Download The Demand Side of the Market

Econ Dept, UMR
Presents
The Demand Side of the
Market
Starring
u
Utility Theory
u
Consumer Surplus
u
Elasticity
Featuring
uThe MU/P Rule
uThe Meaning of Value
uFour Elasticities:
vPrice Elasticity of Demand
vIncome Elasticity
vCross Price Elasticity
vPrice Elasticity of Supply
uThe Elasticity-TR Relationship
In Three Parts
Consumer Choice Theory
Consumer Surplus
Elasticity
A. Price Elasticity of Demand
B. Other Important Elasticities
Part 3
Elasticity
Measures of Response
Consumers and producers move along their
demand and supply curves when the price of the
good changes
QUESTION: HOW CAN WE PREDICT THE
MAGNITUDE OF THESE REACTIONS?
Demand and supply curves shift when factors
other than price change in the marketplace
QUESTION: HOW CAN WE PREDICT THE
MAGNITUDE OF THESE REACTIONS?
ANSWER:
ELASTICITIES!!
A Generic Definition of
Elasticity
uY
= f(x)
u Elasticity, ,,
= %∆y/%∆ x, where ∆ is read
“change in”
u %∆Y = (∆y/y)*100; %∆X = (∆ x/x)*100
u (∆Y/y)/(∆x/x), or
u [(∆Y/∆x)/(x/y)]
u In words, elasticity gives us the estimated
percentage change in one variable, y, in
response to a percentage change in another
variable, x, c.P
Generic Interpretation of Elasticity
u, = %∆Y/%∆x = 2
v This means if x were to change by 1 percent
we would expect y to change by 2 percent
in the same direction, c.p.
u, = %∆Y/%∆x = - 2
v This means if x were to change by 1 percent
we would expect y to change by 2 percent
in the opposite direction, c.p.
Rewriting the Formula for Elasticity
u, = %∆Y/%∆x
u Percentage change,
%∆y = (∆ y/y)*100
v
E.G., Percentage change from 50 to 100 is change
(= +50), divided by the base (=100) times 100 =
(50/100)* 100 = 50%
v
Since the numerator and denominator have 100,
they cancel, and
u, = %∆Y/%∆x = (∆y/y)*(∆x/x) or
u, = (∆Y/∆x)*(x/y)
u It’s this last formula that is most convenient
to use as we see later
Some Important Elasticities
u Price elasticity of demand
%∆ in QD
∆QD
= ,D = %∆ in P
∆P
P
Q
u Cross price elasticity of demand
%∆ in D1
,D1,P2 = %∆ in P =
2
∆D1
P2
∆ P2
D1
u Income elasticity
,I =
%∆ in D
=
%∆ in I
∆D I
∆I D
u Price elasticity of supply
,S =
%∆ in QS
=
%∆ in P
∆QS
P
∆P
Q
This Slide Show Discusses
Price Elasticity of Demand
u Other
Elasticities are discussed in slide
show III.B.
Price Elasticity of Demand
Measures How Responsive
Consumers Are to Changes
in the Price of a Product
Demand
u We
know, from the law of demand, that
price and quantity demanded are
inversely related
u Now, we are going to get more specific
in defining that relationship
u We want to know just how much will
quantity demanded change when price
changes? That is what elasticity of
demand measures
Price Elasticity of Demand
elasticity of demand (,D)
measures the responsiveness of QD of a
good to a change in its P
u Price
%∆ In QD
,D = %∆ in P
v Note that ∆ means “change”
v
u Also note that the law of demand
implies ∆QD ∆P is negative. Our
definition of ,D includes a negative
sign, so ,D will always be a positive
number (I know its confusing but …)
Ambiguity of the Sign of ,D
economists define ,D with a
negative sign, that’s what we do
u Some economists leave the negative sign
out of the formula and then talk about
about the absolute value of ,D
u Some economists are just sloppy and talk
of negative ,D sometimes and positive
sometimes
u Regardless the interpretation is the same:
u Some
v If ,D
= 2 or -2 the meaning is clear, a 10%
change in price is expected to change
quantity demanded in the opposite direction
by 20%
Calculating Elasticity of
Demand
Consider the following Demand Curve:
QD = 16 - 2P
P
6
5
2
1
0
D
4
6
12
14
16
Q/t
Calculating Elasticity
P
A
6
…and let’s say we want to find
the Elasticity of Demand at point A
Notice the slope of the demand
curve, )P/)Q, = -1/2
5
2
1
0
D
4
6
Q/t
Calculating Elasticity
u We know
%∆ in QD
∆Q
= ,D = %∆ in P
∆P
P
Q
u %∆ Can
be calculated as the change divided
by starting point
u In this case, ∆Q D/)P
is -2 (the inverse of the
slope of the demand curve)
u P/Q is 6/4 (we use the initial P and Q as our
base
u,D = - (-2)(6/4) = 3
Calculating Elasticity
P
A
6
Now, let’s find the Elasticity of
Demand at point C
5
C
2
1
0
D
4
12
Q/t
Calculating Elasticity
u Again,
%∆ in QD
∆Q
= ,D = %∆ in P
∆P
P
Q
u ∆QD/∆P is still -2 (the inverse of the slope of
the demand curve)
u P/Q is 2/12 (again use the initial P and Q as
the base
u,D = - (-2)(2/12) = 1/3
Calculating Elasticity
u Note
that ,D is different at different places
along the curve
v Specifically, it gets smaller as you move
down the curve
u Note that elasticity and slope are NOT the
same thing
Calculating Elasticity Using
the Demand Equation
u QD
= 16 - 2p
u The parameter attached to price is
∆QD/∆P, here = -2
u The negative sign in the price elasticity
formula makes - 2 equal to 2
u Select any price and find , D
v For example at P = 7, Q D
v ,D = 2(7/2) = 7
=2
How Do We Interpret Price
Elasticity of Demand?
u The number we get from computing the
elasticity is a percentage - there are no
units
u We can read it as the percentage change
in quantity for a 1% change in price
How Do We Interpret Price
Elasticity of Demand?
u Thus,
if ,D = 2, that means that at that
point on the demand curve, a 1%
change in price will cause a 2% change
in quantity demanded in the opposite
direction. Or if we extrapolate, a 2%
increase in price will cause a 4%
decrease in quantity demanded, c.p.
Extreme Cases of ,D
u Perfectly
inelastic
,D = -%∆ In QD
%∆ in P
v ,D = 0
%∆ in P
v
= 0
,D
u No matter how much price changes,
consumers purchase the same amount of the
good
v No example exists according to the law of
demand, but things like insulin have an
elasticity that is pretty large
v
Perfectly Inelastic, ,D = 0
P
0
Perfectly
Inelastic
Q/t
Extremes Cases of,D
u Perfectly elastic
v
v
v
u
,D = - %∆ In Q
D
%∆ in P
,D = -%∆ In Q
D
%∆ in P
,D = ∞
∞
0
No matter how little the price changes, consumer
purchases drop to zero, or expand to infinity
v As with perfectly inelastic demand no example
exists according to the law of demand, but we
have use for the concept of perfectly elastic when
we look at the behavior of firms
Perfectly Elastic, ,D = ∞
P
Perfectly
Elastic
0
Q/t
Empirical Estimates of ,D
u 0 < ,d <
u If 0 < ,D
v
< 1 we say demand is price inelastic
Any % change in P leads to a smaller % change in
QD
u If ,D
v
∞
= 1 we say demand is unitary elastic
Any % change in P leads to the same % change in
QD
u If 1< ,D <
v
∞ we say demand is price elastic
Any % change in P leads to a larger % change in
QD
The Following Categories Help to
Describe Consumer Responsiveness:
u If
the elasticity coefficient is less than 1
demand is inelastic. Consumers are
relatively unresponsive to price changes.
u If the elasticity coefficient is greater than
1 demand is elastic. Consumers are
relatively responsive to price changes.
u If the elasticity coefficient is equal to 1,
demand is unitary elastic.
Generalizing About Elasticity
u Notice
that the vertical D curve has an
elasticity of zero and the flat D curve has
an elasticity of infinity
u As the demand curve goes from vertical
to horizontal the elasticity goes from 0 to
infinity
u Unfortunately, we can’t say the flatter
the demand curve, the greater the
elasticity
Linear Demand Curves Have
Elastic, Unitary, and Inelastic
Regions
P
10
,D = ∞
ELASTIC ,D > 1
int
o
p
Mid
5
UNITARY ELASTIC
,D = 1
INELASTIC ,D < 1
D
7
,D = 0
14
Q/t
Now that you can calculate the price
elasticity of demand, what would you use it
for?
Why Would a Business Firm
Need to Calculate Them,
and How Would the Firm
Use the Information?
There Is an Important Relationship
Between Price Elasticity of Demand and
Total Revenues:
u When
demand is inelastic, price and
total revenues are directly related.
Price increases generate higher
revenues.
u When demand is elastic, price and total
revenues are indirectly related. Price
increases generate lower revenues.
Total Revenue
u Total revenue = P*Q
u The
firm is interested in how TR (total
revenue) changes as p and q change
Total Revenue Calculation Example
u Price
$1
QD = 100
v TR = $100
u Price
$5
QD = 90
v TR = $450
u Price
$5
QD = 10
v TR = $ 50
u Price
$5
QD = 20
v TR = $100
Total Revenue and Elasticity
u Let’s say demand is inelastic. Then if
the firm raises prices 10%, the sales will
drop by less than 10%: (%∆QD < %∆P)
u In other words, the gain in revenue
from higher prices is greater than the
loss in revenue from lost
sales.Therefore, total revenue will rise
Total Revenue and Elasticity
u If they lowered prices, though, the loss
of revenue from higher prices would be
greater than the gain from increased
sales, so total revenue will fall
Total Revenue and Elasticity
u Let’s
say demand is elastic. Then if the
firm raises prices 10%, the sales will
drop by more than 10% (%∆QD > %∆P)
in other words, the gain in revenue
from higher prices is less than the loss
in revenue from lost sales.Therefore,
total revenue will fall
Total Revenue and Elasticity
u If they lowered prices, though, the loss
of revenue from higher prices would be
less than the gain in revenue from
increased sales, so total revenue will
rise
Total Revenue and Demand
u So we can look at what happens to total
revenue as we move down a demand
curve
u As we move down a demand curve we
know that we start off elastic and as we
lower price we get less and less elastic
(but total revenue rises, since it is
elastic) until we hit the point that we
are inelastic and then as we continue to
lower price, total revenue falls
Total Revenue and Demand
$
Elastic
Elasticity = 1
Inelastic
Demand
Q/t
$
Total Revenue
Q/t
Total Revenue Test
u If
P and total revenue move together
v Demand is inelastic
u If
P and TR move in opposite directions
v Demand is elastic
u If
changes in P doesn’t change TR
v Demand is unitary elastic
TR and Farm Revenue
u In 1988, wheat farmers experienced the worst
drought since the 1930s
u Estimates of the price elasticity of demand for
wheat range from 0.3 to 0.7
u Due to the poor harvest, supply decreased by
14%
u What happened to wheat price?
$2.57 in 1987 and $3.72 in 1988, a 45% increase
v The implied , D = 14/45 = 0.31
v
u What happened to total revenue?
v
It increased (of course for farmers whose crops were
wiped out, their TR fell)
Notice that this gives the firm
information that it can use to
establish pricing policy.
Now...What Factors Help
to Determine Price
Elasticity of Demand?
Determinants Of Price
Elasticity Of Demand
Availability of substitutes -- demand
is more elastic when there are more
substitutes for the product.
u Importance of the item in the budget -demand is more elastic when the item
is a more significant portion of the
consumer’s budget.
u Time frame -- demand becomes more
elastic over time.
u
Determinants of ,D
u Availability
of substitutes
v As there are more substitutes, demand is
more elastic (and vice versa)
u Example:
v Insulin has no substitutes if diabetic and
demand is very inelastic
v Kroger brand cola has many substitutes
and hence, demand is very elastic
Determinants of ,D
u Amount
of consumers budget
v The less expensive a good is as a fraction of
our total budget, the more inelastic the
demand for the good is (and vice versa)
u Example:
v Price of cars go up 10% (from $20,000 to
$22,000)
v Price of soda goes up 10% (from $0.50 to
$0.55)
v Demand is more effected by the price of
cars increasing
Determinants of ,D
u Time
v The longer the time frame is, the more
elastic the demand for a good (and vice
versa)
u Example
- price of gasoline increases
v Immediately: can’t do much, still need to
get to work, school, etc
v Short-run: find a car pool, ride bike, etc
v Long-run: next car you buy uses less gas
Some Estimates of ,D : Short
*
and Long Run
Short Run Long Run
Cigarettes
Water
Physicians’ services
Gasoline
Automobiles
Chevrolets
Electricity, h’hold
Air Travel
----0.6
0.2
----0.1
0.1
0.35
0.4
--0.5 to 1.5
1.5
4.0
1.9
2.4
* The long run is a period so full adjustment occurs. Elasticity
estimates are reported by Browning, et.al., Microeconomic
Theory,5th ed., 1996
The End
Check out other elasticities in III.b.