B.  Elasticity

• Measures responsiveness of one variable to changes in other variables

η = %ΔY / %ΔX

.

1.  Price elasticity of demand

• Measures how sensitive quantity demanded is to changes in the price

η_D = %ΔQ_D / %ΔP

.

a. Calculation

ηD = %ΔQD / %ΔP =

Ex. - P₁ = 10, Q₁ = 200, P₂ = 20, Q₂ = 120

ηD =

= -0.75

Interpretation:  1% increase in P                             => 0.75% decrease in QD

.

b. Categorizing goods

| η_D | > 1     => | %ΔQ_D / %ΔP | > 1    =>  | %ΔQ_D | > | %ΔP |      => elastic

| η_D | = 1     => | %ΔQ_D / %ΔP | = 1    =>  | %ΔQ_D | = | %ΔP |   => unit elastic

| η_D | < 1     => | %ΔQ_D / %ΔP | < 1    =>  | %ΔQ_D | < | %ΔP |      => inelastic

.

c. Factors affecting the price elasticity

(1)  Availability of substitutes

More substitutes => higher elasticity

Less substitutes => lower elasticity

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(2)  Proportion of total expenditures spent on good

Larger proportion => higher elasticity

Smaller proportion => lower elasticity

.

(3)  Unique features

Has unique features => lower elasticity

No unique features => higher elasticity

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(4)  Input used to produce final good

Elasticity of final good higher => higher elasticity

Elasticity of final good lower => lower elasticity

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(5)  Comparisons with substitute products

Comparison easy => higher elasticity

Comparison hard => lower elasticity

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(6)  Tax deductions or insurance

Expenditure tax deductible or covered by insurance => lower elasticity

Expenditure not tax deductible or not covered by insurance => higher elasticity

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(7)  Switching costs

High switching costs => lower elasticity

Low switching costs => higher elasticity

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(8)  Complements

Complementary product => lower elasticity

Not complementary => higher elasticity

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(9)  Brand-level vs. industry-level

Brand-level => higher elasticity

Industry-level => lower elasticity

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(10)  Adjustment time

Longer time => higher elasticity

Shorter time => lower elasticity

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d. Elasticity and the demand curve

(1)  Linear demand

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(2)  Elasticity and the steepness of the demand curve

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(3)  Extreme cases

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e.  Elasticity and revenue

• TR = total revenue = P * Q

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(1)  Elastic demand

| ηD | > 1 => | %ΔQD / %ΔP | > 1 =>  | %ΔQD | > | %ΔP | P QD TR

.

(2)  Inelastic demand

| ηD | < 1 => | %ΔQD / %ΔP | < 1 =>  | %ΔQD | < | %ΔP | P QD TR

f.  Total revenue, marginal revenue, and demand

(1)  Marginal revenue

• Marginal revenue = ΔTR / ΔQ

(2)  Total revenue

2.  Income elasticity

• Measures how sensitive quantity demanded is to changes in income

η_I = %ΔQ_D / %ΔI

.

a.  Calculation

ηI = %ΔQD / %ΔI =

Ex. - I₁ = 40,000, Q₁ = 22, I₂ = 60,000, Q₂ = 28

ηI =

= +0.6

Interpretation:  1% increase in income                           => 0.6% increase in QD

b.  Categorizing goods

η_I < 0 => inferior good

η_I > 0 => normal good

η_I < 1 => noncyclical normal good

η_I > 1 => cyclical normal good

.

3.  Cross-price elasticity

• Measures how sensitive quantity demanded of one product is to changes in the price of another product

η_X,Y = %ΔQ_Y / %ΔP_X

.

a.  Calculation

ηX,Y = %ΔQY / %ΔPX =

Ex. - P_X1 = 9, Q_Y1 = 45, P_X2 = 11, Q_Y2 = 35

ηX,Y =

= -1.25

Interpretation:  1% increase in PX                           => 1.25% decrease in QY

b.  Categorizing goods

η_X,Y > 0 => substitutes  (P_X increases, Q_X decreases, Q_Y increases)

η_X,Y = 0 => no relationship

η_X,Y < 0 => complements  (P_X increases, Q_X decreases, Q_Y decreases)

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4.  Price elasticity of supply

• Measures how sensitive quantity supplied is to changes in income

η_S = %ΔQ_S / %ΔP

.

a.  Calculation

ηS = %ΔQS / %ΔP =

Ex. - P₁ = 49, Q_S1 = 2,400, P₂ = 51, Q_S2 = 2,600

ηS =

= +2.00

Interpretation:  1% increase in P                           => 2.00% increase in QS

b.  Elasticity and the supply curve

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5.  Elasticity estimates