Demand Elasticities and Related Coefficients

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Demand Elasticities and Related Coefficients Powered By Docstoc
					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 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
   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-
      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


                    10   20   30      40     50   60      70

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
 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
 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.

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

   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

 EBL          (0.6)  0.03
 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
            Q P
Relationship Between Flexibilities and

FD     ?

 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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