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