output that can be produced with a
given amount of inputs.
Average product (AP)
• A measure of the output produced per unit of input.
• Average product of labor : APL = QL
• Average product of capital : APK = QK
Example
Consider the following production function when 5 units of
labor and 10 units of capital are combined to produce :

Q = F (10, 5) = 150.
• Average product of labor : APL = 1505 = 30 units per
worker
• Average product of capital : APK = 15010 = 15 units per
unit of capital.
Marginal Product (MP)
The change in total product (output) attributable to the last
unit of an input.
• Marginal product of labor : MPL = ∆Q∆L
• Marginal product of capital : MPK = ∆Q∆K .
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Module 4c: Decision at Margin
Manager's Role in the Production Process
• Produce output on the production function.
• Aligning incentives to induce maximum worker effort.
• Use the right mix of inputs to maximize profits.
Decisions at the Margin

To maximize profits when labor or capital vary in the short
run, the manager will hire
• labor until the value of the marginal product of labor
equals the wage rate (w) : VMPL = w where VMPL =
P ×MPL.
• capital until the value of the marginal product of capital
equals the rental rate (r) : VMPK = r where VMPK =
P ×MPK .
Decisions at the Margin
• Value marginal product : The value of the output produ-
ced by the last unit of an input.
• Law of diminishing returns : The marginal product of an
additional unit of input will at some point be lower than
the marginal product of the previous unit.
Profit-Maximizing Input Usage
• To maximize profits, use input levels at which marginal
benefit equals marginal cost
• When the cost of each additional unit of labor is w, the
manager should continue to employ labor up to the point
where VMPL = w in the range of diminishing marginal
product.
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Module 4d: Production Functions
Common Production Function Forms
• Linear : Assumes a perfect linear relationship between
all inputs and total output
Q = F (K,L) = aK + bL,
where a and b are positive constants.
• Leontief : Assumes that inputs are used in fixed propor-
tions
Q = F (K,L) = min{aK, bL},
where a and b are positive constants.
Cobb-Douglas Production Technology
• It assumes some degree of substitutability among in-
puts
Q = F (K,L) = KaLb,
• where a and b are positive constants.
Linear Production Technology
• Suppose that a firm’s estimated production function is
Q = F (K,L) = 3K + 5L.

• How much output is produced when 5 units of capital
and 10 units of labor are employed ?
Q = F (5, 10) = 3× 5 + 5× 10 = 15 + 50 = 65.
MP and AP
• Linear production
MPK = a,MPL = b, APK =
aK + bL
K
,APL =
aK + bL
L
.
• Cobb-Douglas
MPK = aK
a−1Lb,MPL = bK
aLb−1,
APK = K
a−1Lb, APL = K
aLb−1.

Cobb- Douglas Technology
• Let K = 1 be a fixed input and Q = K0.25L0.75.
• What is the marginal product of labor when 16 units of
labor is hired ?
MPL = 0.75(1)
0.25(16)−0.25 = 0.75× 0.5 = 0.375.
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Module 4e: Isoquant and Isocost
Isoquants and MRTS
Isoquant
• It capture the tradeoff between combinations of inputs
that yield the same output in the long run, when all in-
puts are variable.
Marginal rate of technical substitutions (MRTS)
• The rate at which a producer can substitute between
two inputs and maintain the same level of output.
• Absolute value of the slope of the isoquant.
MRTSKL =
MPL
MPK
.

K
L
Q=10
Q=30
Q=60
Q=90
Increasing Output
0
Isoquants and MRTS
K
L
∆L
∆L
0
Diminishing Marginal rate of technical substitutions
Isocost
• Combination of inputs that yield the same cost.

wL+ rK = C.
• or, re-arranging to the intercept-slope formulation :
K =
C
r
− w
r
L.
Changes in isocost
• For given input prices, isocosts farther from the origin
are associated with higher costs.
• Changes in input prices change the slopes of isocost
lines.
K
LC
w
C
r
0
K = Cr −

w
r L
Isocost
K
LC1
w
C1
r
C0
w
C0
r
0
C1
C0
Changes in the isocosts C1 > C0
K

LCw0
C
r
C
w1
0
Changes in the isocost line w1 > w0
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Module 4f: Cost Minimization
Cost Minimization
Producing at the lowest possible cost.
• Cost-minimizing input rule.
• Produce at a given level of output where the marginal
product per dollar spent is equal for all input.
MPL
w
=
MPK
r
.

• Equivalently, a firm should employ inputs such that the
marginal rate of technical substitution equals the ratio
of input prices.
MPL
MPK
=
w
r
.
K
K∗
C1
r
C0
w
LC0
w
C1
wL
∗
Q=60
0

Example : Minimum cost is C0, Inputs (K∗ , L∗ )
Optimal Input Bundle
• To minimize the cost of producing a given level of out-
put, the firm should use less of an input and more of
other inputs when that input’s price rises.
• It is easy to draw isoquant - iscocost diagram to verify
this observation.
Cost Function
Mathematical relationship that relates cost to the cost-
minimizing
input associated with an isoquant.
• Short-run costs
• Fixed costs (FC) : do not change with changes in output ; in-
clude the costs of fixed inputs used in production.
• Sunk costs.
• Variable costs, V C(Q) : costs that change with changes in
outputs ; include the costs of inputs that vary with output.
Total Cost TC(Q) = FC + V C(Q).
• Long-run costs :
• All costs are variable, and there is no fixed costs.
Average and Marginal Cost

• Average costs
• Average Fixed cost : AFC = FCQ
• Average Variable cost : AV C = V C(Q)Q
• Average Total cost : AT C = C(Q)Q
• Marginal cost (MC) :
• The (incremental) cost of producing an additional unit of out-
put.
• MC = ∆C∆Q .
C(q)
q
AFC
AVC
AC
MC
0
Relation among AFC, AV C, AC, MC
Minimum of AVC and AC
• Average variable cost attains it's minimum at the output
q where MC = AV C.
• Average cost attains it's minimum at the output q where
MC = AC.

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Module 4g: Cost Function
Fixed Cost and Sunk Cost
Fixed costs
• Cost that does not change with output.
Sunk costs
• Cost that is forever lost after it has been paid.
Irrelevance of Sunk Costs
• A decision maker should ignore sunk costs to maximize
profits or minimize losses.
Example of Cost Function
Cubic cost function
• Costs are a cubic function of output ; provides a reaso-
nable approximation to virtually any cost function.
C(Q) = F + aQ+ bQ2 + cQ3,
• where a, b, c, and F are constants and F represents the
fixed cost.
Marginal cost function : MC(Q) = a+ 2bQ+ 3cQ2.
Minimum AC

• AC attains it's minumum at output Q such that
AC =
F
Q
+ a+ bQ+ cQ2 = a+ 2bQ+ 3cQ2 = MC.
Long-run Costs
• In the long run, all costs are variable since a manager
is free to adjust levels of all inputs.
Long-run average cost curve
• A curve that defines the minimum average cost of pro-
ducing alternative levels of output allowing for optimal
selection of both fixed and variable factors of produc-
tion.
Return to Scale
Economies of scale
• Declining portion of the long-run average cost curve as
output increases.
Diseconomies of scale
• Rising portion of the long-run average cost curve as out-
put increases.
Constant returns to scale
• Portion of the long-run average cost curve that remains
constant as output increases.

Multi-product Cost Function
Economies of scope
• Exist when the total cost of producing Q1 and Q2 toge-
ther is less than the total cost of producing each of the
type of output separately.
C(Q1, 0) + C(0, Q2) > C(Q1, Q2).
Cost complementarity
• Exists when the marginal cost of producing one type of
output decreases when the output of another good is
increased.
∆MC1(Q1, Q2)
∆Q2
< 0.
Example of Multi-product Cost Function
C(Q1, Q2) = F + aQ1Q2 +Q
2
1 +Q
2
2.
• For this cost function MC1 = aQ2 + 2Q1 and MC2 =
aQ1 + 2Q2.

• When a < 0, an increase in Q2 reduces the marginal
cost of producing product 1, and cost function exhibits
cost complementarity.
• If a > 0, there are no cost complementarities.
• Economy of scope exists whenever F − aQ1Q2 > 0.
Module 3: Elasticity, and
Demand Estimation
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Learning Objectives
(1) Apply various elasticities of demand as a quantitative
tool to forecast changes in revenues, prices, and/or units
sold.
(2) Illustrate the relationship between the elasticity of de-
mand and total revenues.

(3) Discuss three factors that influencewhether the demand
for a given product is relatively elastic or inelastic.
(4) Explain the relationship between marginal revenue and
the own price elasticity of demand.
Learning Objectives
(5) Show how to determine elasticities from linear and log-
linear demand functions.
(6) Explain how regression analysis may be used to esti-
mate demand functions.
(7) How to interpret and use the output of a regression.
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Module 3b: Elasticity Concept
Elasticity
• A measure of the responsiveness of one variable to
changes in another variable.
• The percentage change in one variable that arises due
to a given percentage change in another variable.
• In case of demand, percentage change in quantity de-
manded due to a given percentage change in price.

Definition of Elasticity
• The elasticity between two variables, say P (price) and
Q (quantity) is mathematically expressed as :
εQ,P =
%∆Q
%∆P .
• Here %∆Q denotes percentage change in quantity, Q
and %∆P denotes percentage change in price, P .
Measurement of Elasticity
Two important aspects of the elasticity are
• Sign of the relationship :
• Positive,
• Negative.
• Absolute value of elasticity magnitude relative to unity :
• |εQ,P | > 1 implies Q is highly responsive to changes in P .
• |εQ,P | < 1 implies Q is slightly responsive to changes in P .
Own Price Elasticity of Demand
• Measures the responsiveness of a percentage change
in the quantity demanded of good X to a percentage
change in its price. εQdX ,PX =
%∆QdX
%∆PX .

• Sign : negative by law of demand.
• Absolute value of elasticity magnitude relative to unity :
• |εQdX ,PX | > 1 : Elastic.
• |εQdX ,PX | < 1 : Inelastic.
• |εQdX ,PX | = 1 : Unitary elastic.
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Module 3c: Linear Demand and Elasticity
Linear Demand, Elasticity, and Revenue
• Consider a linear demand :
Inverse Demand : P = 40−2Q Demand : Q = 20−0.5P.
• P = 10, Q = 15, Revenue = P ×Q = 10× 15 = 150.
Linear Demand, Elasticity, and Revenue
• There is a convenient expression for the elasticity of de-
mand for linear demand functions.
εQ,P =
1
slope of inverse demand
× P

Q
.
• εQ,P = 1−2 ×
10
15 = −0.333.
• Demand is therefore inelastic.
Linear Demand and Elasticity
• It is easy to infer that elasticity varies along a linear in-
verse demand curve.
• This is becasue the slope remains constant and the ra-
tio of P and Q changes along the demand curve.
Total Revenue and Elasticity
• When demand is elastic :
• A price increase (decrease) leads to a decrease (increase) in
total revenue.
• When demand is inelastic :
• A price decrease (increase) leads to a decrease (increase) in
total revenue.
• When demand is unitary elastic :
• Total revenue is maximized.
Two Extremes of Elasticity

• Perfectly elastic (inverse) demand curve :
• is horizontal with εQ,P = −∞.
• Perfectly inelastic (inverse) demand curve :
• is verticall with εQ,P = 0.
Price
Quantity
εQ,P = −∞
0
Perfectly elastic (inverse) demand
Price
Quantity
εQ,P = 0
0
Perfectly inelastic (inverse) demand
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Module 3d: Applications
Marginal Revenue and εQ,P
• The marginal revenue (MR) can be derived from a mar-
ket demand curve.
• It measures the additional revenue due to a change in
output.
MR = P
(
1 + εQ,P
εQ,P
)
.
• If −∞ < εQ,P < −1, MR > 0.
• If εQ,P = −1, MR = 0.
• If −1 < εQ,P , MR < 0.
Price
8
4
Quantity1890
Unit elastic demand, MR = 0.
Inelastic demand, MR < 0.

Elastic demand, MR > 0.
Linear Demand and Marginal Revenue
Cross Price Elasticity
• Measures responsiveness of a percent change in de-
mand for good X due to a percent change in the price
of good Y .
εQdX ,PY =
%∆QdX
%∆PY
.
• If εQdX ,PY > 0, then X and Y are substitutes.
• If εQdX ,PY < 0, then X and Y are complements.
Example
• Suppose it is estimated that the cross-price elasticity of
demand between clothing and food is −0.18.
• If the price of food is projected to increase by 10%, by
how much will demand for clothing change ?
−0.18 = εQdX ,PY =
%∆QdX
10
→ %∆QdX = −1.8.

• So the demand for clothing is expected to decline by
1.8% when the price of food increases by 10%.
Cross Price Elasticity
• Cross-price elasticity is important for firms selling mul-
tiple products.
• Price changes for one product impact demand for other
products.
• Assessing the overall change in revenue from a price
change for one good when a firm sells two goods is :
∆R =
[
RX
(
1 + εQdX ,PX
)
+RY εQdY ,PX
]
× %∆PX .
.. ECON 563
Module 3e: Income Elasticity

Income Elasticity
• Measures responsiveness of a percent change in de-
mand for good X due to a percent change in income.
εQdX ,M =
%∆QdX
%∆M .
• If εQdX ,M > 0, then X is a normal good.
• If εQdX ,M < 0, then X is an inferior good.
Example
• Suppose that the income elasticity of demand for trans-
portation is estimated to be 1.80.
• If income is projected to decrease by 15%, what is the
impact on the demand for transportation ?
1.8 = εQdX ,M =
%∆QdX
−15
→ %∆QdX = −27.
• Demand for transportation will decline by 27%.
• Since demand decreases as income declines, transpor-
tation is a normal good.
Elasticities for Linear Demand Functions
• Given a linear demand function :

QdX = α0 + αXPX + αY PY + αMM + αHPH
• Own price elasticity : αX · PXQdX .
• Cross price elasticity : αY · PYQdX .
• Income elasticity : αM · MQdX .
Example
Linear Demand QdX = 100− 3PX + 4PY − 0.01M + 2PH .
• where PX = $25 per unit, PY = $35, the company uti-
lizes 50 units of advertising (PH), and average consu-
mer income is $20, 000.
QdX = 100− 3(25) + 4(35)− 0.01(20000) + 2(50) = 65.
• Own price elasticity : −3 · 2565 = −1.15
• Cross price elasticity : 4 · 3565 = 2.15
• Income elasticity : −0.01 · 2000065 = −3.08
Elasticities for Non-linear Demand Functions
• Given a non-linear demand function :
lnQdX = β0 + βX lnPX + βY lnPY + βM lnM + βH lnPH
• Own price elasticity : βX .
• Cross price elasticity : βY .
• Income elasticity : βM .

Example
Demand for raincoats lnQdX = 10 − 1.25 lnPX + 3 lnR −
2 lnAY .
• whereR denotes the daily amount of rainfall andAY the
level of advertising on good Y.
• What would be the impact on demand of a 10 percent
increase in the daily amount of rainfall ?
εQdX ,R = 3 =
%∆QdX
%∆R → 3 =
%∆QdX
10
.
• A 10% increase in rainfall will lead to a 30% increase in
the demand for raincoats.
.. ECON 563
Module 3f: Demand Estimation
Regression Analysis
How do we obtain information on the demand function ?
• Published studies
• Hire consultant

• Statistical technique called regression analysis using
data on quantity, price, income and other important va-
riables.
Ordinary Least Squares Regression
• True (or population) regression model.
Y = a+ bX + e.
• a unknown population intercept parameter
• b unknown population slope parameter
• e random error term with mean zero and standard de-
viation σ.
OLS Regression
Y = a∗ + b∗ X.
• a∗ least squares estimate of the unknown parameter a
• b∗ least squares estimate of the unknown parameter b.
• The parameter estimates a∗ and b∗ represent the values
of a and b that result in the smallest sum of squared
errors between a line and the actual data.
OLS Regression on Excel
• To use the linear regression tool in Excel, the Data Ana-
lysis Toolpak must be installed.
• To verify if it is installed, click Data from the Excel main
menu.

• If you see the Data Analysis command in the Analysis
group (far right), the Data Analysis Toolpak is already
installed.
• If it is not installed, it is easy to install it from theOptions
menu.
• Once installed, the linear regression command can be
used directly.

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