aaec 3315 agricultural price theory chapter 3 market demand and elasticity
TRANSCRIPT
AAEC 3315Agricultural Price Theory
Chapter 3
Market Demand and Elasticity
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
Market Demand
Earlier, we derived the demand curve for an individual consumer that will maximize their utility based upon their preferences and budget constraint.
Remember that we derived an individual consumer’s demand curve from his/her Price Consumption curve (PCC).
The Demand Curve represents quantity demanded at various price levels.
Q
P
Individual DemandCurve
P1
P2
Q1 Q2
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.
Q
P
P1
P2
Q1 Q2
D1
D2
Market Demand
Given the two demand curves D1 and D2 Note that
at price=$2,Consumer 1 buys 10 unitsConsumer 2 buys 20 units Thus the market demand at P=$2 is 30 units
At price=$1,Consumer 1 buys 22 unitsConsumer 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 consumer’s demand curves.
Q
P
$2
$1
10 22
D1
D2
20 30 52
Market Demand
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.
Q
P
P1
P2
Q1 Q2
Market Demand
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.
Q
P
D
D1
D2
Functional Relationship for Demand
Market Demand Function-Qd = f (P, T, I, R, N)Where,P = Own PriceT = Tastes of consumersI = Consumer IncomeR = Price of related goodsN = # of consumers in the market place
An example demand function for beer;Qb = 100 – 30 Pb – 20 Pc + .005IWhere, 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
Q
P1
P2
Q1 Q2
Market Demand
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 + 125Qb = 55 billion 6-packs.
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 by 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.
Own Price Elasticity of Demand (ED)
Own Price Elasticity of demand is defined as the percentage change in the quantity demanded relative to a percentage change in its own price.
Calculating Own Price Elasticity of Demand from a Demand Function:
Using calculus:Q
P
P
QEd
Own Price Elasticity of Demand (ED)
Given a demand function:Qb = 100 – 30 Pb – 20 Pc + .005I, where, Qb = Quantity demanded of beer in billion 6-packs, Pb = Price of beer per 6-pack ($5), Pc = Price of a pack of chips ($1), and I = Annual household income ($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:
7272.255
5)30(
Q
P
P
QEd
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
Classifications of Own-Price Elasticity of Demand
Classifications: Inelastic demand ( |ED| < 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| > 1 ): a change in price brings about a relatively larger change in quantity demanded (ex. expensive wine).
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.
Calculating Cross Price Elasticity of Demand from a Demand Function:
Using calculus:y
x
x
ydyx
Q
P
P
QE
Cross Price Elasticity of Demand (Edyx)
Given a demand function:Qb = 100 – 30 Pb – 20 Pc + .005I, where, Qb = Quantity demanded of beer in billion 6-packs, Pb = Price of beer per 6-pack ($5), Pc = Price of a pack of chips ($1), and I = Annual household income ($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:
3636.055
1)20(
b
c
c
bdbc
Q
P
P
QE
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 > 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 < 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)
Income Elasticity of Demand (EI)
Shows the percentage change in the quantity demanded of good Y in response to a percentage change in Income.
Calculating Income Elasticity of Demand from a Demand Function:
Using calculus: y
yI
Q
I
I
QE
Income Elasticity of Demand (EI)
Given a demand function:Qb = 100 – 30 Pb – 20 Pc + .005I, where, Qb = Quantity demanded of beer in billion 6-packs, Pb = Price of beer per 6-pack ($5), Pc = Price of a pack of chips ($1), and I = Annual household income ($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:
2727.255
25000)005.0(
b
bI
Q
I
I
QE
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 > 0, then the good is considered a normal good (ex.
beef). If EI < 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
Market Demandfrom the Seller’s Perspective
Consumer demand or consumer expenditure is the receipt or revenue for the seller.
So, let us look at demand from the other side of the market, i.e., the seller side of the market.
Total Revenue: From the market demand, we can easily determine the total revenue of the seller at each price by multiplying the price per unit by the quantity sold a that price TR = P. Q And let’s say TR = 20 Q – 0.5 Q2
Market Demandfrom the Seller’s Perspective
Average Revenue: Average revenue is simply the total revenue divided by quantity. AR = P. Q / Q = P Or, for TR = 20 Q – 0.5 Q2
AR = 20 – 0.5 Q
Marginal Revenue: Marginal revenue is the amount of change or addition to the total revenue attributed to the addition of 1 unit to sales. MR = ∂TR/∂Q Or, for TR = 20 Q – 0.5 Q2
MR = 20 – 1Q
Market Demandfrom the Seller’s Perspective
Given that
AR = 20 – 0.5 Q
MR = 20 – 1Q Note that both AR and MR have
the same y-intercept. Also note that the MR has a
slope twice as that of the slope of the AR.
Graphically, this means that both the AR and MR curves have the same price-axis intercept and the MR curve is twice as steep as the AR or the demand curve.
P
Q
AR orMarket Demand
MR
Relationships Among AR, MR, and TR
AR = Demand MR curve is twice as steep as
the AR Curve MR is the slope of the TR
Curve As long as MR is + ve, TR is
increasing with output When MR = 0, TR is at its
maximum When MR is – ve, TR
declines When AR = 0, TR = 0
$/unit
Q
AR orMarket Demand
MR
Q
$
TR
Relationships Among Price, MR, and Elasticity of Demand
1
1
.
11.1
).()(
PMR
QP
PQ
PQ
P
P
QPMR
Q
PQPMR
Q
PQ
Q
QPMR
Q
QP
Q
TRMR
Note that the price elasticity of demand is always negative; thus in using this relationship, the elasticity coefficient must always be entered as a negative number.
Relationships Among Price Elasticity of Demand, MR and TR
Remember that :
1
1PMR
When η is elastic MR is positive When η is unitary MR = 0 When η is inelastic MR is negative
Now Let us look at TR
Q
AR orMarket Demand
$/unit
MR > 0
Elastic
Inelastic
Unitarily Elastic
MR = 0MR < 0
Q
$
TR
η MR TR when P TR when P
Elastic Positive Increases Decreases
Unitary Zero Constant Constant
Inelastic Negative Decreases Increases