Download Elastic demand

Review

Demand curve, consumer surplus

Price elasticity of demand
Lecture 10
Elasticity and Empirical Estimation
Price Elasticity of Demand

Understanding the concept of Elasticity of Demand is necessary to
successfully apply demand-oriented pricing
Elasticity = Q2 - Q1 (P1 + P2)
P2 - P1 (Q1 + Q2)
Corresponds to
different time
periods.
where
P = price per unit
Q = quantity demanded in units
1,2 = time periods
Price Elasticity of Demand (E)
E measures the responsiveness of customer demand to
changes in the service’s price.
Elastic demand
= % change in demand > % change in price
Inelastic demand = % change in demand < % change in price
Rare
-4
-3
-2
Elastic demand
Buyers are price sensitive
-1.0 -.8 -.6
-.4
0
Inelastic demand
Buyers are price insensitive
Consumers have lots of choice (substitutes) when products are elastic.
Measuring Elasticity of Demand
Dell Computers recently cut the price of a poor selling notebook
from $1599 to $1399. Sales averaging 14,000 units in the first
period rose to 20,000 in the second period.
Q2-Q1 (P1+P2 )
P2-P1 (Q1+Q2 )
1. What is EP for the notebook?
20-14
2998
X
= -2.64
34
1399-1599
2. Interpret EP.
Elastic and buyer are sensitive to price.
3. Did revenues rise or fall after the price cut?
1599*14,000 = 22.3m
1399*20,000 = 27.9m
Good move for Dell
Why is Price Elasticity Important?

Fact: sales revenue will be maximized when price
elasticity is equal to -1.



Elastic demand: decrease in price leads to increase in sales
revenue
Inelastic demand: increase in price leads to increase in sales
revenue
Fact: in the monopoly situation, optimal margin is related
to the elasticity in the following way:
 Optimal margin = -1/(Elasticity)
Why is Price Elasticity important?
Computing Elasticity for Linear Demand


Suppose the demand curve is q = A – B*p

How to compute price elasticity?
Suppose the Inverse demand curve is p = a – b*q

How to compute price elasticity?
Solving for Profit-Maximizing Price

Stick with the inverse demand function p = a – b*q
 Step 1: Increase the quantity produced until the marginal revenue
equals the marginal cost.
Rev  p  q  (a  bq)  q  aq  bq 2
Marginal Rev  a  2bq
Marginal Cost  c
*
Marginal revenue and marginal cost equates at the optimal quantity q
a  2bq  c
*
q* 
ac
2b
More on the Optimal Quantity

In a linear demand model
q* 
ac
2b

Optimal quantity increases with consumers’ highest willingness-to-pay (a)

Optimal quantity decreases with production costs (c)

Optimal quantity increases with elasticity of the market (1/b)
Solving for Profit-Maximizing Price

Step 2: Compute the optimal price by substituting into the inverse
demand function
p  a  bq
p*  a  bq*
ac
q 
2b
*
ac
p 
2
*
More on the Optimal Price

In a linear demand model  p*  a  c
2

Optimal price increases with consumers’ highest willingness-to-pay (a)

Optimal price increases with production costs (c)

Optimal quantity is not affected by the elasticity of the market (1/b)
Solving for Profit-Maximizing Price

Step 3: Compute the optimal profit level
Total Profit  ( p  c)  q  F


At optimum, q 
*
ac
2b
p* 
ac
2
( p*  c )  q*  F
Maximal profit is:
ac
ac
(
 c) 
F
2
2b
(a  c) 2

F
4b
More on the Optimal Profit

2
(
a

c
)
In a linear demand model optimal profit is
4b

Optimal profit increases with consumers’ highest willingness-to-pay (a)

Optimal profit decreases with production costs (c)

Optimal profit is increases with the elasticity of the market (1/b)
Role of Fixed Cost



Denote fixed cost by F
Decision Rule when Fixed cost has not been incurred

Invest if the optimal profit > F

Do not invest if the optimal profit < F
Decision Rule when Fixed has already been incurred

Invest if the optimal profit > 0
Market Selection

A Firm usually can choose to which market to enter.

Each market will have different fixed costs and demand curve.

Market entry decision depends on the optimal profits of both
markets.
Market Selection: An Example


Consider two markets described by the inverse demand functions:
 p1 = 100 – 0.5*q1 and
 P2 = 50 – 0.1*q2
The market-specific fixed cost associated with operating in markets 1
and 2 are F1 = F2 = $500.

Marginal Cost is assumed to be the same at $10

The firm can chooses only one market to serve
Market Selection: An Example

Total Profits at Market #1/ Market #2?


Computation follows the three-step procedure outlined above
Which market should be entered?



Enter Market # 1 if the total profit at Market # 1 is higher
Enter Market # 2 if the total profit at Market # 2 is higher
Need to also account for the fixed cost when we compute the total profit.
Market Selection: An Example

Computing the Expected Profit at Market #1 p1 = 100 – 0.5*q1



Step 1: Increase the quantity produced until the marginal revenue equals
the marginal cost.
100  10
q1* 
 90
2*0.5
Step 2: Compute the optimal price by substituting into the inverse demand
function
100  10
p1* 
 $55
2
Step 3: Compute the optimal profit level
(100  10) 2
 
 F  $3550
4  0.5
*
1
Market Selection: An Example

Practice
Computing the Expected Profit at Market #2 p2 = 50 – 0.1*q2



Step 1: Increase the quantity produced until the marginal revenue equals
the marginal cost.
Step 2: Compute the optimal price by substituting into the inverse demand
function
Step 3: Compute the optimal profit level
Empirical Demand Estimation

Linear Regression Model
y  0  1 x1  2 x2  ...  2 xK  


Interpretation of coefficient
Computation of price elasticity
Empirical Demand Estimation

Log-Log Model
ln y  0  1 ln x1  2 ln x2  ...  2 ln xK  


Interpretation of coefficient
Computation of price elasticity
Empirical Demand Estimation - Illustration

Demand Estimation Excel Worksheet
Next Lecture

Price Discrimination I