Elasticity and Demand

Elasticity and Demand

Elasticity concept is very important to business decisions.

It measures the responsiveness of quantity demanded to changes in price

It is also important for public policy-makers when dealing with tax issues on commodities – if we increase cigarette taxes, what will happen to the consumption of cigarettes?

The Coefficient of Demand Elasticity

The coefficient of demand elasticity is defined as the ratio of the percentage change in quantity demanded to the percentage change in price.

P

QE

%

%

Classifying Elasticity Numbers

Elasticity Responsiveness Coefficient Value

Elastic |%Q| > |%P| |E| > 1

Unitary Elastic |%Q| = |%P| |E| = 1

Inelastic |%Q| < |%P| |E| < 1

Using Elasticity Information

Suppose we know that the price elasticity of demand for automobiles is –4.0 and manufactures plan on increasing auto prices by 10% this year. What doe we predict will happen to the number of automobiles that will be sold?

P

QE

%

%

Answer:-4.0 = X/0.10 orX = (-4.0)0.10 orX = -0.40

Thus, we predict a 40 percent reduction in quantity demanded

Elasticity and Total Revenue

Total Revenue(TR) is merely the firms sales measured in dollar terms.

It can be obtained by taking the price(P) of a product times the number of units sold(Q).

TR = P x Q Remember that demand curves are negatively

sloped – so quantity demanded will decrease when price is increased and vice-versa.


TR = P x Q For any price change, if quantity demanded

remains constant, total revenue will move in the same direction. This is often referred to as the price effect on total revenue.

However, in most cases quantity demanded will not remain constant but will move in the opposite direction of price. This will be the quantity effect.


To determine what happens to TR when price is changed requires looking at the relative sizes of the price and quantity effects – which is embodied in the elasticity coefficient.


What happens to TR if price increases and demand is elastic?

TR = P X Q


What happens to TR if price increases and demand is inelastic?

TR = P X Q

Elasticity and Total RevenueElastic Inelastic Unitary

Q effect dominates

P effect dominates

No effect dominates

Price rises TR falls TR rises No change in TR

Price falls TR rises TR falls No change in TR

Factors Affecting Demand Elasticity

Three Important Factors Related to Elasticity– Availability of substitutes – directly related to

elasticity– Percentage of a consumer’s budget – directly

related to elasticity– Time period of adjustment – directly related to

elasticity

Calculating Demand Elasticity

Two basic “types” of elasticity that can be calculated.– Arc elasticity

• compute elasticity over an arc or interval on the demand curve

• very imprecise if interval is wide

– Point elasticity• compute elasticity at a point on the demand curve

• very precise

Computing Arc Elasticity

PAVEP

QAVEQ

E

Calculating Point ElasticityLinear Demand: P=a+bQ

aP

PE

Calculating Point ElasticityAn Application

Suppose the demand for a good is P=1000-20Q, calculate the point price elasticity of demand at a price of $800.

4200

800

1000800

800

aP

PE

Elasticity Along a Demand Curve

If a demand curve is negatively sloped and linear, – the elasticity will vary from point to point– elasticity will be higher the higher the price

Q

P

P

Q

P

P

Q

Q

PP

QQ

E

Reciprocal of slope

Other Elasticities

Elasticity is a concept from applied mathematics.

It can be applied to any functional relationship.

We develop two additional demand elasticities– Income– Cross price

Income Elasticity

Measures the responsiveness of quantity demanded to changes in income.

M

QEM

%

%

Income Elasticity

M

QEM

%

%

If EM is positive we have a normal good.

If EM is negative we have an inferior good.

Cross Price Elasticity

Measures the responsiveness of one good to a change in the price of another good.

Y

XXY P

QE

%

%

Cross Price Elasticity

Y

XXY P

QE

%

%

If cross price elasticity is positive, goods X and Y are substitutes.

If cross price elasticity is positive, goods X and Y are complements.

If cross price elasticity is zero, goods X and Y are independent.

Demand, Marginal Revenue, and Elasticity

Marginal Revenue (MR) is the change in Total Revenue(TR) in response to increasing output (Q) by a single unit.

MR is the slope of the total revenue curve. MR is also the derivative of the total

revenue function.

Note corrections from originals.

Relationships

If Demand: P=100-2Q (note linear) TR = PQ = (100-2Q)Q = 100Q-2Q2

MR = TR`= 100-4Q– MR is also linear– MR has same intercept as demand– MR decreases at twice the rate of demand– MR will always be less than price for all units

sold but the first

Relationship between MR, P & E

1

1

EPMR

What if E = -0.5? Note inelastic.

What if E=-4.0? Note elastic.

See Figure 3.7.

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Elasticity and Demand