Download Demand Analysis and Market Equilibrium (Chapter 3)

A Primer on
Demand Analysis
and Market Equilibrium
Chapter 3 (Hirschey)
pp 77-109
Key Concepts




Demand
Supply
Market equilibrium
Elasticity
A number of issues arise in the agribusiness
environment that center attention on
demand.
Consumer Demand or Customer
Demand
 Demand is the quantity of a good/service that
customers (consumers) are willing and able to
purchase during a specified period of time under a
given set of economic conditions.
 Derived from constrained utility (satisfaction)
maximization
Demand Curve
• The Demand Curve shows the theoretical relation between
price and quantity demanded, holding all other factors
constant.
• Axes: price is on y-axis, quantity on the x-axis
• Example: Demand curve for Lipton tea,
Q=2500 – 500P
• Key question: How are these numbers obtained?
Demand Curve for Lipton Tea
Average price
per package 5
Demand Curve
Q = 2,500 – 500P
4
P = 5 – .002Q
3
inverse demand
curve
2
1
500
1000
1500
2000
2500
packages of Lipton tea
Own-Price Effects
• Movement along a given demand curve reflects a change
in price and quantity of the commodity in question.
• Answer the following question:
•
What happens to the quantity demanded if the price
changes (exogenously) holding all other factors constant?
• Law of demand:
•
The demand curve is negatively sloped.
•
An increase (a decrease) in own price leads to a decrease (an
increase) in quantity demanded.
•
A very important empirical finding in economics.
Other Factors Affecting Demand
 Prices of other products
 Income
 Advertising (positive information)
 Food Recalls or Food Scares (negative information)
 Health and nutrition factors
 Lifestyle factors
 Tastes and preferences
Translations of the Theoretical Construct
into a Quantitative Appraisal
1. Q = a-bP
2. Q = a0 – a1P + a2I + a3A + a4PS
own-price effect
(-)
•
•
•
income effect
(+)
advertising
effect
(+)
price of substitute product
(+)
The coefficients a0, a1, a2, a3, and a4 are labeled the demand
parameters.
We expect certain signs and magnitudes of the demand
parameters according to economic theory.
Different versions of the model for applied analysis are
possible.
Demand Curve: Example
Shifts in Demand
Changes in any factors other than the product
price lead to a shift of the demand curve.
Supply
 Supply: quantity that a firm is willing and able to
provide at a given price, holding other factors constant.
 Factors affecting supply:
 Price
 Production costs
 Technology
 Government policy (e.g. price supports, taxes,
subsidies, etc…)
Supply Curve
 Supply curve shows the relation between price and the quantity
supplied, holding all other factors constant.
 Question: What happens to the quantity supplied if the product
price changes?
 No Law of Supply: supply curve can be upward/downward
sloping, vertical, horizontal.
 Change in the supply curve:
 A change in the product price leads to a movement along the supply
curve (change in quantity supplied).
 A change in any factors other than the product price leads to a shift of
the supply curve (change in supply).
Supply Curve (con’t.)
Market Equilibrium
 Supply = Demand
 Example:

Automobile:
 Supply: Qs = -42,000,000+2,000p
 Demand: Qd = 20,500,000-500p
Surplus, Shortage, and Market
Equilibrium
Elasticity
 Concept: a measure of responsiveness or sensitivity
 Elasticity analysis helps answer questions such as:
 Can Microsoft increase revenue if it increases the price of
any of its software products?
 How do oil prices change if OPEC restricts output?
 How large a tax is needed to discourage a substantial
number of people from smoking?
 If Congress passes a law forcing firms to provide health
care, how effectively can firms pass on the full amount of
these mandatory fees to consumers?
 If a proposed tax on sugar-sweetened beverages occurs,
what are the implications concerning sales for those
beverages?
Elasticity (con’t.)
 Elasticity: the percentage change in y due to a unit percentage
change in x:
 change from (x1,y1) into (x2, y2)
% change in y %y
E yx 

% change in x %x
 Point elasticity
y
y1
y2
y 2  y1
% y
y 2  y 1 x1
y1
E yx 


x1
x2
x
2

x
1
% x
x 2  x1 y 1
x1
 dy x
if y is a function of x only

y / y y x  dx y



x / x x y  y x if y is a function of x and others

 x y
x
Demand Elasticity
 Own-price elasticity
 Cross-price elasticity
 Income elasticity
 Other elasticity concepts
Own-Price Elasticity of Demand
 Own-Price Elasticity of Demand: summarizes the
sensitivity of the quantity demanded response due to
own-price changes.
 Interpretation: 1% increase (decrease) in the
product price leads to an ε% decrease (increase) in
quantity demanded.
Own Price Elasticity (Con’t.)
%Q
 Price Elasticity Formula: E P 
%P
 The product price changes from p1 to p2, and the quantity
changes from Q1 to Q2 correspondingly.
 Point Elasticity:
Q 2  Q1
%Q
Q 2  Q1 p 1
Q1
Ep 


p
2

p
1
%p
p 2  p 1 Q1
p1
 dQ p
if Q is a function of p only
Q / Q Q p  dp Q



p / p p Q  Q p if Q is a function of p and others
 p Q
Own-Price Elasticity: Examples
 Linear demand: Q = a-b*P
 Constant elasticity demand: Q = a*p-b
 Why is the own-price elasticity negative?
Types of Own-Price Elasticity
 Elastic: the % change in quantity demanded is greater
than the % change in price.
 Inelastic: the % change in quantity demanded is less than
the % change in price.
 Unitary: the % changes in quantity demanded and price
are the same.
 Special cases:
 Perfectly elastic
 Perfectly inelastic
Perfectly Inelastic Demand Curve: εp = 0
Price per unit ($)
Perfectly Elastic Demand Curve: εp = ∞
Price Elasticity of Demand Varies
Along Linear Demand Curve
Figure 4.10
Price Elasticity and Revenue Maximization
 Revenue: R = p*Q, Marginal revenue MR:
dR
dp
Q dp
Q/ p
1
 pQ
 p(1 
)  p(1 
)  p(1  )
dQ
dQ
p dQ
dQ / dp
ep
 The change in revenue if the price goes down:
MR 
Elastic demand
Inelastic demand
Unitary demand
↑
↓
No change
 Linear demand case: P = a-b*Q
 Price elasticity:
ep
1

b
p
Q
 Marginal revenue: MR = a-2*b*Q
 Total revenue is maximized where MR = 0
Own-Price Elasticity,
Marginal Revenue, and
Revenue Maximization
Own-Price Elasticity and Optimal
Pricing
 Optimal pricing (in what sense?): MR=MC
 Assumption: a firm can affect market price (under
what conditions?)
 Optimal price:

1 
MR  P1    MC
 EP 

1 
P  MC / 1  
 EP 
Cross-price Elasticity
 What-if Question: If the price of product x
changes, how much does the quantity demanded of
product y change?
 Interpretation: Measures how responsive demand
is to changes in prices of other goods, holding
everything else constant.
 Examples
Cross Price Elasticity (cont’)
 Formula:
E AB
%Q A

%PB
 Point elasticity:
E AB 
QA PB
PB QA
 dQA pB
if QA is a function of pB only (not likely)
QA / QA QA pB  dpB QA



pB / pB pB QA  QA pB if Q is a function of p and others
A
B
 pB QA
 Examples
Demand Curve for Lipton Tea
PLipton Tea
Rightward demand shift due to
a rise in the price of Nestea
D1
D0
QLipton Tea
 Suppose the price of Nestea rises, all other factors
invariant?
Demand Curve for Lipton Tea
PLipton Tea
Leftward demand shift due to a
rise in the price of hamburgers
D0
D1
QLipton Tea
 Suppose the price of hamburgers rises, all other factors
invariant?
Cross-Price Elasticity (Con’t.)
 Substitutes vs Complements
 Two goods are Substitutes if a price increase
(decrease) in one good leads to an increase (decrease)
in quantity demanded of the other good. Examples:
butter and margarine; cotton and polyester; beef, pork,
and chicken.
 Two goods are Complements if a price increase
(decrease) in one good leads to a decrease (increase)
in quantity demanded of the other good. Examples:
chips and salsa; computers and software; shoes and
socks.
Income Elasticity
 Income Elasticity:
%Q
EI 
%I
a measure of
responsiveness of the quantity demanded to
income.
 Point elasticity:
EI 
Q I
I Q
 dQ I
if Q is a function of I only
Q / Q Q I 
 dI Q



I / I
I Q  Q I if Q is a function of I and others

 I Q
PLipton Tea
Rightward shift in the demand
curve for Lipton Tea due to a rise
in income
D1
D0
QLipton Tea
 Suppose the income of consumers rises, all other factors
invariant?
Income
IB
IA
QA
QB
QLipton Tea
 As drawn, what kind of good is Lipton Tea?
Income Elasticity (Con’t.)
 Necessary goods: products for which demand is positively
related to income; EI>0 and EI<1. (Engel curve is positively
sloped)
 Luxury goods: products for which demand is positively related
to income; EI > 1. (Engel curve is positively sloped)
 Normal goods: either necessary goods or luxury goods
 Inferior goods: products for which consumer demand declines
as income rises; EI<0. (Engel curve is negatively sloped)
Summary:
 Demand, Supply, and Market Equilibrium
 Elasticity:
 Own-price elasticity
 Cross-price elasticity (shift in the demand curve)
 Income elasticity (shift in the demand curve)
 Engel curve