DEMAND FUNCTIONS
&
ELASTICITIES OF DEMAND
Definition of DEMAND:
Refers to the number of units of a particular good or
service that consumers are willing to buy under stated conditions of
time, place, price, and so forth.(Ceteris Paribus)
Thus demand is a function of a number of independent
variables or demand determinants; it can be expressed as an
algebraic equation or by a graph or table.
11/24/2011 BADM4300-Demand Analysis-Prof.
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Demand Applications
• Problem #1: The Pueblo Viejo Company, a
department store, conducted a study of the
demand for men’s ties. It found out that the
average daily demand, Q, in terms of price, P, is
given by the following equation:
• Q = 60 – 5P.
a) How many ties per day can the store expect to
sell at a price of $3 per tie?
b) If the store wants to sell 20 ties per day, what
price should it charge?
c) What would be the demand if the store offered
to give the ties away?
BADM4300-Demand that anyone would be
d) What is the highest priceAnalysis-Prof.
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Demand Applications
• Problem #2: Digimill, Inc.
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Answer to Problem #1
a) Replace P by 3 in the equation:
Q = 60 – 5(3)
Q = 60 – 15
Q = 45 ties
b) Replace Q by 20 in the equation:
20 = 60 – 5P
20 – 60 = -5P
-40 = -5P
$8 = P
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Answer to Problem #1
Continuation
c) We should assume that P = 0, and substitute P by
its value in the equation:
Q = 60 –5(0)
Q = 60 –0
Q = 60 ties
d) We should assume that the highest price that
someone will be willing to pay is the price to buy
the minimum units, that is 1:
1 = 60 –5P
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1 – 60 =Analysis-Prof.
BADM4300-Demand
-5P
-59 = -5P
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Answer to Problem #1
Continuation
DEMAND TABLE
P Q TR MR
$ 12
10
8
6
4
2
0
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Use the following equation to fill on the TR column: TR = P x Q
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DEMAND TABLE
P Q TR MR
$ 12 0
10 10
8 20
6 30
4 40
2 50
0 60
Substituting P by its corresponding value in the demand
11/24/2011 BADM4300-Demand Analysis-Prof.
equation, Q = 60 - can
5P, youDevaris f ill the Q column.
DEMAND TABLE
P Q TR MR
$ 12 0 0
10 10 100
8 20 160
6 30 180
4 40 160
2 50 100
0 60 0
Multiplying column 1 and 2, you obtain the results
11/24/2011 BADM4300-Demand Analysis-Prof.
f or the 3rd. Column: TR = P x Q
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Demand Equation
Qd = 60 – 5P
• Demand Table
Demand Curve
P Q 14
$ 12 0 12
10
10 10 8
Price
8 20 6
6 30 4
2
4 40
0
2 50 20 40 60
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Quantity
0 60 Devaris
DEMAND LAW
• Inverse relationship between price (P) and
quantity demanded (Qd):
– When Price increases, quantity demanded
decreases.
• P Qd
– When price decreases, quantity demanded
increases.
• P Qd
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DEMAND LAW
Continuation
• There are 2 effects which explain the inverse
relationship between the price of a product and the
quantity demanded:
– 1. The Substitution Effect:
• When the price of a product decreases, new buyers will enter
the market. The product will be cheaper relative to other
products and the consumers will substitute them for the
product whose price has decreased,
– 2. The Income Effect:
• Consumers will by more when the price is lower.
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QUANTITY DEMANDED
VS
CHANGE IN DEMAND
• Change in Quantity Demanded( Qd):
– Movement along the demand curve from point A to
point B and is caused only by a change in the price of
the product.
• Change in Demand (D):
– A shift in the demand curve caused by a change in any
of the factors determinants of demand (Ceteris
Paribus), other than the price of the product, such as:
• Number of consumers in the market.
• Tastes and preferences of the consumers,
• Consumers’ income,
• Price of other products,
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• Price expectations. Devaris
ELASTICITIES OF DEMAND
• Price elasticity of demand
– d = %Qd / %P
• Income elasticity of demand
– d = %Qd / %TR
• Cross elasticity of demand
– dx/y = %Qdx / %Py
• Advertising elasticity
– d = %Qd / %PE
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DETERMINANTS OF
DEMAND
• The determinants of demand are variables
that affect the amount of a product
purchased.
• 1. Number of Consumers:
– More consumers in a market, greater demand,
– Less consumers in a market, less demand
• 2. Consumers’ Tastes & Preferences:
– Mode or Fad
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DETERMINANTS OF
DEMAND
Continuation
• 3. Consumers Income
– Normal Goods: goods for which demand is
positively (directly) related to income, e.g.,
steak, clothes, leisure time.
Income elasticity of demand d is positive
– Inferior Goods: goods for which demand is
negatively (inversely) related to income, e.g.,
potatoes, bread.
Income elasticity of demand d is negative
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DETERMINANTS OF
DEMAND
Continuation
• 4. Price of Closely Related Goods
– A) Substitutes. If products A and B are substitutes, a price
increase in A will generate an increase in the demand for
B.Example, when the price of beef increases, the demand for
chicken increases.
• Cross elasticity of demand dx/y is positive.
– B) Complements. If products a and B are complements, a price
increase in A will generate a decrease in the demand for
B.Example, when the price of bread increases, the demand for jelly
decreases.
• Cross elasticity of demand dx/y is negative
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• 5. Consumer Expectations Devaris
PRICE ELASTICITY OF
DEMAND
Defined as a percentage of change in the
quantity demanded that is caused by a one percent
change in price, ceteris paribus.
General Formula:
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d
DETERMINANTS
of
PRICE-ELASTICITY
• 1)Luxury Goods - more elastic and
Necessity Goods – less elastic.
• 2) Expensive Goods –more elastic and
Cheap Goods – less elastic.
• 3) More Substitutes – more elastic and
Less Substitutes – less elastic.
• 4) Time Period: the longer the time period
– more elastic.
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TYPES OF ELASTICITY
MEASUREMENTS
• Point-Elasticity Formula
– Q1 – Q0 P1 – P0 or Q/Q0
– Q0 P0 P/P0
• Arc-Elasticity Formula
Q1 – Q0 P1 – P0
– Q1 + Q0 P1 + P0
2 2
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ELASTIC VS INELASTIC
• If = , demand is perfectly elastic
• If > 1, demand is elastic
• If = 1, unitary elasticity
• If < 1, demand is inelastic
• If = 0, perfectly inelastic
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DEMAND, REVENUE &
PRICE ELASTICITY
• Elastic Demand:
– If Price increases, Total Revenue decreases
– If Price decreases, Total Revenue increases
• Unitary elasticity:
– If Price increases, Total Revenue constant
– If Price decreases, Total Revenue constant
• Inelastic Demand
– If Price increases, Total Revenue increases
– If Price decreases, Total Revenue decreases
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MARGINAL REVENUE &
PRICE ELASTICITY
• Elastic Demand:
– Marginal Revenue is positive
– As P , Qd and TR .
• Unitary elasticity:
– Marginal Revenue is equal to 0
– As TR reaches it maximum.
• Inelastic Demand
– Marginal Revenue is negative
– As P , Qd and TR .
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• Page 27 Cross-Elasticity of Demand
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Utility Theory
• Utility theory helps to explain why the
demand curve is downward sloping. A
rational individual’s objective is to
maximize Total Utility from his/her income.
This result is reached when the utility
obtained from the last dollar spent on each
commodity purchased is the same.
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Utility Maximization
• Utility maximization can be expressed
mathematically as:
– Marginal Utility of A = Marginal Utility of B
Price of A Price of B
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How to Measure Utility
• There are two ways to measure utility:
– 1) Cardinal – numerically assigned values of
utils received from any good. A “util” is any
arbitrary unit of satisfaction.
– 2) Ordinal – establish a ranking among goods,
without assigning specific units of satisfaction.
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Principle of Diminishing
Marginal Utility
• States that Equal increments of additional
consumption of a good result in
successively smaller additions of utility
(satisfaction) to the consumer. Thus, when a
person is thirsty, the first glass of water
tastes great, the second less so, the third
even less.
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Indifference Curves
• Indifference curves are all combinations of
goods X and Y (e.g., wine and cheese) that
give equal utility to a consumer. The farther
the indifference curve is from the origin, the
higher the level of utility. Hence, any point
on I3 on the following graph represents
greater utility than any point on I1 or I2.
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Indifference Curves
Continuation
• The 3 Characteristics of Indifference Curves:
– 1) Indifference curves are nonlinear, because of
the diminishing marginal utility.
– 2) Indifference curves can not intersect,
– 3) they are negatively sloped,
– 4) and they are convex to the origin.
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Budget Line
• A budget constraint line depicts all
combinations of two goods that can be
purchased with a given income at the given
prices of the two goods.
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Budget Line
Continuation
• The budget constraint is a straight line
because its slope is constant.
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Budget Line
• Properties of Budget Constraint:
– 1) A change in Income causes a parallel shift in
the Budget Constraint.
– 2) A change in the Price of one of the goods
causes a change in the slope of the Budget
Constraint.
– 3) If the relative Prices of both goods change
proportionately, a parallel shift in the Budget
Line occurs.
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Utility Maximization
• Utility is maximized when the budget line is
tangent to the highest possible Indifference
Curve. At that point, the individual receives
the highest level of utility (satisfaction)
possible, given a fixed income.
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Utility Maximization
• In the following
diagram, Utility is
maximized at point E,
where the Budget
Constraint Line is
tangent to the
Indifference Curve.
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