workbook-style exercise on demand and elasticity · workbook-style exercise on demand and...

Workbook-Style Exercise on Demand and Elasticity

This is a workbook-style exercise that reviews and clarifies several conceptsabout demand and elasticity, such as the following:

1 What is the relationship between (a) market demand and (b) thedemand curve of a single firm in the market?

2 Why is the demand curve for a product category less elastic than thedemand curve for a particular product within that category?

3 What happens to one firm’s demand curve when a competing firmchanges its price?

See solutions at the end.

P1 Sep–Oct 2012 • Timothy Van Zandt • Prices & Markets

Session X • Exercise on Demand and Elasticity Slide 1

Exercise on Demand and Elasticity

1.➥ Scenario: Airbus and Boeing.

2. From Airbus’ demand function to Airbus’ demand curve.

3. How elasticity of Airbus’ demand depends on Boeing’s price.

4. Market demand for airplanes.

5. Elasticity of market demand vs. elasticity of Airbus’ demand.

6. Solutions.



Scenario

Product category: Passenger jets.

Dominated by two firms: Airbus (A) and Boeing (B).

(For simplicity, imagine that each firm produces one kind of jet, and thesetwo jets make up the entire product category.)

Hypothetical demand functions:

QA = 60 − 3PA + 2PB

QB = 60 − 3PB + 2PA




1.✓ Scenario: Airbus and Boeing.

2.➥ From Airbus’ demand function to Airbus’ demand curve.

3. How elasticity of Airbus’ demand depends on Boeing’s price.



6. Solutions.



Firm’s demand curve

A firm’s demand curve: How does demand for a single branded productrespond when the price of just that product changes?

Airbus’ demand function:

QA = 60 − 3PA + 2PB

By Airbus’ demand curve, we mean QA as a function only of PA , keepingPB fixed at some level. (See, e.g., Exercise 3.2 in FPM Chapter 3.)



Airbus’ demand curve: two examples See solutionsat the end.

Suppose PB = 24 . Write the formula for Airbus’ demand curve:

QA = 60 − 3PA + (2 × 24)

=⇒ QA = 108 − 3PA .


QA = 60 − 3PA + (2 × 30)

=⇒ QA = 120 − 3PA .



Airbus’ demand curve: the graphs See solutionsat the end.

Graph Airbus’ demand curve when PB = 24 and when PB = 30 :

Pi

Qi

10

20

30

40

30 60 90 120





2.✓ From Airbus’ demand function to Airbus’ demand curve.

3.➥ How elasticity of Airbus’ demand depends on Boeing’s price.



6. Solutions.



Elasticity of Airbus’ demand

Let’s compare the elasticity of Airbus’ two demand curves:

for PB = 24 and for PB = 30 .

Elasticity varies along all a demand curve.

For example, the elasticity of each of the two linear demand curves that

you derived in Slide 6 and graphed in Slide 7 varies from 0 (at PA = 0 ) to

infinity (at Airbus’ choke price P̄A ).

So what does it mean for one curve to be more elastic than the other?

Answer: We compare the elasticity at each price.

For example, consider the elasticity of Airbus’ demand at PA = 24 …



Elasticity of Airbus’ demand: calculations See solutionsat the end.

What is Airbus’ elasticity of demand (at PA = 24 ) when PB = 24 ?

From QA = 108 − 3PA , choke price is P̄A = 36 :

=⇒ EA =24

36 − 24=

2412

= 2



=⇒ EA =24

40 − 24=

2416

= 1.5



What happens in general?

Did you find a higher elasticity given PB = 24 than given PB = 30 ?

You should have.

For linear demand, elasticity is higher at a price the lower is the choke price:

EA =PA

P̄A − PA

Airbus’ choke price when PB = 24 is P̄A = 36 , whereas

Airbus’ choke price when PB = 30 is P̄A = 40 .

This numerical example illustrates an empirical regularity:

A firm’s demand curve becomes less elastic when the price of asubstitute good goes up.






3.✓ How elasticity of Airbus’ demand depends on Boeing’s price.

4.➥ Market demand for airplanes.


6. Solutions.



Market demand

Market demand: How does aggregate demand for the entire productcategory respond when the prices of all products in the category go up?

Aggregation problem: Need to define … QA= 60 − 3PA + 2PB

QB= 60 − 3PB + 2PA• aggregate output

• a price index

How do you “add” products that are different (different size airplanes,different qualities, etc.)?

How do you create an index of prices?



Usually hard, but in this case easy

In general, there is no single right answer to the aggregation problem. It isis part science, part art.

But our numerical example avoids these subtleties by using symmetricdemand functions.

We can just add the two quantities:

Q = QA + QB

For a price index, we use the average price:

P =PA + PB

2



Aggregation: Calculation See solutionsat the end.

Write the aggregate demand Q as a function of the average price P :

QA + QB = (60 − 3PA + 2PB ) + (60 − 3PB + 2PA )

= 120 − PA − PB

︸︷︷︸Q

= 120 − 2(

PA + PB

2

)︸︷︷︸

P

⇓Q = 120 − 2P



Summary: Market demand versus Airbus’ demand

MARKET DEMAND

Q = 120 − 2P

P

Q

10

20

30

40

50

60

30 60 90 120

(From slide 15)

AIRBUS’ DEMAND (If PB = 24 )

QA = 108 − 3PA

Pi

Qi

10

20

30

40

50

60

30 60 90 120

(From slides 6 & 7)







4.✓ Market demand for airplanes.

5.➥ Elasticity of market demand vs. elasticity of Airbus’ demand.

6. Solutions.



Comparing the elasticities See solutionsat the end.

Calculate the elasticity of the market demand curve at P = 24 :

From Q = 120 − 2P , choke price is P̄ = 60 :

=⇒ E =24

60 − 24=

2436

= 0.67

It is much lower than the elasticity of Airbus’ demand curve at PA = 24 ,given PB = 24 . Why? (Answer on next slide.)



Explanation

The elasticity of Airbus’ demand curve measures the following:

Suppose Airbus raises its price by 1%, whereas Boeing’s price staysconstant. By what percentage does Airbus’ demand fall?

The elasticity of the market demand curve measures the following:

Suppose both firm’s prices go up by 1%. By what percentage doestotal demand fall?

Answer to the first question > answer to the second question:

In the first case, buyers may switch to Boeing’s product.In the second case, a buyer’s only alternative is to buy nothing.



Broader idea

This illustrates a broader idea brought up in Session 3: The more weaggregate across products, the less elastic is demand. For example:

demand for computer monitors

less elastic than

demand for LCD monitors

less elastic than

demand for Acer LCD monitors

less elastic than

demand for the Acer AL1916 19” widescreen monitor







4.✓ Market demand for airplanes.

5.✓ Elasticity of market demand vs. elasticity of Airbus’ demand.

6.➥ Solutions.


Session X • Exercise on Demand and Elasticity Slide 1S

Airbus’ demand curve: two examples Solution toSlide 6.


QA = 60 − 3PA + (2 × 24)

=⇒ QA = 108 − 3PA .


QA = 60 − 3PA + (2 × 30)

=⇒ QA = 120 − 3PA .



Airbus’ demand curve: the graphs Solution toSlide 7.

Graph Airbus’ demand curve when PB = 24 and when PB = 30 :

Pi

Qi

10

20

30

40

30 60 90 120

PB = 30 ⇒ QA = 120 − 3PA

PB = 24 ⇒ QA = 108 − 3PA



Elasticity of Airbus’ demand: calculations Solution toSlide 10.



=⇒ EA =24

36 − 24=

2412

= 2



=⇒ EA =24

40 − 24=

2416

= 1.5



Aggregation: Calculation Solution toSlide 15.

Write the aggregate demand Q as a function of the average price P :

QA + QB = (60 − 3PA + 2PB ) + (60 − 3PB + 2PA )

= 120 − PA − PB

︸︷︷︸Q

= 120 − 2(

PA + PB

2

)︸︷︷︸

P

⇓Q = 120 − 2P



Comparing the elasticities Solution toSlide 18.

Calculate the elasticity of the market demand curve at P = 24 :

From Q = 120 − 2P , choke price is P̄ = 60 :

=⇒ E =24

60 − 24=

2436

= 0.67

It is much lower than the elasticity of Airbus’ demand curve at PA = 24 ,given PB = 24 . Why? (Answer on next slide.)



workbook-style exercise on demand and elasticity · workbook-style exercise on demand and...

Documents