Lecture Managerial economics (Ninth edition): Chapter 6 – Thomas, Maurice

Chapter 6 - Elasticity and demand. In this chapter, you will learn to: Explain how price elasticity of demand (E) is used to measure the responsiveness or sensitivity of consumers to a change in the price of a good, explain the role that price elasticity plays in determining how a change in the price of a commodity affects the total revenue (TR = P × Q) received, list and explain several factors that affect the elasticity of demand,...

Chapter 6

Elasticity and Demand

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• P & Q are inversely related by the law of

• The larger the absolute value of  E , the more sensitive  buyers are to a change in price

Price Elasticity of Demand (E)

% P

• Measures responsiveness or sensitivity

of consumers to changes in the price of

a good

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Price Elasticity of Demand (E)

Elasticity Responsiveness E

Elastic Unitary Elastic Inelastic

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Price Elasticity of Demand (E)

• Percentage change in quantity

demanded  can be predicted for a given

percentage change in price as:

• % Qd = % P x E

• Percentage change in price required for

a given change in quantity demanded can be predicted as:

• % P = % Qd ÷ E

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Price Elasticity & Total Revenue

Elastic

Quantity-effect dominates

• Percentage of consumer’s budget

• The greater the percentage of the consumer’s budget spent 

on the good, the more elastic is demand

• Time period of adjustment

• The longer the time period consumers have to adjust to price  changes, the more elastic is demand

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Calculating Price Elasticity of Demand

• Price elasticity can be calculated

by multiplying the slope of demand

quantity ( P/Q)

% Q E

% P

Q Q P P

 100

 100

Q P

P Q

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Calculating Price Elasticity of Demand

• Price elasticity can be measured at

an interval (or arc) along demand,

or at a specific point on the demand curve

• If the price change is relatively small, a point  calculation is suitable

• If the price change spans a sizable arc along the  demand curve, the interval calculation provides a better  measure

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Computation of Elasticity Over an Interval

• When calculating price elasticity of

demand over an interval of demand, use the interval or arc elasticity formula

E

Average  Average 

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Computation of Elasticity at a Point

• When calculating price elasticity at a

point on demand, multiply the slope of demand ( Q/ P), computed at the point

of measure, times the ratio P/Q, using

the values of P and Q at the point of

measure

• Method of measuring point elasticity

depends on whether demand is linear or curvilinear

Then express demand as , where

and the slope parameter

is

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Point Elasticity When Demand is Linear

• Compute elasticity using either of the two

formulas below which give the same value for E

Q    or   P A

W h e r e    and   ar e  value s  o f  pr ic e  and  quant it y d e m and e d

at  t h e  point  o f  m e as ur e  alo ng  d e m and , and  

is  t h e  pr ic e ­int e r c e pt  o f  d e m and

P Q

A ( a'/ b )

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Point Elasticity When Demand is Curvilinear

• Compute elasticity using either of two

equivalent formulas below

E

W h e r e    is  t h e  s lo pe  o f  t h e  c ur ve d  d e m and  at

t h e  po int  o f  m e as ur e ,   and   ar e  value s  o f  pr ic e  and   quant it y d e m and e d  at  t h e  po int  o f  m e as ur e , and    is  

t h e  pr ic e ­int e r c e pt  o f  t h e  t ang e nt  line  e x t e nd e

• For curvilinear demand, no general rule

about the relation between price and quantity

S pe c ial c as e  o f    wh ic h  h as  a c o ns t ant

pr ic e  e las t ic it y (e qual t o )  f o r  all pr ic e s 

b

Q aP

b

S pe c ial c as e  o f    wh ic h  h as  a c o ns t ant

pr ic e  e las t ic it y (e qual t o )  f o r  all pr ic e s 

b

Q aP

b

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Constant Elasticity of Demand

(Figure 6.3)

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Marginal Revenue

• Marginal revenue (MR) is the change

in total revenue per unit change in output

• Since MR measures the rate of

change in total revenue as quantity changes, MR is the slope of the total

revenue (TR) curve

TR MR

Q

Managerial EconomicsManagerial Economics

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18

Demand, MR, & TR (Figure 6.4)

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Demand & Marginal Revenue

• When inverse demand is linear, P 

= A + BQ   (A > 0, B < 0)

• Marginal revenue is also linear, intersects the  vertical (price) axis at the same point as demand, & 

is twice as steep as demand

       MR = A + 2BQ

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Linear Demand, MR, & Elasticity

(Figure 6.5)

Elastic       ( E > 1) Table 6.4

TR decreases as Q  increases       (P  decreases)

TR is maximized

TR increases as Q  increases     (P  decreases)

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Marginal Revenue & Price Elasticity

• For all demand & marginal revenue

curves, the relation between marginal revenue, price, & elasticity can be

expressed as

1 1

MR P

E

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Income Elasticity

• Income elasticity ( EM) measures the

responsiveness of quantity demanded

to changes in income, holding the price

of the good & all other demand determinants constant

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Cross-Price Elasticity

• Cross-price elasticity ( EXY) measures the

responsiveness of quantity demanded of good X to changes in the price of related good Y , holding the price of good X & all other demand determinants for good X

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Interval Elasticity Measures

• To calculate interval measures of

income & cross-price elasticities, the following formulas can be employed

R XR

R

P

Q E

Average  Average 

P

Q