Demand Elasticities and Related Coefficients

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Demand Elasticities and Related Coefficients
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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.)

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Elasticities

• Elasticities are used to estimate responsiveness
  of Q to changes in P and are in percentages so
  one can make comparisons across commodities

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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.

Point elasticity for own-price or At a given
point on a demand curve.
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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.

Arc elasticity
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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

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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) PQ
• 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.

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Example of Effect of Elasticity on Total Revenue

• If P100 and Q100, 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
  (10199.5).
• 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
  (10198.5).
• 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.

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Income Elasticity

• The income elasticity measures the sensitivity of
  quantity demanded to changes in income, other
  factors held constant

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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

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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)

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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 gt 0
• Inferior good Ey lt 0

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Cross-Price Elasticities

• Cross-price elasticities measure the
  responsiveness of demand for one good in relation
  to a change in price for another good.

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Characteristics of Cross-Price Elasticities

• If Eij gt 0 then the two goods are substitutes
• If Eij lt 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.

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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.

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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

• Implications of this are
• Cross-price elasticities are large (close
  substitutes exist) then
• the goods own price elasticity must also be
  large (in terms of
• absolute value) or, in other words, less
  elastic.
• 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.

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Symmetry Condition

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

Where the R represent the proportion of income
spent on that good. 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.
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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., )

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.
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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

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.
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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.

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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

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Relationship Between Flexibilities and
Elasticities
The flexibility is actually a lower bound for the
elasticity
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Relationships Among Flexibilities

• Demand is inelastic if
• Demand is elastic if
• Substitutes if
• Compliments if