AAEC 3315 Agricultural Price Theory

1
AAEC 3315Agricultural Price Theory

• Chapter 3
• Market Demand and Elasticity

2
Market Demand

• To Gain an Understanding of
• Derivation of Market Demand
• Demand Functions
• Own Price Elasticity of Demand
• Cross Price Elasticity of Demand
• Income Elasticity of Demand

3
Market Demand

• Earlier, we derived the demand curve
• Shows utility-maximizing consumption decisions
• Remember that we derived an individual consumers
  demand curve from his/her Price Consumption curve
  (PCC).
• The Demand Curve represents quantity demanded at
  various price levels.

P
P1
P2
Individual Demand Curve
Q
Q1
Q2
4
Market Demand Curve

• D1 is the demand curve for consumer 1.
• For every single consumer there will be a
  separate demand curve.
• If we have two consumers in the market, then we
  will have two individual demand curves, D1 and D2.

P
P1
P2
D2
D1
Q
Q1
Q2
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Market Demand

• Given the two demand curves D1 and D2
• Note that
• at price2,
• Consumer 1 buys 10 units
• Consumer 2 buys 20 units
• Thus the market demand at P2 is 30 units
• At price1,
• Consumer 1 buys 22 units
• Consumer 2 buys 30 units.
• Thus the market demand is 52 units.
• Thus, the aggregate or market demand is obtained
  by the horizontal summation of all individual
  consumers demand curves.

P
Market Demand
2
1
D2
D1
10
22
Q
20
30
52
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Market Demand

• Market Demand - a schedule showing the amounts of
  a good consumers are willing and able to purchase
  in the market at different price levels during a
  specified period of time.
• Change in its own price results in a movement
  along the demand curve.

P
P1
P2
Market Demand
Q
Q1
Q2
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Factors that Shift the Demand Curve

• Population
• Tastes
• Income
• Normal good
• Inferior good
• Price of Related Goods
• Substitutes - increase in the price of a
  substitute, the demand curve for the related good
  shifts outward ( vice versa)
• Complements - increase in the price of a
  complement, the demand curve for the related good
  shifts inward ( vice versa)
• Expectations
• Expectations about future prices, product
  availability, and income can affect demand.

P
D1
D
D2
Q
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Functional Relationship for Demand

• Market Demand Function-
• Qd f (P, T, I, R, N)
• Where,
• P Own Price
• T Tastes of consumers
• I Consumer Income
• R Price of related goods
• N of consumers in the market place
• An example demand function for beer
• Qb 100 30 Pb 20 Pc .005I
• Where,
• Qb Quantity demanded of beer in billion
  6-packs
• Pb Price of beer per 6-pack
• Pc Price of a pack of chips
• I Annual household income

P
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Working with a Demand Function

• Suppose the demand function for beer is given by
• Qb 100 30 Pb 20 Pc .005I, where, Qb
  Quantity demanded of beer in billion 6-packs, Pb
  Price of beer per 6-pack, Pc Price of a pack
  of chips, and I Annual household income.
• If the price of a 6-pack of beer is 5, price of
  a bag of chips is 1, and the annual household
  income is 25,000 per year, what would be the
  total quantity of beer that will be sold per
  year?
• Qb 100 30(5) 20(1) .005(25000)
• Qb 100 150 20 125
• Qb 55 billion 6-packs.

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Responsiveness of the Quantity Demanded to a
Price Change

• Earlier, we indicated that, ceteris paribus, the
  quantity of a product demanded will vary
  inversely to the price of that product. That is,
  the direction of change in quantity demanded
  following a price change is clear.
• What is not known is the extent to which quantity
  demanded will respond to a price change.
• To measure the responsiveness of the quantity
  demanded to change in price, we use a measure
  called PRICE ELASTICITY OF DEMAND.

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What Determines Price Elasticity of Demand?

• Availability of close substitutes
• How a product is defined can affect how well
  other products substitute for it
• Budgetary importance
• Price elasticity is low for goods that are
  relatively inexpensive
• Time frame
• Price might affect demand more in the long run,
  as consumers adjust

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Own Price Elasticity of Demand (ED)

• Own Price Elasticity of demand is defined as the
  percentage change in the quantity demanded
  resulting from a 1 percent change in its own
  price.
• Point Elasticity of Demand When changes in
  quantity demanded and price are small, the
  elasticity measure is called point elasticity
  because it measures the elasticity at a point on
  the demand curve.
• Algebraically

(1/-25)X(125/1) - 0.04x125 -
5 (2/-50)x(100/2) - 0.04x50 -
2 (1/-40)x(50/4) - 0.025x12.5 - 0.3
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Own Price Elasticity of Demand (ED)

• Arc Elasticity of Demand When changes in
  quantity demanded and price are large, we employ
  the concept of Arc Elasticity of Demand that uses
  the average value of price and quantity.
• Algebraically

(1/-25)X(225/3) - 0.04x75 -
3 (2/-50)x(150/6) - 0.04x25 -
1 (1/-40)x(60/9) - 0.025x6.67 - 0.17
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Own Price Elasticity of Demand (ED)

• Calculating Own Price Elasticity of Demand from a
  Demand Function
• Using calculus
• Given a demand function
• Qb 100 30 Pb 20 Pc .005I
• Let Pb 5,
• Pc 1, and
• I 25,000
• Qb 100 30(5) 20(1) .005(25000) 55
• Taking partial derivative of the demand function
  with respect to price and substituting values for
  P and Q we get

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Using Own Elasticity of Demand

• Elasticity is a pure ratio independent of units.
• Since price and quantity demanded generally move
  in opposite direction, the sign of the elasticity
  coefficient is generally negative.
• Interpretation If ED - 2.72 A one percent
  increase in price results in a 2.72 decrease in
  quantity demanded

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Classifications of Own-Price Elasticity of Demand

• Classifications
• Inelastic demand ( ED lt 1 ) a change in price
  brings about a relatively smaller change in
  quantity demanded (ex. gasoline).
• Unitary elastic demand ( ED 1 ) a change in
  price brings about an equivalent change in
  quantity demanded.
• Elastic demand ( ED gt 1 ) a change in price
  brings about a relatively larger change in
  quantity demanded (ex. expensive wine).

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Cross Price Elasticity of Demand

• Shows the percentage change in the quantity
  demanded of good Y in response to a change in the
  price of good X.
• EDYX Change in QDY / change in PX
• Algebraically
• Read as the cross-price elasticity of demand for
  commodity Y with respect to commodity X.
• Units of Y demanded Price of X EDYX___________
• 60 10
• 40 12
• (-20/2)x(10/60) - 1.66

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Cross Price Elasticity of Demand (Edyx)

• Calculating Cross Price Elasticity of Demand from
  a Demand Function
• Using calculus
• Given a demand function
• Qb 100 30 Pb 20 Pc .005I,
• Pb 5,
• Pc 1, and
• I 25,000
• Qb 100 30(5) 20(1) .005(25000) 55
• Taking partial derivative of the demand function
  for beer with respect to price of chips and
  substituting values for Pc and Q we get

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Classification of Cross-price elasticity of
Demand

• Interpretation
• If Edyx - 0.36 A one percent increase in
  price of chips results in a 0.36 decrease in
  quantity demanded of beer
• Classification
• If (Edyx gt 0) implies that as the price of good
  X increases, the quantity demanded of Good Y also
  increases. Thus, Y and X are substitutes in
  consumption (ex. chicken and pork).
• (Edyx lt 0) implies that as the price of good X
  increases, the quantity demanded of Good Y
  decreases. Thus Y X are Complements in
  consumption (ex. bear and chips).
• (Edyx 0) implies that the price of good X has
  no effect on quantity demanded of Good Y. Thus,
  Y X are Independent in consumption (ex. bread
  and coke)

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Income Elasticity of Demand (EI)

• Shows the percentage change in the quantity
  demanded of good Y in response to a percentage
  change in Income.
• EI Change in QY / change in I
• Algebraically
• Units of Y demanded Income EI
• 100 1200
• 150 1600

(50/400)x(1200/100) 1.5
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Income Elasticity of Demand (EI)

• Calculating Income Elasticity of Demand from a
  Demand Function
• Using calculus
• Given a demand function
• Qb 100 30 Pb 20 Pc .005I, where,
• Pb 5,
• Pc 1, and
• I 25,000
• Qb 100 30(5) 20(1) .005(25000) 55
• Taking partial derivative of the demand function
  with respect to income and substituting values
  for Q and I we get

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Income Elasticity of Demand (EI)

• Interpretation
• If EI 2.27 A one percent increase income
  results in a 2.27 increase in quantity demanded
  of beer
• Classification
• If EI gt 0, then the good is considered a normal
  good (ex. beef).
• If EI lt 0, then the good is considered an
  inferior good (ex. roman noodles)
• High income elasticity of demand for luxury goods
• Low income elasticity of demand for necessary
  goods