Demand and Elasticity

Consider the following cases:

Making Sales Targets

A Public Transportation Problem:

Can the daily ridership fluctuations be controlled through a pricing strategy?

The Airliners’ Pricing Problem:

How can an airliner fill its plains while maximizing its profit?

220

TR 0 = 220 x 120 = 26,400

TR1 = 180 x 140 = 25,200

TR2 = 180 x 200 = 36,000

120

180

0 Q

D 2

D 1

140 200

Note: Slope and Scale

oo

A B

Elasticity

A general definition:

“Elasticity” is a (standard) measure of the degree of sensitivity ( or responsiveness) of one variable to changes in another variable.

The price elasticity of Demand

The (self) price elasticity of demand is a measure of the degree of sensitivity of demand to changes in the (self) price, ceteris paribus.

Determining Price Elasticity

Percentage Change in Quantity

Ep =

Percentage Change in Price

Change in Quantity

Quantity

Ep =

Change in Price

Price

Ep (a --- b) = (10/8)/(-2/10) = -6.25

Ep (c ---d ) = (10/80)/(-2/4) = -.25

P

Q

D

ab

cd2

4

8

10

8 18 80 90

What does the elasticity “measure” really measure? The elasticity measure is a ratio between

two percentage measures: the percentage change in one variable over the percentage change in another variable

A price elasticity of -6.25 means that for each one percent change in price the quantity demanded will change by 6.25 percent.

Arc (Price) Elasticity

P

Q

D24

Note that if we increased the price,

(from 8 to 10 or 2 to 4)

the original P and Q would be 2 and 8 and 18 and 90, respectively.

Ep = (-10/18)/(2/8) = -2.22

Ep = (-10/90)/(2/2) = -.11

810

8 18 80 90

a

b

c

d

Arc Elasticity

To get the average elasticity between two points on a demand curve we take the average of the two end points (for both price and quantity) and use it as the initial value:

Q2-Q1 10

(Q1+Q2) 8+18

Ea = = -3.49

P2-P1 -2

(P1+P2) 10+8

Elasticity and the Price Level

Along a linear demand curve as the price goes up, |elasticity | increases.

Note that between points "a" and "b" the (arc) elasticity of the above demand curve is -3.49, whereas between "c" and "d" it is -.17.

P

D

8 18 80 90

a

b

c

d24

810

| Ep | > 1 : Elastic

| Ep | < 1 : Inelastic

| Ep | = 1 : Unit-elastic

E =-3.49

E = -.17

Point Elasticity Q

---------

Q1+Q2 Q P1+P2 Q P

E = ------------ = ------- . ------- = ------- . ------

P P Q1+Q2 P Q

---------

P1+P2

dQ P

Or, = ------ . -----

dP Q

P,MR

Q

Q

TR

0

0

| E | = 1

Q = C - b P

C 1P = ----- - ----- Q b b

C 2MR = ------ - ------ Q b b

C

DMR

Note: In the demand equation dQ/dP = -b

That means

PE p = -b ----- Q

A note about marginal revenue:

Recall: TR = P.Q ; P = f (Q ) Marginal Revenue = Change in TR resulting from

producing (selling) one additional unit of output.

TR (P.Q) d P d Q

MR = ------ = -------- = ------ .Q + ------ .P

Q Q d Q d Q

d P Q P 1

= ( -----. ----- + ------ ).P = P. ( ------- + 1 )

d Q P P E

0 Q

Q = C - b P

Slope= -1/b

Slope=-2/bD

MR

C

P, MR

dQ ---- = - bd p

dQ P PE = ----- . ----- = -b . ------ d p Q Q

1MR = P. ( 1 + ---- ) E

Special Cases

P

D

D

Q0 0 Q

Infinitely (price) elastic Infinitely price inelastic

Important Observations

•When demand is elastic, a decrease in price will result is an increase in the revenue (sales).

•When demand is inelastic, a decrease in price will result is a decrease in the revenue (sales).

•When demand is unit-elastic, an increase (or a decrease) in price will not change the revenue (sales).

What Determines Elasticity

Necessities versus luxuries

Eating at restaurants

Groceries Availability of substitutes

Chicken versus beef How much of our income a good takes

Salt versus Nike sneakers The passage of time

Elasticity and Passage of Time

DoD1D2D3

QoQ’oQ1Q2Q3

Q

P

O

Other Elasticity Measures

Recall: “Elasticity” is a (standard) measure of the degree of sensitivity ( or responsiveness) of one variable to changes in another variable.

Income Elasticity: a measure of the degree of sensitivity of demand for a good (or service) to changes in consumers’ (buyers’) income

Cross Price Elasticity: a measure of the degree of sensitivity of demand for a good (or service) to changes in the price of another good or service

Income Elasticity of Demand A measure of the degree of responsiveness of demand

(for a good) to a change in income, ceteris paribus.

(Shift of the demand curve)

Q2-Q1

Q2+Q1 d Q I

EI = = or = ------ . ------

I2-I1 d I Q

I1+I2

Cross (Price) Elasticity A measure of the degree of responsiveness of the

demand for one good (X) to a change in the price of another good (Y):

(Shift of demand curve)

Qx2- Qx1

Qx2+Qx1 d Qx Py

Ec = or = ----------- . -------

Py2- Py1 d Py Qx

Py1+Py2