MANAGERIAL ECONOMICS
II: DEMAND AND SUPPLY
Introduction
Demand theory is one of the core theories of
microeconomics and consumer behaviour.
It attempts at answering questions regarding the
magnitude of demand for a product or service
based on its importance to human wants.
It also attempts to assess how demand is impacted
by changes in prices and income levels and
consumers preferences/utility.
Based on the perceived utility of goods and services
to consumers, companies are able to adjust the
supply available and the prices charged.
Introduction......
In economics, demand has a specific meaning distinct
from its ordinary usage. In common language we treat
‘demand’ and ‘desire’ as synonymously. This is
incongruent from its use in economics.
In economics, demand refers to effective demand which
implies three things:
• Desire for a commodity
• Sufficient money to purchase the commodity, rather the
ability to pay
• Willingness to spend money to acquire that commodity
Introduction......
The following should also be noted about demand:
• Demand always alludes to demand at price. The term
‘demand’ has no meaning unless it is related to price. For
instance, the statement, 'the weekly demand for potatoes
in city X is 10,000 kilograms' has no meaning unless we
specify the price at which this quantity is demanded.
• Demand always implies demand per unit of time. Therefore,
it is vital to specify the period for which the commodity is
demanded. For instance, the statement that demand for
potatoes in city X at birr 8 per kilogram is 10,000 kilograms
again has no meaning, unless we state the period for which
the quantity is being demanded.
Introduction......
A complete statement would therefore be as follows:
‘The weekly demand for potatoes in September 2016 in Addis Ababa
at birr 8 per kilogram was 10,000 kilograms'.
It is necessary to specify the period and the price because demand for
a commodity will be different at different prices of that commodity
and for different periods of time.
• The demand must relate to a specific market as well
Thus, we can define demand as follows:
“The demand for a commodity at a given price is the amount of it
which will be bought per unit of time at that price at a particular
market”.
The Law of Demand
We have considered various factors that fashion the
demand for a commodity. As explained the first and
the most important factor that determines the demand
of a commodity is its price.
If all other factors (noted above) remain constant, it may
be said that as the price of a commodity increases, its
demand decreases and as the price of a commodity
decreases its demand increases. This is a general
behaviour observed in a market.
This gives us the law of demand:
The law of demand states that “the quantity demanded
of a good or service is inversely related to the selling
price, ceteris paribus”.
The law of demand.....
The demand curve
Symbolically, the law of demand may be summarised as:
and
The above equation states that QD, the quantity demanded of a good or service, is
functionally related to the selling price P. The Inequality sign asserts that quantity
demanded and price are inversely related.
This relationship is illustrated in the demand curve. The downward-sloping demand
curve illustrates the inverse relationship between the quantity demanded of a good or
service and its selling price.
The law of demand.....
Assumptions of the Law of Demand
1. Income level should remain constant: The law of demand
operates only when the income level of the buyer remains
constant. If the income rises while the price of the commodity
does not fall, it is quite likely that the demand may increase.
Therefore, stability in income is an essential condition for the
operation of the law of demand.
2. Tastes of the buyer should not alter: Any alteration that takes
place in the taste of the consumers will in all probability
thwart the working of the law of demand. It often happens
that when tastes or fashions change people revise their
preferences. As a consequence, the demand for the
commodity which goes down the preference scale of the
consumers declines even though its price does not change.
The law of demand.....
3. Prices of other goods should remain constant: Changes in
the prices of other goods often impinge on the demand for
a particular commodity. If prices of commodities for which
demand is inelastic rise, the demand for a commodity other
than these in all probability will decline even though there
may not be any change in its price. Therefore, for the law of
demand to operate it is imperative that prices of other
goods do not change.
4. No new substitutes for the commodity: If some new
substitutes for a commodity appear in the market, its
demand generally declines. This is quite natural, because
with the availability of new substitutes some buyers will be
attracted towards new products and the demand for the
older product will fall even though price remains
unchanged.
Hence, the law of demand operates only when the market for
a commodity is not threatened by new substitutes.
The law of demand.....
5. Price rise in future should not be expected: If the
buyers of a commodity expect that its price will rise in
future they raise its demand in response to an initial
price rise. This behaviour of buyers violates the law of
demand. Therefore, for the operation of the law of
demand it is necessary that there must not be any
expectations of price rise in the future.
6. Advertising expenditure should remain the same: If the
advertising expenditure of a firm increases, the
consumers may be tempted to buy more of its product.
Therefore, the advertising expenditure on the good
under consideration is taken to be constant.
The law of demand.....
Why does the demand curve slope downwards?
The reasons behind the law of demand i.e. inverse
relationship between price and quantity demanded are
following:
• Substitution Effect: When the price of a commodity
falls it becomes relatively cheaper if price of all other
related goods, particularly of substitutes, remain
constant. In other words, substitute goods become
relatively costlier. Since consumers substitute cheaper
goods for costlier ones, demand for the relatively
cheaper commodity increases. The increase in demand
on account of this factor is known as substitution
effect.
The law of demand.....
• Income Effect: As a result of fall in the price of a
commodity, the real income of its consumer increase at
least in terms of this commodity. In other words,
his/her purchasing power increases since she/he is
required to pay less for the same quantity.
The increase in real income (or purchasing power)
encourages demand for the commodity with reduced
price. The increase in demand on account of increase
in real income is known as income effect. It should
however be noted that the income effect is negative in
case of inferior goods.
The law of demand.....
• Diminishing Marginal Utility: Diminishing
marginal utility as well is to be held responsible
for the rise in demand for a product when its
price declines.
When an individual purchases a product, She/he
swaps Her/his money revenue with the product
in order to increase their satisfaction. She/He
continues to purchase goods and services as long
as the marginal utility of money (MUm) is lesser
than the marginal utility of the commodity
(MUc). Given the price of a commodity, they
modify their purchase so that MUc = MUm.
The law of demand.....
This plan works well under both Marshallian assumption
of constant MUm as well as Hicksian assumption of
diminishing MUm. When price falls, (MUm = Pc) <
MUc.
Thus, equilibrium state is upset. To get back his
equilibrium state, i.e., MUm = PC, = MUC, he buys
more quantities of the commodity.
For, when the supply of a commodity rises, its MU falls
and once again MUm = MUC.
For this reason, demand for a product rises when its price
falls.
The law of demand.....
Exceptions to the Law of Demand
• Apprehensions about the future price: When consumers
anticipate a constant rise in the price of a long-lasting
commodity, they purchase more of it despite the price rise.
They do so with the intention of avoiding the blow of still
higher prices in the future. Likewise, when consumers expect
a substantial fall in the price in the future, they delay their
purchases and hold on for the price to decrease to the
anticipated level instead of purchasing the commodity as soon
as its price decreases. These kinds of choices made by the
consumers are in contradiction of the law of demand.
•
Status goods: The law does not concern the commodities
which function as a ‘status symbol’, add to the social status or
exhibit prosperity and opulence e.g. gold, precious stones,
rare paintings and antiques, etc. Rich people mostly purchase
such goods as they are very costly.
THE MARKET DEMAND CURVE
The quantity of a commodity which an individual is
willing to buy at a particular price of the commodity
during a specific time period, given his money income,
his taste and prices of substitutes and complements, is
known as individual demand for a commodity.
The total quantity which all the consumers of a
commodity are willing to buy at a given price per time
unit, other things remaining the same, is known as
market demand for the commodity.
In other words, the market demand for a commodity is
the sum of individual demands by all the consumers (or
buyers) of the commodity, per time unit and at a given
price, other factors remaining the same.
The Market Demand Curve.....
Table: Price and Quantity Demanded
The Market Demand Curve.....
The law of demand is a theoretical explanation of the expected behaviour of individual
economic units when confronted with a change in the price of a commodity.
The individual demands for commodity X are given by DA, DB and Dc, respectively. The
horizontal summation of these individual demand curves results into the market
demand curve (DM) for the commodity X. The curve DM represents the market
demand curve for commodity X when there are only three consumers of the
commodity.
The Market Demand Curve is the Horizontal Summation of Individual Demand
Curves.
THE DEMAND FUNCTION
The functional relationship between the demand for a
commodity and its various determinants may be expressed
mathematically in terms of a demand function, thus:
Dx = f (Px, Py, M, T, A, U) where,
•
•
•
•
•
•
•
•
Dx = Quantity demanded for commodity X.
f = functional relation.
Px = The price of commodity X.
Py = The price of substitutes and complementary goods.
M = The money income of the consumer.
T = The taste of the consumer.
A = The advertisement effects.
U = Unknown variables or influences.
The demand function...
The above-stated demand function is a complicated
one. Again, factors like tastes and unknown
influences are not quantifiable. Economists,
therefore, adopt a very simple statement of
demand function, assuming all other variables,
except price, to be constant.
Thus, an over-simplified and the most commonly
stated demand function is: Dx = f (Px), which
connotes that the demand for commodity X is the
function of its price. The traditional demand
theory deals with this demand function
specifically.
The demand function...
Let us consider three hypothetical individual demand
functions for a product:
QD,1=a1+b1P...........................a
QD,2=a2+b2P............................b
QD,3=a3+b3P............................c
where the QD,i terms represent the individual’s demand for the
commodity, the ai terms are positive constants, and the bi
terms the unit change in quantity demanded given a change
in the selling price.
The demand function...
For any given price, the market demand curve is the sum of the
horizontal distances from the vertical axis to each individual
demand curve.
Summing together the above equations ( a,b, and c) we get:
QD,1 +QD,2 +QD,3 = (a1 + a2 + a3 ) + (b1 + b2 + b3 )P
Or
QD = a + bP
where a = a1+ a2 + a3 and b = b1+ b2 + b3. In general, for the
consumer case:
where QD,M is market demand
The demand function...
Problem : Suppose that the total market
demand for a product comprises the demand
of three individuals with identical demand
equations.
QD,1 =QD,2 =QD,3 = 50 - 25P
a) What is the market demand equation for this
product?
b) Draw the market demand curve.
The demand function...
Solution: The market demand curve is the horizontal
summation of the individual demand curves.
The market demand equation is:
QD=Qd1+Qd2+Qd3=
(50 - 25P)+(50 - 25P)+(50 - 25P)=150 - 75P
The demand function...
Problem: Suppose that the total market demand for
a product consists of the demands of individual 1
and individual 2. The demand equations of the
two individuals are given by the following
equations:
Qd1=20-2p and Qd2=40-5p
a) What is the market demand equation for this
product?
b) Draw the market demand curve.
OTHER DETERMINANTS OF MARKET DEMAND
Other demand determinants include income,
consumer preferences, the prices of related
goods, price expectations, and population.
Shifts in a price-demand curve may take place
owing to the change in one or more of other
determinants of demand.
OTHER DETERMINANTS OF MARKET DEMAND……
OTHER DETERMINANTS OF MARKET DEMAND…..
Market demand curve Consisting the all determinant variables:
Dx = f (Px, Py, M, T, A, E, U) where,
•
•
•
•
•
•
•
•
•
Dx = Quantity demanded for commodity X.
f = functional relation.
Px = The price of commodity X.
Py = The price of substitutes and complementary goods.
M = The money income of the consumer.
T = The taste or preference of the consumer.
A = The advertisement effects.
E= Price expectations.
U = Unknown variables or influences
OTHER DETERMINANTS OF MARKET DEMAND…..
Problem: Suppose that the demand for a popular brand of a fruit drink
is given by the equation: Qx=10-5Px+0.001I+10Py
Where:
• Qx= monthly consumption of the fruit per family in gallons.
• Px= price per gallon of the fruit drink=2.00birr.
• I= median annual family income=20,000birr.
• Py= price per gallon of a competing brand of friut drink=2.50birr.
Required:
a. Interpret the parameter estimates.
b. Calculate the monthly consumption of the gallon given the
parameters.
c. Rewrite the demand function.
d. Suppose that a median annual family income increased to 30,000.
How does this change the answer to part b.
OTHER DETERMINANTS OF MARKET DEMAND…..
Solution
a. According to our demand equation in Qx, a 1 birr increase in the
price of the fruit drink will result in a 5-gallon decline in monthly
consumption of fruit drink per family. A 1,000 birr increase in
median annual family income will result in a 1-gallon increase in
monthly consumption of fruit drink per family. Finally, a 1 birr
increase in the price of the competing brand of fruit drink will
result in a 10-gallon increase in monthly consumption of the fruit
drink per family. In other words, the two brands of fruit drink are
substitutes.
b. Substituting the stated values into the demand equation yields
Qx = 10 - 5(2.00) + 0.001(20, 000) + 10(2.50) = 45 gallons
c. Qx = 55 - 5Px
d. Qx = 10 - 5(2.00) + 0.001(30,000) + 10(2.50) = 55 gallons
THE LAW OF SUPPLY
Definition: The law of supply asserts that quantity supplied
of a good or service is directly (positively) related to the
selling price, ceteris paribus.
Symbolically: QS = g(P)
Fig. The supply curve
where: dQs/dP > 0
THE LAW OF SUPPLY…
The upward-sloping supply curve illustrates the positive
relationship between the quantity demanded of a good
or service and its selling price. The market supply curve
shows the various amounts of a good or service that
profit-maximizing firms are willing to supply at each
price. As with the market demand curve, the market
supply curve is also the horizontal summation of the
individual firms’ supply curves.
The market supply curve establishes a relationship
between price and quantity supplied. Changes in the
price and the quantity supplied of a good or service are
represented diagrammatically as a movement along
the supply curve. Changes in supply determinants are
illustrated as a shift in the entire supply curve.
DETERMINANTS OF MARKET SUPPLY
Of course, the market price of a good or service is not the only
factor that influences a firm’s decision to alter the quantity
supplied of a particular good or service.
To get a “feel” for whether a firm will increase or decrease the
quantity supplied of a particular good or service (assuming
the product’s price is given) in response to a particular
supply-side stimulus, let us assume that the firms that
make up the supply side of the market are “profit
maximizers.” Total profit is defined as:
π(Q) =TR(Q) -TC(Q)
Where π is total profit, TR is total revenue, and TC is the total
cost, which are defined as functions of total output Q.
DETERMINANTS OF MARKET SUPPLY…
Moreover, total revenue may be expressed as the product of
the selling price of the product times the quantity sold i.e
TR=PQ
Total cost, on the other hand, is assumed to be an increasing
function of a firm’s output level, which is a function of the
productive resources used in its production.
The following Equation expresses total cost as a function of
labor and capital inputs:
TC=f(L,K)
DETERMINANTS OF MARKET SUPPLY…
If the firm purchases productive resources in a
perfectly competitive factors market, the total
cost function might be expressed as:
TC =TFC +TVC =TFC+PLL + PKK
Where TFC represents total fixed cost (a constant),
PL is the price of labor, which is determined
exogenously, L the units of labor employed, PK is
the rental price of capital, also determined
exogenously, and K the units of capital employed.
DETERMINANTS OF MARKET SUPPLY…
The above explanations try to indicate that as a firm’s output level
expands, the costs associated with higher output levels increase.
In general, let us say that the change in any factor that causes a firm’s
profit to increase will result in a decision to increase the quantity
the firm supplies to the market, other things remaining the same.
Conversely, any change that causes a decline in profits will result in a
decline in quantity supplied, other things remaining the same.
We have already seen that an increase in product price, which
increases total revenue, will result in an increase in the quantity
supplied, or a movement to the right and along the supply function.
OTHER SUPPLY DETRMINANTS
Table: Impacts on supply arising from changes in factors determining
supply
QS = f (P, PL , E, R, Ps , Pc , Pe , F)
THE MARKET MECHANISM: THE INTERACTION OF DEMAND AND
SUPPLY
On the curve given left, the market equilibrium price
is P*. At that price, the quantity of a good or service
that buyers are able and willing to buy is precisely
equal to Q*, the amount that firms are willing to
supply.
At a price below P*, the quantity demanded exceeds
the quantity supplied.
Fig. Market Equilibrium
In this situation, consumers will bid among themselves for the available supply of Q,
which will drive up the selling price. Buyers who are unable or unwilling to pay the
higher price will drop out of the bidding process. At the higher price, profit-maximizing
producers will increase the quantity supplied. As long as the selling price is below P*,
excess demand for the product will persist and the bidding process will continue. The
bidding process will come to an end when, at the equilibrium price, excess demand is
eliminated. In other words, at the equilibrium price, the quantity demanded by buyers
is equal to the quantity supplied.
THE MARKET MECHANISM: THE INTERACTION OF
DEMAND AND SUPPLY
Problem : The market demand and supply
equations for a product are:
Qd=25-3P
Qs=10+2P
where Q is quantity and P is price.
Required: What are the equilibrium price and
quantity for this product?
CHANGES IN SUPPLY AND DEMAND: THE ANALYSIS OF PRICE
DETERMINATION
Suppose, for example, that medical
research finds that coffee have highly
desirable
health
characteristics,
triggering an increase in the public’s
preference for coffee.
DEMAND SHIFTS
Other things remaining constant, this would
result in a right-shift in the demand
curve for coffee. This results in an
increase in the equilibrium price and
quantity demanded for coffee.
on the other hand if research discovers that coffee exhibited highly
undesirable health properties, one could have predicted a reduction in the
demand for coffee, or a left-shift in the demand curve, resulting, in turn, in
a decline in both equilibrium price and quantity demanded.
CHANGES IN SUPPLY AND DEMAND……
SUPPLY SHIFTS
Suppose there is a sharp decline in the
price of coffee inputs. The result will be an
increase in the supply of coffee at every
price, other things remaining the same.
This, of course, would result in a rightshift of the supply function. The result,
which is illustrated in the left figure, is a
decline in the equilibrium price and an
increase in quantity supplied.
Conversely, a left-shift in the supply curve would have raised the equilibrium
price and lowered the equilibrium quantity. In either the case of a demand
shift or a supply shift, the effect on the equilibrium price and quantity is
unambiguous.
CHANGES IN SUPPLY AND DEMAND…..
DEMAND AND SUPPLY SHIFTS
When changes in both demand and supply occur simultaneously, it is more difficult
to predict the effect on price and quantity demanded. This can be illustrated by
considering four possible cases.
Figure C
Case 1: An Increase in Demand and an
Increase in Supply
As illustrated in Figure C a right-shift in both
the demand and supply curves yields an
ambiguous increase in quantity demanded.
The effect on the equilibrium price,
however, is indeterminate.
CHANGES IN SUPPLY AND DEMAND…..
As shown earlier, if the increase in supply is relatively less
than the increase in demand, the result will be a net increase
in price. This is seen in Figure C by comparing the market
clearing price at E with E’.
On the other hand, if there occurs a large increase in supply,
relative to the increase in demand, the result will be a net
decrease in the equilibrium price. This is seen by comparing
the market clearing price at E with E” in Figure C.
CHANGES IN SUPPLY AND DEMAND…..
Case 2: An Increase in Demand and a
Decrease in Supply
As illustrated in Figure D, a right-shift in the
demand curve and a left shift in The
supply curve result in an ambiguous
increase in the equilibrium price, although
the effect on the equilibrium quantity is
indeterminate. If the decrease in supply is
relatively less than the increase in
demand, the result will be an increase in
equilibrium price and quantity.
Figure D
CHANGES IN SUPPLY AND DEMAND…..
This is seen in Figure D by comparing the equilibrium price and quantity at E
with E’. If, however, the decrease in supply is relatively more than the
increase in demand, the result will be an increase in the equilibrium price
but a decrease in the equilibrium quantity. This can be seen by comparing
the equilibrium price and quantity at E with E”.
CHANGES IN SUPPLY AND DEMAND…..
Case 3: A Decrease in Demand
and a Decrease in Supply
As can be seen in Figure E, a
left-shift in both the demand
and supply curves will result
in an unambiguous decline
in the equilibrium quantity
and
an
indeterminate
change in the equilibrium
price.
Figure E
CHANGES IN SUPPLY AND DEMAND…..
If the decrease in supply is relatively less than the decrease in demand, the
result will be a decrease in the equilibrium price and quantity. This is seen
by comparing equilibrium price and quantity at E with E’ in Figure E.
If, however, the decrease in supply is relatively greater than the decrease in
demand, the result will be a decrease in the equilibrium quantity, but an
increase in the equilibrium price. This can be seen by comparing the
equilibrium price and quantity at E with E” in figure E.
CHANGES IN SUPPLY AND DEMAND…..
Case 4: A Decrease in Demand and an
Increase in Supply
In our final case, a left-shift in the
demand curve and a right-shift
in the supply curve will result
in an ambiguous decline in the
equilibrium price, but an
indeterminate change in the
equilibrium quantity. This
situation is depicted in Figure
F.
Figure F.
CHANGES IN SUPPLY AND DEMAND…..
If the increase in supply is relatively less than the decrease in demand, the
result will be a decrease in the equilibrium price and quantity. This is seen
by comparing the equilibrium price and quantity at E with E” in figure F.
If, however, the increase in supply is relatively greater than the decrease in
demand, the result will be an increase in the equilibrium quantity and a
decrease in the equilibrium price. This can be seen by comparing the
equilibrium price and quantity at E’ with E” in Figure F.
CHANGES IN SUPPLY AND DEMAND…..
Problem : The market supply and demand equations for a
given product are given by the expressions:
QD = 200 - 50P
QS = -40 + 30P
a. Determine the equilibrium price and quantity.
b. Suppose that there is an increase in demand to QD = 300 50P Suppose further that there is an increase in supply to
QS = -20 + 30P, What are the new equilibrium price and
quantity?
c. Suppose that the increase in supply had been
QS = 140 + 30P Given the demand curve in part b, what are
the equilibrium price and quantity?
d. Diagram your results.
CHANGES IN SUPPLY AND DEMAND…..
Solution
a. Equilibrium is characterized by the condition QD = QS.
Substituting, we have
200 - 50P = -40 + 30P, P* = 3
Q* = 200 - 50(3) = -40 + 30(3) = 50
b. Substituting the new demand and supply equations into the
equilibrium equations yields
300 - 50P = -20 + 30P, P* = 4, Q* = 300 - 50(4) = -20 + 30(4) = 100
c. 300 - 50P = 140 + 30P, P* = 2, Q* = 300 - 50(2) = 140 + 30(2) = 200
Elasticity of Demand
While the law of demand establishes a relationship between price and
quantity demanded for a product, it does not tell us exactly as how
strong or weak the relationship happens to be. This relation, as
already discussed, is inverse baring some rare exceptions.
However, a manager needs an exact measure of this relationship for
appropriate business decisions. Elasticity of demand is a measure,
which comes to the rescue of a manager here. It measures the
responsiveness of demand to changes in prices as well as changes
in income.
A manager can determine almost exactly how the demand for her/his
product would change when he changes his price or when her/his
rivals alter prices of their products. She/he can also determine how
the demand for her/his product would change if incomes of her/his
consumers go up or down. Elasticity of demand concept and its
measurements are therefore very important tools of managerial
decision making.
Elasticity of Demand….
In this unit, we will discuss the following kinds of
demand elasticity:
• Price Elasticity: Elasticity of demand for a
commodity with respect to change in its price.
• Cross Elasticity: Elasticity of demand for a
commodity with respect to change in the price
of its substitutes.
• Income Elasticity: Elasticity of demand with
respect to change in consumer’s income.
Elasticity of Demand….
PRICE ELASTICITY OF DEMAND
Price elasticity of demand can be calculated using either of the mid
point formula or the point elasticity.
Consider the figure below with a demand equation of Qd=127-50p
Elasticity of Demand….
The Mid-Point Formula
It should be clear that the choice of A or B as
the starting point can have a significant
impact on the calculated value of Ep.
One way of overcoming this dilemma is to use
the average value of QD and P as the point of
reference in calculating the averages.
The resulting expression for the price elasticity
of demand is referred to as the midpoint
formula.
Elasticity of Demand….
The derivation of the midpoint formula is:
Elasticity of Demand….
Using the data from the foregoing illustration, we find that the price elasticity
of demand as we move from point A to point B is:
On the other hand, moving from point B to point A yields identically the same
result.
Elasticity of Demand….
Problem: Suppose that the price and quantity
demanded for a good are $5 and 20 units,
respectively. Suppose further that the price of
the product increases to $20 and the quantity
demanded falls to 5 units. Calculate the price
elasticity of demand.
Elasticity of Demand….
Solution. Since we are given two price–quantity
combinations, the price elasticity of demand
may be calculated using the midpoint formula:
Elasticity of Demand….
POINT-PRICE ELASTICITY OF DEMAND
The point-price elasticity of demand is defined as:
where dQD/dP is the slope of the demand function
at a single point. It is, in fact, the first derivative
of the demand function.
Elasticity of Demand….
Problem: The demand equation for a product is
QD = 50 - 2.25P.
Required: Calculate the point-price elasticity of
demand if P = 2.
Solution
Elasticity of Demand….
Problem: Suppose that the demand equation
for a product is QD = 100 - 5P. If the price
elasticity of demand is -1, what are the
corresponding price and quantity demanded?
Elasticity of Demand….
Elasticity of Demand….
PRICE ELASTICITY OF DEMAND: SOME DEFINITIONS
Now that we are able to calculate the price elasticity of demand at any point
along a demand curve, it is useful to introduce some definitions.
As indicated earlier, in general we will consider only absolute values of ep,
denoted symbolically as |ep|. Since ep may assume any value between
zero and negative infinity, then |ep| will lie between zero and infinity.
.
Elasticity of Demand….
Elasticity of Demand….
In some cases, however, the elasticity remains the same
throughout the length of the demand curve. Such
demand curves can be placed in the following
categories: (i) perfectly inelastic (e = 0); (ii) unitary
elastic (e = 1); and (iii) perfectly elastic (e = ∞). These
three types of demand curves are illustrated below:
Elasticity of Demand….
INCOME ELASTICITY OF DEMAND
Perhaps the second most frequently estimated measure of
elasticity, after the price elasticity of demand, is the income
elasticity of demand, which is defined as
where I represents some measure of aggregate consumer
income. The income elasticity of demand measures the
percentage change in the demand for a good or service
given a percentage change in income. From the managerial
decision-making perspective, the income elasticity of
demand is used to evaluate the sales sensitivity of a good
or service to economic fluctuations.
Elasticity of Demand….
Commodities for which eI > 0 are referred to as normal goods. Sales of
normal goods rise with increases in income, and vice versa. Normal
goods may be further classified as either necessities or luxuries.
A commodity is classified as a necessity if 0 < eI < 1
The sales of such goods (electricity, rent, food, etc.) are relatively
insensitive to economic fluctuations.
A commodity is classified as a luxury if eI ≥ 1. Such commodities
(jewelry, luxury automobiles, yachts, furs, restaurant meals, etc.)
are very sensitive to economic fluctuations.
Commodities in which eI < 0 are referred to as inferior goods. Sales of
inferior good fall with increases in income, and vice versa. While it
is difficult to identify inferior goods at the market level, it is easy to
hypothesize the existence of inferior goods for individuals.
Elasticity of Demand….
CROSS-PRICE ELASTICITY OF DEMAND
Another frequently used elasticity measure is the crossprice elasticity of demand, which is defined as:
The cross-price elasticity of demand measures the
percentage change in the demand for good X given a
percentage change in the price of good Y. The crossprice elasticity of demand is used to evaluate the sales
sensitivity of a good or service to changes in the price
of a related good or service.
Elasticity of Demand….
An interpretation of the cross-price elasticity of
demand follows from the sign of the first
derivative, since the second term on the righthand side of Equation is always positive.
When ey > 0, this indicates that the good in
question is a substitute, and when the ey < 0,
the good In question is a complement.
Elasticity of Demand….
OTHER ELASTICITIES
Elasticity is a perfectly general concept.
Whenever a functional relationship exists,
then an elasticity measure in principle exists.
That is, for any function y = f(x1, . . . , xn),
there exists an elasticity measure such that e
= (dy/dxi) (xi/y), for all i = 1, . . . , n.
Elasticity of Demand….
Problem: Rubicon & Styx has estimated the following demand function
for its world-famous hot sauce, Sergeant Garcia’s Revenge,.
Q = 62 - 2P + 0.2I + 25A
where Q is the quantity demanded per month , P is the price per unit, I
is an index of consumer income, and A is the company’s advertising
expenditures per month . Assume that P = 4, I = 150, and A = 4.
Required:
a. Calculate the quantity demanded.
b. Calculate the price elasticity of demand. According to your
calculations, is the demand for this product elastic, inelastic, or unit
elastic? What, if anything, can you say about the demand for this
product?
c. Calculate the income elasticity of demand. Is this product a normal
good or an inferior good? Is it a luxury or a necessity?
d. Calculate the advertising elasticity of demand. Explain your result.
Elasticity of Demand….