# PRICE THEORY

```DEMAND(PRICE)
THEORY
1
Oyugi J. Nyanjong’
Economics Department
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DEMAND THEORY
•Def: A theory is an analytical
structure or framework designed to
explain
a
set
of
empirical
observations.
•Economic theory typically proceeds
with
an assumption of ceteris paribus
2
i.e. holding other variables constant.
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DEMAND THEORY ‘ctd
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 An economic theory can therefore be defined
as a statement or a set of related statements
about cause and effect relationships between
two or more economic variables.
 Demand Theory.; when a price of a product
rises, ceteris paribus, people tend to buy less of
it i.e. when the price rises, the quantity
demanded falls. Conversely, a fall in the price
of a good or service, ceteris paribus will
result in more of it being purchased.
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DEMAND THEORY ‘ctd
Consider
the
following hypothetical
demand schedule for
a Safaricom mobile
service user in a
typical month.
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Demand Schedule
Price (per
Quantity demanded
minute)
(calls per day)
0
30
5
25
8
7
12
3
20
1
25
0
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Demand
Schedule’ctd
The demand schedule above can be
plotted graphically to form a demand
curve
a demand curve is a graphic
representation
that
shows
the
relationship between the price of a
commodity
and
the
quantity
demanded of the same.
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Demand Curve
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Terminologies
Demand –the desire or want of a
consumer to acquire a good or service
provided he/she is willing and able to
pay for the same.
Quantity demanded – this is the
amount (or no. of units) of a good or a
service that a consumer is willing and
able to purchase in a given period
and for a given price.
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Terminologies ‘ctd
 Normal good: A good or service whose
demand increases with increase in consumer’s
income.
 Inferior good: : A good or service whose
demand decreases with increase in consumer’s
income.
 Engel’s curve: A graph that plots the
combination of points of a consumer’s income
and the quantity demanded of a good or
service.
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Engel curve for a normal
good
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Engel curve for an inferior good
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Determinants
of Dd
Own price –ve
Price of related goods.May either be:
Substitutes
Complements
Income
Accumulated wealth
Tastes &amp; Preferences
Future expectations
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Movements
along dd curve
result from a change in
quantity demanded of a good
or service.
Caused by a change in price
of a good or service resulting in
a
movement
along
the
demand curve, as illustrated.
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Movements
along dd curve ‘ctd
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Movements along dd curve ‘ctd
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An increase in price from P1
to P2 moves the level of
demand from point a. to b.
at the same time the
quantity decreases from Q1
to Q2.
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Shifts in dd curve
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When other factors other than a
good’s own price price change, a shift
in the demand curve ensues. This is
referred to as change in demand.
For a normal good, an increase in
income results in an
outward(rightward) shift of the
demand curve i.e. an increase in
demand, as shown below.
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Shifts
in dd curve: effect of increase in income
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for a Normal Good
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Shifts in dd curve
For an inferior good, an
increase in income results
in an inward(leftward) shift
of the demand curve i.e. a
decrease in demand, as
shown below.
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Shifts in dd curve: effect of
increase in income for an
Inferior Good
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Demand Functions
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 Def: Are mathematical expressions of the
relationship between a goods own price and the
quantity demanded of the same.
 Take the following form:
P=a + bQ
 Where,
 P= goods own Price
 Q=quantity demanded.
 a= y-intercept
 b= slope of dd curve.
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Demand functions’ctd
In some instances, e.g. in
calculating elasticities, the
inverse form of the dd function
is used, i.e.
Q=a + bP
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ELASTICITY
Def: Given two variables, say
x &amp; y, elasticity measures the
degree of responsiveness of x
to 1% changes in y.
 Is a ratio,
is
independent of units, thus
simplifying data analysis.
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Mathematical definition
Given two variables, x and y, their
elasticity will be as below:
 x, y
 ln x x y


.
 ln y y x
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Price elasticity of demand
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 Def:it’s the ratio of percentage change in quantity
demanded to the 1% change in price.
 Mathematically,
 ln Qd Qd
P
 

X
 ln P
P
Qd
 where,


=Price elasticity of demand
P
 Ln
Qd
= own price of a good or service
=natural logarithm
= quantity demanded
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Types of elasticities: Perfect inelasticity
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When the quantity demanded
of a good a service doesn’t
respond at all to a change in
price, the percentage change in
quantity demanded is zero.
This implies that its elasticity is
zero and this Is said to be
perfectly inelastic.
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Types of elasticities: Perfect
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inelasticity
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Types of elasticities: Perfect
elasticity
a small increase in price causes
quantity demanded to drop
immediately to zero.
In reality, markets exhibiting perfect
elasticity’s are rare, e.g. agricultural
goods market, where due to high
supply of the same, farmers aren’t
able to change more than the
current market price for their
produce.
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Types of elasticities: Perfect elasticity
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Types of elasticities: Unitary
Elasticity
It is a demand relationship in
which the percentage change in
quantity demanded equals the
percentage change in price in
absolute
value.
i.e.%ΔQd=%ΔP
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Types of elasticities: Point &amp; Arc Elasticity
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Arc elasticity
Def: the coefficient of price elasticity
between two points on the demand
curve.
Point elasticity
Def: the coefficient of price elasticity
of a unique point on the demand
curve.
Point elasticity more accurate.
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Arc elasticity
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Arc elasticity formula
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Point elasticity
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Interpreting elasticities
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Determinants of Elasticity
Availability of Close
Substitutes
Necessary vs Luxury
goods
Duration/ Time Horizon
Proportion of purchase
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Calculating elasticity
 Recall: Given
y  f ( x)  x
dy
n 1
 nx
dx
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Calculating elasticity
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Given the following demand function:
Q  50  5.5 P
Calculate the price elasticity of
demand at, P  20 and Q  50
Solution
Recall:
=5.5*(20/50)=2.2
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Interpretation: the good’s dd is elastic.
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Calculating elasticity
Calculate elasticity at P=30,
Q=165
Solution
=5.5*(30/165)=1.0
Interpretation: the good’s dd is
unitary elastic.
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Calculating Elasticity
 At P=30, Q=200
Solution
=5.5*(30/200)=0.825
Interpretation: the good’s dd is
inelastic.
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Cross-price elasticity of demand(cpe)
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measures
the
responsiveness
of
quantity demanded of one good
(good x) due to a 1% change in price
of another related good (good y).i.e.
 ξ y,x =
%∆in Qd of y / % ∆ in price of x
Substitute goods have +ve cpe.
Complement goods have –ve cpe.
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Computation of cpe
Is computed using the following formulae:


 Q x Py

.
 P y Qx
x, y
y,x
 Qy
x
x
y
P

.
P Q
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Calculating cpe
The following two demand
functions represent the demand
for two related goods, x and y, at
Njokerio market.
Qx = 1,000 -2.5Px +3.2Py
Qy = 750 +5.8Px – 4.5Py
Calculate cpe of good X at Py =
20 and Qx = 35
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Calculating cpe
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
x, y
but


 Qx
 Py
 Qx
 Py

x, y
 1.829
Oyugi J. Nyanjong'
P
.
Q
y
x
 3 .2
20
 3 .2 (
)
35
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Worked example
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 The demand functions of two related goods, x
and y ,bought in Toi Market are as below:
Qx  1,000  4.8Px  3.2 Py
Q y  750  5.5Px  4.5Py
 Given the demand schedule below, calculate
cpe at the following points.
Px  10, Px  45
Py  28, Py  45
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Worked example continued
45
10
15
20
25
30
35
40
45
50
500
485
450
417
400
375
300
270
250
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42
35
30
28
25
22
20
18
255
312
330
347
370
379
390
395
400
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Solution 1
At
𝑃𝑥 =10

Q P
   P .Q
Q
but
 5 .5
 P
y
x
x
y
y,x
y
x


y,x
10
 5.5(
)
255
 0.216
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Solution 2
At
𝑃𝑥 =45

Q P
   P .Q
Q
but
 5 .5
 P
y
x
x
y
y,x
y
x


y,x
45
 5.5(
)
395
 0.627
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Solution 3
 Qx
y
y
x
P
   P .Q
Q
but
 3 .2
P
x, y
At 𝑃𝑦 =28
x
y


x, y
28
 3 .2 (
)
400
 0.224
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Solution 4
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 Qx
y
y
x
P
   P .Q
Q
but
 3 .2
 P
x, y
At 𝑃𝑦 =45
x
y


x, y
45
 3 .2 (
)
500
 0.288
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Interpreting cross price
elasticities
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Exceptions to the Law of Demand
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Giffen goods
Veblen goods:Goods of
ostentation(conspicuous consumption)
Expectation to price changes
Conspicuous necessities(TVs, fridges)
Emergencies:natural
calamities,depression
Ignorance
Change in fashion:
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Uses of elasticities
increase prices of g &amp; s.
whether
to
Government: In levying taxes(beer,
cigarrettes),Welfare distribution(Cnmsr,
producer, govt surplus)
Balance of payments:
Environment:
Helps explain price instabilities.
Price discrimination:
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𝜺𝝆 &amp; indirect taxation policy
 Success of indirect taxation policy
depends on whether 𝜺𝝆 is elastic or
inelastic.
More successful if good has
inelastic dd(Why)
 Also depends on taxation policy
objective
Change
consumption
behaviour?
Change production behaviour?
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𝜺𝝆 &amp; indirect taxation policy
continued
Suppose the policy is targeted at
reduction in consumption of a certain
good or service(say cigarettes), whose 𝜺𝝆
is inelastic.
Policy likely to fail, since ↑ taxes= ↑ P,
but Qd will fall less than proportionately
to consumer expenditure.
→A rise in total expenditure, →policy
objective defeated
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𝜺𝝆 &amp; indirect taxation policy:
Example of inelastic good
1.
Suppose a litre of petrol costs KSh 100, as a result 10 litres are
demanded
2.
Suppose the govt. introduces an indirect tax of KSh 50.
3.
Suppose that, as a result, Qd falls from 10l to 8l
1.
Total exp. B4 tax=𝟏𝟎𝟎 ∗ 𝟏𝟎𝒍 = 𝑲𝑺𝒉 𝟏, 𝟎𝟎𝟎
2.
Total exp after tax=𝟏𝟓𝟎 ∗ 𝟖𝒍 = 𝑲𝑺𝒉 𝟏, 𝟐𝟎𝟎
3.
Total ∆exp(↑)=𝟏, 𝟐𝟎𝟎 − 𝟏, 𝟎𝟎𝟎 = 𝑲𝒔𝒉 𝟐𝟎𝟎
Observations:
%∆P=50%
%∆Qd=20%
→inelastic gd
Conclusion: policy fails, since ↑ 𝑷 →↑ consumer exp.
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𝜺𝝆 &amp; indirect taxation policy:
Example of inelastic good
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𝜺𝝆 &amp; indirect taxation policy: Example of
elastic good
1. Suppose a litre of petrol costs KSh 100, as a result 10 litres
are demanded
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2. Suppose the govt. introduces an indirect tax of KSh 50.
3. Suppose that, as a result, Qd falls from 10l to 4l
1. Total exp. B4 tax=100 ∗ 10𝑙 = 𝐾𝑆ℎ 1,000
2. Total exp after tax=150 ∗ 4𝑙 = 𝐾𝑆ℎ 600
3. Total ∆exp(↓)=1,000 − 600 = 𝐾𝑠ℎ 400
Observations:
%∆P=50%
%∆Qd=60%
→elastic gd
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Conclusion: policy succeeds, since ↑ 𝑃 →↓ consumer exp.
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𝜺𝝆 &amp; indirect taxation policy: Example
of elastic good
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comparison
Inelastic good
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Elastic good
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Demand curves &amp; Price Elasticity of
Demand
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Law of Supply
Refers to the positive relationship between
price and quantity of a good or service
supplied i.e. an increase in the market price
will lead to an increase in quantity supplied,
ceteris paribus. Conversely, a decrease in the
market price will lead to a decrease in
quantity supplied .
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Supply Curve
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Determinants of Supply
Cost of production
Production costs depend mainly on two
factors:
The price and quantities of input by the firm
The available technology
Price of related products
Cow vs Hide
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MOVEMENT/SHIFT IN SUPPLY CURVES
Movement – when the
price of a good or service
changes ceteris paribus a
change
in
quantity
supplied follows i.e. a
movement along the
supply curve takes place.
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MOVEMENT
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SHIFT
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Price Elasticity of Supply
This measure the response of a quantity
of a good or service supplied to a 1%
change in price of that good.
ξ S = %∆ in Qs / %∆ in price
In output markets the elasticity of supply
is likely to be a positive number.
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Price Elasticity of Supply
‘CTD
 3 conditions for price elasticity
 s  1 : Pr ice elastic
 s  1 : Pr ice inelastic
 s  1 : Unitary
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Determinants of elasticity of supply
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Availability of spare capacity
Inventory levels
Availability of
production.
variable
factors
of
Ease with which resources can be
shifted from one industry to another
Ease of substitution
Number of firms
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Price Determination
At any moment, 3 conditions prevail
in every market:
Excess demand – Qd&gt;Qs
Excess supply – Qd&lt;Qs
Equilibrium – Qd=Qs
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Equilibrium
A mkt is in eq. when:
No need for change in strategy
by economic agents.
Economic agents’ decisions are
compatible with each other, can
take place simultaneously.
Eq.occurs at the intersection
between demand, supply curves.
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Market equilibrium
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Excess
supply(Price floors)
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Excess demand(Price
ceilings)
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Effect of quantity regulation
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CONSUMER SURPLUS
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Effects of increase in supply
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Effect of increase in
demand
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