1 Elasticity Chapter 5. 2 ELASTICITY elasticity A general concept used to quantify the response in one variable when another variable changes

1

Elasticity

Chapter 5

2

ELASTICITY

elasticity A general concept used to quantify the response in one variable when another variable changes.

B

ABA

%

% respect to with of elasticity

3

PRICE ELASTICITY OF DEMAND

SLOPE AND ELASTICITY

Slope Is Not a Useful Measure of Responsiveness

4


price elasticity of demand The ratio of the percentage of change in quantity demanded to the percentage of change in price; measures the responsiveness of demand to changes in price.

pricein change %

demandedquantity in change % demand of elasticity price

5


TYPES OF ELASTICITY

Elastic-3.0-30%+10%Bananas

Unitarily elastic-1.0-10%+10%Beef

Inelastic-0.1-1%+10%Basic telephone service

Perfectly inelastic0.0

ELASTICITY(% QD ÷ %P)

0%

% CHANGEIN QUANTITY DEMANDED

(% QD)

+10%Insulin

% CHANGE INPRICE(% P)PRODUCT

Hypothetical Demand Elasticities for Four Products

Elastic-3.0-30%+10%Bananas

Unitarily elastic-1.0-10%+10%Beef

Inelastic-0.1-1%+10%Basic telephone service

Perfectly inelastic0.0

ELASTICITY(% QD ÷ %P)

0%

% CHANGEIN QUANTITY DEMANDED

(% QD)

+10%Insulin

% CHANGE INPRICE(% P)PRODUCT

Hypothetical Demand Elasticities for Four Products

6


perfectly inelastic demand Demand in which quantity demanded does not respond at all to a change in price.

inelastic demand Demand that responds somewhat, but not a great deal, to changes in price. Inelastic demand always has a numerical value between zero and -1.

inelastic if % change in quantity demanded < % change in price

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Perfectly Elastic and Perfectly Inelastic Demand Curves

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A warning: You must be very careful about signs. Because it is generally understood that demand

elasticities are negative (demand curves have a negative slope), they are often reported and discussed without the negative sign.

For example, a technical paper might report that the demand for housing “appears to be inelastic with respect to price, or less than 1 (0.6).” What the writer means is that the estimated elasticity is -.6,

which is between zero and -1. Its absolute value is less than 1.

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unitary elasticity A demand relationship in which the percentage change in quantity of a product demanded is the same as the percentage change in price in absolute value (a demand elasticity of -1).

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elastic demand A demand relationship in which the percentage change in quantity demanded is larger in absolute value than the percentage change in price (a demand elasticity with an absolute value greater than 1).

perfectly elastic demand Demand in which quantity drops to zero at the slightest increase in price.

elastic if % change in quantity demanded > % change in price

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A good way to remember the difference between the two “perfect” elasticities is:

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CALCULATING ELASTICITIES

CALCULATING PERCENTAGE CHANGES To calculate percentage change in quantity

demanded using the initial value as the base, the following formula is used:

100% x demandedquantity in change

demandedquantity in change %1Q

100% x -

1

12

Q

QQ

13


We can calculate the percentage change in price in a similar way. Once again, let us use the initial value of P—that is, P1—as the base for calculating the percentage. By using P1 as the base, the formula for calculating the percentage of change in P is simply:

100% x pricein change

pricein change %1P

100% x -

1

12

P

PP

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ELASTICITY IS A RATIO OF PERCENTAGES Once all the changes in quantity demanded and

price have been converted into percentages, calculating elasticity is a matter of simple division. Recall the formal definition of elasticity:

pricein change %

demandedquantity in change % demand of elasticity price

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THE MIDPOINT FORMULA midpoint formula A more precise way of calculating

percentages using the value halfway between P1 and P2 for the base in calculating the percentage change in price, and the value halfway between Q1 and Q2 as the base for calculating the percentage change in quantity demanded.

100% x 2 / ) (

demandedquantity in change demandedquantity in change %

21 QQ

100% x 2 / ) (

-

21

12

QQ

QQ

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Using the point halfway between P1 and P2 as the base for calculating the percentage change in price, we get

100% x 2 / ) (

pricein change pricein change %

21 PP

100% x 2 / ) (

-

21

12

PP

PP

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ELASTICITY CHANGES ALONG A STRAIGHT-LINE DEMAND CURVE

Demand Curve for Lunch at the

Office Dining Room

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10121416182022

$1110

9876543210

QUANTITY DEMANDED(LUNCHES PER MONTH)

PRICE(PER LUNCH)

Demand Schedule for Office Dining Room Lunches

02468

10121416182022

$1110

9876543210

QUANTITY DEMANDED(LUNCHES PER MONTH)

PRICE(PER LUNCH)

Demand Schedule for Office Dining Room Lunches

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ELASTICITY AND TOTAL REVENUE In any market, P x Q is total revenue (TR) received

by producers:

When price (P) declines, quantity demanded (QD) increases. The two factors, P and QD, move in opposite directions:

TR = P x Qtotal revenue = price x quantity

Effects of price changeson quantity demanded:

and

D

D

QP

QP

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Because total revenue is the product of P and Q, whether TR rises or falls in response to a price increase depends on which is bigger, the percentage increase in price or the percentage decrease in quantity demanded.

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If the percentage decline in quantity demanded following a price increase is smaller than the percentage increase in price, total revenue will rise.

If the percentage decline in quantity demanded following a price increase is larger than the percentage increase in price, total revenue will fall.

Effects of price increase ona product with elastic demand: x D TRQP

Effects of price increase ona product with inelastic demand: x D TRQP

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The opposite is true for a price cut. When demand is elastic, a cut in price increases total revenues:

When demand is inelastic, a cut in price reduces total revenues:

effect of price cut on a productwith elastic demand: x D TRQP

effect of price cut on a productwith inelastic demand: x D TRQP

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THE DETERMINANTS OF DEMAND ELASTICITY

AVAILABILITY OF SUBSTITUTES Perhaps the most obvious factor affecting demand elasticity is

the availability of substitutes.

THE TIME DIMENSION The elasticity of demand in the short run may be very different

from the elasticity of demand in the long run. In the longer run, demand is likely to become more elastic, or

responsive, simply because households make adjustments over time and producers develop substitute goods.

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OTHER IMPORTANT ELASTICITIES

INCOME ELASTICITY OF DEMAND income elasticity of demand Measures the

responsiveness of demand to changes in income.

incomein change %

demandedquantity in change % demand of elasticity income

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CROSS-PRICE ELASTICITY OF DEMAND cross-price elasticity of demand A measure

of the response of the quantity of one good demanded to a change in the price of another good.

X

Y

of pricein change %

demanded ofquantity in change % demand of elasticity price-cross

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ELASTICITY OF SUPPLY elasticity of supply A measure of the response

of quantity of a good supplied to a change in price of that good. Likely to be positive in output markets.

pricein change %

suppliedquantity in change % supply of elasticity

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POINT ELASTICITY

Elasticity at a Point Along a Demand Curve

Consider the straight-line demand curve. We can write an expression for elasticity at point C as follows:

1

1

1

1 QQ

100

100 QQ

%

% elasticity

Q

P

P

Q

PP

PPP

Q

1

1

1

1 QQ

100

100 QQ

%

% elasticity

Q

P

P

Q

PP

PPP

Q

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POINT ELASTICITY

Note that Q/P is the reciprocal of the slope of the

curve.

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Point Elasticity Changes Along

a Demand Curve

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1 Elasticity Chapter 5. 2 ELASTICITY elasticity A general concept used to quantify the response in one variable when another variable changes