Econ 2020ch6

ECON 2020Priniciple of Microeconomics

Chapter 6: Elasticity

Hyeon Joon Shin

Assistant Professor of EconomicsThe Falls School of Business, Anderson University

Semester II, 2014-15

Shin (FSB, Anderson Univ.) Semester II, 2014-15 1 / 14

Price Elasticity of Demand

The law of demand says that, other things being equal, consumers buymore (or less) of a product, when its price declines (or rises).

ProblemConsider two products, gasoline and diamond. The price of gasoline pergallon is $2, and that of diamond per carat is $2,000. By the law ofdemand, when the price of each product rises, its quantity demandeddeclines. Suppose that both prices increase by the same rate of 10%.Which product�s quantity demanded would decline further? Explain why.

A Product�s Price Elasticity of Demand (Ed ) A measure of howmuch consumers buy more (or less) of it when its pricefalls (or rises).

A change in quantity demanded due to a price change varies product toproduct and over di¤erent price ranges for the same product.

Coe¢ cient of the Price Elasticity of Demand

Suppose that when the price of a good changes from P0to P

00, its

quantity demanded changes from Q0d to Q

The price elasticity of demand can be measured as the coe¢ cient Ed :

��percentage change in quantity demandedpercentage change in price

��=

��Q00d �Q

Q 0d� 100

P 00�P 0P 0

� 100

�� =��4QdQd

� 1004PP � 100

��=

��4Qd4P � PQd

��

4P = P 00 � P 0: change in price

4Qd = Q00d �Q

0d : change in quantity demanded

00, its

��=

��Q00d �Q

Q 0d� 100

P 00�P 0P 0

� 100

�� =��4QdQd

� 1004PP � 100

��=

��4Qd4P � PQd

��

4Qd = Q00d �Q

00, its

��=

��Q00d �Q

Q 0d� 100

P 00�P 0P 0

� 100

�� =��4QdQd

� 1004PP � 100

��=

��4Qd4P � PQd

��

4Qd = Q00d �Q

00, its

��=

��Q00d �Q

Q 0d� 100

P 00�P 0P 0

� 100

�� =��4QdQd

� 1004PP � 100

��=

��4Qd4P � PQd

��4P = P 00 � P 0

: change in price

4Qd = Q00d �Q

00, its

��=

��Q00d �Q

Q 0d� 100

P 00�P 0P 0

� 100

�� =��4QdQd

� 1004PP � 100

��=

��4Qd4P � PQd

��4P = P 00 � P 0

: change in price4Qd = Q

00d �Q

Coe¢ cient of the Price Elasticity of Demand (cont�d)

ProblemSuppose that quantity demanded of X is 20 at the price of $4, and it is 10at the price of $5. Calculate coe¢ cient of the price elasticity of demandfor X in both cases when the price rises from $4 to $5 and the price fallsfrom $5 to $4.

Co¢ cients of the price elasticity of demand in both cases should be thesame. Unfortunately, however, they are NOT.Therefore, we use the midpoint formula for calculating elasticity.

P = average of two pricesQd = average of two quantities demanded

We ignore the minus sign and simply present the absolute value of thecoe¢ cient Ed .

ProblemRedo the above problem, using the midpoint formula.

Co¢ cients of the price elasticity of demand in both cases should be thesame. Unfortunately, however, they are NOT.

Therefore, we use the midpoint formula for calculating elasticity.

P = average of two prices

Qd = average of two quantities demanded

Interpretation of Ed

Elastic vs. inelastic demand:

Ed > 1 : elastic

Ed < 1 : inelastic

Ed = 1 : unit-elastic

Demand is elastic when a speci�c percentage change in price results ina larger percentage change in quantity demanded.Demand is inelastic when a speci�c percentage change in price resultsin a smaller percentage change in quantity demanded.Demand is unit-elastic when a speci�c percentage change in priceresults in the same percentage change in quantity demanded.

Interpretation of EdElastic vs. inelastic demand:

Ed > 1 : elastic

Ed < 1 : inelastic

Ed > 1 : elastic

Ed < 1 : inelastic

Demand is elastic when a speci�c percentage change in price results ina larger percentage change in quantity demanded.

Demand is inelastic when a speci�c percentage change in price resultsin a smaller percentage change in quantity demanded.Demand is unit-elastic when a speci�c percentage change in priceresults in the same percentage change in quantity demanded.

Ed > 1 : elastic

Ed < 1 : inelastic

Demand is elastic when a speci�c percentage change in price results ina larger percentage change in quantity demanded.Demand is inelastic when a speci�c percentage change in price resultsin a smaller percentage change in quantity demanded.

Demand is unit-elastic when a speci�c percentage change in priceresults in the same percentage change in quantity demanded.

Ed > 1 : elastic

Ed < 1 : inelastic

Interpretation of Ed (cont�d)

Perfectly elastic vs. perfectly inelastic demand:

Ed = ∞ : perfectly elastic

Ed = 0 : perfectly inelastic

Demand is perfectly elastic when a percentage change in price resultsin zero quantity demanded.Demand is perfectly inelastic when a percentage change in priceresults in no change whatsoever in quantity demanded.

ProblemDerive the demand curve representing each of perfectly elastic demandand perfectly inelastic demand.

Demand is perfectly elastic when a percentage change in price resultsin zero quantity demanded.

Demand is perfectly inelastic when a percentage change in priceresults in no change whatsoever in quantity demanded.

Perfectly elastic vs. perfectly inelastic demand (cont�d)

The Total-Revenue (TR) Test

The Importance of Ed for Firms

Total Revenue (TR) The total amount of earnings that a sellerreceives from the sale of a product:

TR = P �Q

Total revenue is calculated by multiplying the product price (P) by thequantity sold (Q).In the theory of the �rm, Ed is related to the e¤ect of price changes ontotal revenue and thus on pro�t, other things being equal.

"When a �rm changes the price of a product, whether its total revenue(and thus its pro�t) rises or falls relies on the price elasticity of demandfor the product."

TR = P �Q

Total revenue is calculated by multiplying the product price (P) by thequantity sold (Q).

In the theory of the �rm, Ed is related to the e¤ect of price changes ontotal revenue and thus on pro�t, other things being equal.

TR = P �Q

The Relationship between Ed and TR

ExampleConsider a �rm that wants to increase the price of its product in order toincrease its total revenue (and thus its pro�t). Can the price increase raisethe �rm�s total revenue?

Case (1): elastic demand (Ed > 1)

P " and Q ## =) TR = (P �Q) #The �rm should not increase but decrease the price of the product.

Case (2): inelastic demand (Ed < 1)

P "" and Q # =) TR = (P �Q) "The �rm should increase the price of the product.

Case (3): unit-elastic demand (Ed = 1)

P " and Q # =) TR = (P �Q)No e¤ect of the price increase on total revenue

P " and Q ## =) TR = (P �Q) #

The �rm should not increase but decrease the price of the product.

P "" and Q # =) TR = (P �Q) "

The �rm should increase the price of the product.

P " and Q # =) TR = (P �Q)

No e¤ect of the price increase on total revenue

Price Elasticity along a Linear Demand Curve

Price Elasticity along a Linear Demand Curve and the TR Test

We know that price elasticity of demand varies with product to product.Also, price elasticity of demand varies over di¤erent price ranges of thesame linear demand curve.

ExamplePrice Elasticity of Demand for Movie Tickets and the TR Test:

Price Elasticity along a Linear Demand Curve and the TR TestWe know that price elasticity of demand varies with product to product.

Also, price elasticity of demand varies over di¤erent price ranges of thesame linear demand curve.

Price Elasticity along a Linear Demand Curve and the TR TestWe know that price elasticity of demand varies with product to product.Also, price elasticity of demand varies over di¤erent price ranges of thesame linear demand curve.

Price Elasticity along a Linear Demand Curve and the TR Test(cont�d)

Determinants of Price Elasticity of Demand

1 Substitutability

The more (or the less) substitutable products, the greater (or thesmaller) price elasticity of demand.

ExampleDemand for Snickers bar is highly elastic because it is very substitutable for others(e.g. Twix and Milky Way)

2 Luxuries vs. Necessities

The demand for a luxury good is elastic, whereas the demand for anecessary good is inelastic.

ExampleElectricity is regards as a necessity, so its demand is inelastic. Demand for Cruisetravel in the Atlantic Ocean is elastic.

Determinants of Price Elasticity of Demand1 Substitutability

Income Elasticity of Demand

Income Elasticity of Demand (EI ) A measure of how muchconsumers buy more or less of a good when theirincome changes:

EI =percentage change in quantity demanded

percentage change in income

=4Qd4I �

Normal Goods vs. Inferior Goods

EI > 0 : Normal GoodEI < 0 : Inferior Good

=4Qd4I �

EI > 0 : Normal Good

EI < 0 : Inferior Good

=4Qd4I �

Cross (Price) Elasticity of Demand

Cross Elasticity of Demand (EXY ) A measure of how muchconsumers buy more or less of good X when the price ofgood Y changes:

EXY =percentage change in quantity demanded of X

percentage change in price of Y

=4Qd ,X4PY

� PYQd ,X

Substitutes vs. Complements vs. Independent Goods

EXY > 0 : X and Y are substitutesEXY < 0 : X and Y are complementsEXY = 0 : X and Y are independent of each other

=4Qd ,X4PY

� PYQd ,X

=4Qd ,X4PY

� PYQd ,X

=4Qd ,X4PY

� PYQd ,X

EXY > 0 : X and Y are substitutes

EXY < 0 : X and Y are complementsEXY = 0 : X and Y are independent of each other

=4Qd ,X4PY

� PYQd ,X

EXY > 0 : X and Y are substitutesEXY < 0 : X and Y are complements

EXY = 0 : X and Y are independent of each other

=4Qd ,X4PY

� PYQd ,X

Econ 2020ch6

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