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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?

TR 0 = 220 x 120 = 26,400TR1= 180 x 140 = 25,200TR2 = 180 x 200 = 36,000

D 2

D 1

220

180

Q

0

140

200

120

Elasticity

A general definition:

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

Thepriceelasticity 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

a

10

b

8

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

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

c

4

d

2

D

Q

80

90

8

18

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.

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

Arc (Price) Elasticitya

b

10

8

c

4

d

2

D

Q

8

18

80

90

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

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

Elasticity and the Price Level| Ep | > 1 : Elastic

| Ep | < 1 : Inelastic

| Ep | = 1 : Unit-elastic

a

E =-3.49

b

10

8

E = -.17

c

4

d

D

2

8

18

80

90

Point Elasticity |elasticity | increases.

Q

---------

Q1+Q2 QP1+P2 Q P

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

P P Q1+Q2 P Q

---------

P1+P2

dQ P

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

dP Q

P,MR |elasticity | increases.

Q = C - b P

C 1

P = ----- - ----- Q

b b

C 2

MR = ------ - ------ Q

b b

| E | = 1

D

MR

Q

0

TR

C

Note:

In the demand equation

dQ/dP = -b

That means

P

E p = -b -----

Q

Q

0

A note about marginal revenue: |elasticity | increases.

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

Q = C - b P |elasticity | increases.

dQ P P

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

d p Q Q

dQ

---- = - b

d p

P, MR

1

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

E

Slope= -1/b

Slope=-2/b

D

MR

Q

0

C

Special Cases |elasticity | increases.

P

D

D

0

Q

Q

0

Infinitely (price) elastic

Infinitely price inelastic

Important Observations |elasticity | increases.

- 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 |elasticity | increases.

- 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

Other Elasticity Measures |elasticity | increases.

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 |elasticity | increases.

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 |elasticity | increases.

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

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