1. Review
Demand curve, consumer surplus
Price elasticity of demand

2. Lecture 10 Elasticity and Empirical Estimation

3. Corresponds to different time periods.
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)
where
P = price per unit
Q = quantity demanded in units
1,2 = time periods
Corresponds to different time periods.

4. Buyers are price sensitive Buyers are price insensitive
Rare -4 -3 -2
-.8
-.6
-.4
Buyers are price sensitive
Buyers are price insensitive
Consumers have lots of choice (substitutes) when products are elastic.

5. Measuring Elasticity of Demand
Dell Computers recently cut the price of a poor selling notebook
from $1599 to $ Sales averaging 14,000 units in the first
period rose to 20,000 in the second period.
What is EP for the notebook?
Interpret EP.
Did revenues rise or fall after the price cut?
Q2-Q1
(P1+P2 )
P2-P1
(Q1+Q2 )
20-14
2998 X =
-2.64 34
Elastic and buyer are sensitive to price.
1599*14,000 = 22.3m
Good move for Dell
1399*20,000 = 27.9m

6. 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)

7. Why is Price Elasticity important?

8. 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

9. 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.
Marginal revenue and marginal cost equates at the optimal quantity

10. More on the Optimal Quantity
In a linear demand model
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)

11. Solving for Profit-Maximizing Price
Step 2: Compute the optimal price by substituting into the inverse demand function

12. More on the Optimal Price
In a linear demand model
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)

13. Solving for Profit-Maximizing Price
Step 3: Compute the optimal profit level
At optimum,
Maximal profit is:

14. More on the Optimal Profit
In a linear demand model optimal profit is
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)

15. 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

16. 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.

17. 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

18. 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.

19. 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.
Step 2: Compute the optimal price by substituting into the inverse demand function
Step 3: Compute the optimal profit level

20. 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

21. Empirical Demand Estimation
Linear Regression Model
Interpretation of coefficient
Computation of price elasticity

22. Empirical Demand Estimation
Log-Log Model
Interpretation of coefficient
Computation of price elasticity

23. Empirical Demand Estimation - Illustration
Demand Estimation Excel Worksheet

24. Next Lecture
Price Discrimination I