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

P

Q

Q

P

P

Q

Point elasticity for own-price or

At a given point on a demandcurve.

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.

10

10

10

1

PP

PP

QQ

QQo

= Arc elasticity

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

Y

Q

Q

Y

Y

QEy

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-adding activities for food

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

01020304050607080

10 20 30 40 50 60 70

Income

Con

sum

pti

on

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 people tend to buy more and also buy higher 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.

i

j

j

iij Q

P

P

QE

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

0...321 iyiiiii EEEEE

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 theincome elasticity in absolute value.

Symmetry Condition

The symmetry condition indicates what the relationship between cross-price elasticities must be.

)( iyjyjjii

jij EERE

R

RE

Where the “R” represent the proportion of income spent on thatgood. This implies that cross-price elasticities are symmetric, i.e., , when the proportion of income spent on both goods is equal and their income elasticities are also equal.

jiij EE

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., )6.0LBE

03.0)6.0(02.0

001.0BLE

Or, assuming that the income elasticities are equal then a 1% change inthe price of lamb will only result in a .03% change in the quantity of beefdemanded even though a 1% change in the price of beef will generatea 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”

1...2211 nynYY ERERER

If proportion of income spent on a good changes, then the incomeelasticities and proportions of incomes spent on the other goods mustchange 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

Q

PF

Relationship Between Flexibilities and Elasticities

?1

DD EF

The flexibility is actually a lower bound for the elasticity

Relationships Among Flexibilities

Demand is inelastic if Demand is elastic if

Substitutes if

Compliments if

1DF

1DF

0ijF

0ijF