# Demand Elasticities and Related Coefficients

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```					Demand Elasticities and
Related Coefficients
Demand Curve
 Demand curves are assumed to be
downward sloping, but the responsiveness of
quantity (Q) to changes in price (P) is not the
same for all commodities
 Units of commodities are also different
(bushels, lbs. kg., etc.)
Elasticities
 Elasticities are used to estimate
responsiveness of Q to changes in P and are
in percentages so one can make
comparisons across commodities
Own-Price Elasticity
 The most commonly used elasticity is the “own-
price” elasticity. This means the responsiveness
of the quantity demanded of a commodity to a
change in its own price.

Q P Q P

Point elasticity for own-price or
At a given point on a demand

P Q P Q
curve.
Arc Elasticity
 Over larger segments of the demand curve (i.e., for
relatively large changes in price), the arc elasticity may be
more appropriate because it give an average elasticity
over the affected portion of the demand curve.

Qo  Q1 P0  P1
=   Arc elasticity
Q0  Q1 P0  P1
Degree of Responsiveness
 The own price elasticity is said to be:
   Elastic if the absolute value of the elasticity is
greater than 1
   Inelastic if the absolute value of the elasticity
is less than 1
   Unitary elastic if the absolute value of the
elasticity is equal to 1
What Does the Degree of
Responsiveness Tell Us
 Essentially the degree of responsiveness
indicates what will happen to total revenue
(i.e., sales) when price changes
 Total revenue (TR) = P*Q
   Because demand curves are downward
sloping P and Q vary inversely. That is, if P
increases (decreases) then Q decreases
(increases). Consequently, the effect of a
change in price on TR is uncertain and
depends on the elasticity of demand.
Example of Effect of Elasticity on
Total Revenue
 If P=100 and Q=100, then TR =10,000 (100 * 100)
 If ED = -0.5 and P increases by 1% to 101, then Q decreases by
one-half of 1% to 99.5. The effect is that TR actually increases
to 10,049 (101*99.5).
 If instead ED=-1.5 and P increases by 1% to 101, then Q
decreases by one and one-half % to 98.8. The effect is than TR
decreases to 9,948.5 (101*98.5).
 So, with inelastic demand TR increases (decrease) as P
increases (decreases). With elastic demand TR decreases
(increases) as P increases (decreases).
 The demand for most agricultural commodities is inelastic which
means TR to that commodity goes up when P increases.
Income Elasticity
 The income elasticity measures the sensitivity
of quantity demanded to changes in income,
other factors held constant:

Q Y Q Y
Ey      
Y Q Y Q
Lessons from Income Elasticities
 Income elasticities for food are generally
thought to decline as income increases.
Total amount of food consumed may not
change much as income increases, but
expenditures on food may increase as
income increases.
   Market growth for bulk commodities is likely
most easily achieved in developing economies
   Market growth in developed economies is
likely for highly processed, or other value-
Engle Curve
 The graphical relationship between consumption and income is referred
to as the Engle Curve or function
 Empirically, income elasticities are sometimes measured using
expenditures rather than total consumption (expenditure elasticity)
Engle Curve

80
Consumption

70
60
50
40
30
20
10
0
10   20   30      40     50   60      70

Income
Properties of Income and
Expenditure Elasticities
 Expenditure elasticities tend to be larger than
income elasticities.
 The expenditure elasticity capture quality and
quantity effects since as income changes
quality
 Normal good = Ey > 0
 Inferior good = Ey < 0
Cross-Price Elasticities
 Cross-price elasticities measure the responsiveness
of demand for one good in relation to a change in
price for another good.

Qi Pj
Eij 
Pj Qi
Characteristics of Cross-Price
Elasticities
 If Eij > 0 then the two goods are substitutes
 If Eij < 0 then the two goods are compliments

 If Eij = 0 then good i is independent from good j.
 The larger the cross-price elasticity (in terms of absolute value)
the closer the relationship between the two goods.
Relationships Among Elasticities
 Demand theory dictates that an exhaustive
set of elasticities (price, income, and cross)
have certain qualities. These qualities are:
   Homogeneity condition
   Symmetry condition
   Engle aggregation condition
 These conditions are used to calculate a
number of elasticities from just a few. These
conditions are also referred to as
“restrictions” on elasticities.
Homogeneity Condition
 States that for any good the sum of its own price
elasticity, all of the cross price elasticities associated
with the good, and its income elasticity =0

Eii  Ei1  Ei 2  Ei 3  ...  Eiy  0

Implications of this are:
1. Cross-price elasticities are large (close substitutes exist) then
the good’s own price elasticity must also be large (in terms of
absolute value) or, in other words, less elastic.
2. If the cross-price elasticities are small then both the own-price elasticity
will tend to be more inelastic and will more closely resemble the
income elasticity in absolute value.
Symmetry Condition
 The symmetry condition indicates what the
relationship between cross-price elasticities
must be.

Rj
Eij         E ji  R j ( E jy  Eiy )
Ri

Where the “R” represent the proportion of income spent on that
good. This implies that cross-price elasticities are symmetric, i.e.,
Eij  E ji , when the proportion of income spent on both goods is equal
and their income elasticities are also equal.
Example Using Symmetry Condition
 Lamb = 0.1% of expenditures
 Beef = 2% of expenditures
 If a 1% increase in the price of beef increases
demand for lamb by 0.6% (i.e., cross price elasticity
of beef on lamb of 0.6 (i.e., E  0.6 )LB

0.001
EBL          (0.6)  0.03
0.02
Or, assuming that the income elasticities are equal then a 1% change in
the price of lamb will only result in a .03% change in the quantity of beef
demanded even though a 1% change in the price of beef will generate
a 0.6% change in the quantity of lamb demanded.
Engle Aggregation Condition
 The Engle Aggregation condition states that the sum
of all the income elasticities weighted by the
proportion of income spent on each good equals 1.
For “n” goods”

R1 E1Y  R2 E2Y  ...  Rn Eny  1

If proportion of income spent on a good changes, then the income
elasticities and proportions of incomes spent on the other goods must
change to offset it.
Price Flexibilities
 Elasticities assume that Q adjusts to changes
in P, but in the case of agricultural
commodities, P must typically adjust to what
Q is. That is, Q is often fixed during a given
production period or, in general, is not able to
adjust much in relative terms after a
production decision is made. As a result, P
must adjust to this Q rather than the other
way around.
 The responsiveness of P to changes in Q is
called the “flexibility.”
Price Flexibility Cont’
 F = % changes in P as quantity changes.
 Flexibilities are useful in studying agricultural
commodity markets because supply is often fixed or
close to being fixed because:
   Seasonal nature of supply
   Perishability
   Biological lag in reacting to price signals

P Q
F
Q P
Relationship Between Flexibilities and
Elasticities

1
FD     ?
ED

The flexibility is actually a lower bound for the elasticity
Relationships Among Flexibilities
 Demand is inelastic if FD  1
 Demand is elastic if       FD  1

 Substitutes if   Fij  0

 Compliments if Fij  0

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