1. Managerial Economics and Organizational Architecture, 5e Chapter 4: Demand
McGraw-Hill/Irwin
Copyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved.

2. Demand Function
A mathematical representation of the relationship between the quantity demanded and all factors influencing demand:
Q = f(X1, X2,… Xn)
where Q is quantity demanded and the Xis are the factors influencing demand
4-2

3. Demand for PTC Tickets Q = 117 - 6.6P + 1.66Ps - 3.3Pr + 0.00661I
where P is PTC ticket price, Ps is price of symphony tickets, Pr is price of nearby restaurant meals, and I is average per capita income
4-3

4. Variable Values Suppose the variables have the following values:
Ps = $50
Pr = $40
I = $50,000
How many tickets will PTC sell?
4-4

5. The Demand Curve
Substitute variable values (except for P) into the equation and simplify:
P = Q
This is the equation for the demand curve.
Law of demand – as the price of a good rises, the quantity demanded falls
4-5

6. Graphing the Demand Curve$ $
Income = 51,000 61 60 60
Income = $50,000
Ticket price (in dollars) D1 D D0 Q Q
400
406.0
Quantity of PTC tickets
Quantity of PTC tickets
4-6

7. Price Elasticity of Demand
Measures the responsiveness of quantity demanded to changes in price
Often referred to as elasticity of demand
Helps firms determine the effect of price changes on total revenue
4-7

8. Demand Elasticity
The price elasticity of demand is given by
4-8

9. Calculating Elasticity Arc Price Elasticity
Information requirements:
Quantity demanded before and after the price change Q1 Q2
Price before and after the price change P1 P2
4-9

10. Calculating Elasticity Arc Price Elasticity
4-10

11. Arc Price Elasticity $ η = -[ΔQ/(Q1 + Q2)/2] ÷ [ΔP/(P1 + P2)/2] 60
=-[-67/( )/2] ÷ [10/(30+40)/2]
= 1.4
Ticket price in dollars
(133, $40) P2
(200, $30) P1 D Q2 Q1
400
4-11
Quantity of PTC tickets

12. Price Changes and Total Revenue
If demand is elastic (>1), price and total revenue move in opposite directions
If P↑ then TR↓
If P↓ then TR↑
If demand is inelastic (<1), price and total revenue move together
If P↑ then TR↑
If P↓ then TR↓
4-12

13. Range of Price Elasticities$ $ D
η = 0 D
η = ∞
Price (in dollars)
Price (in dollars) Q Q
Quantity
Quantity
Perfectly nelastic
Perfectly lastic
4-13

14. Determinants of Price Elasticity
Availability of substitutes
few substitutes for salt
many substitutes for milk at the supermarket
Size of good in consumer budget
paper clips versus a car
Time period for consumer adjustment
over time consumers find alternative goods
4-14

15. Price Changes and Total Revenue
Total revenue is P x Q
For PTC, P=60-.15Q
And TR = (60-.15Q)Q=60Q-.15Q2
Marginal revenue, MR, is
TR/Q=60-.30Q
4-15

16. Demand, Total Revenue, & Marginal Revenue$ 60
Elastic demand (n > 1)
Ticket price (in dollars) 30
n = 1
Inelastic demand (n < 1) Q $
6,000
Total revenue (in dollars) Q
4-16
200
Quantity of PTC tickets

17. Other Demand Influences
Complements versus substitutes
Cross price elasticity of demand
4-17

18. Cross Price Elasticity
For substitutes, ηXY > 0
If the price of Pepsi rises, the demand for Coke rises
For complements, ηXY < 0
If the price of peanut butter rises, the demand for jelly falls
4-18

19. Income Income elasticity of demand
Normal goods – demand rises as income increases (>0)
Inferior goods – demand falls as income increases (<0)
4-19

20. Network Effects
Demand for a good increases as the number of users of the good increases
fax machines
High Definition DVD versus Blu-Ray
4-20

21. Product Attributes Managers must understand consumer demand
What product attributes are important to consumers?
price
product design
packaging
promotion
4-21

22. Product Life Cycle Q Introduction Growth Maturity Decline
Industry quantity of output
Product life cycle T
Time
4-22

23. Demand Estimation Three general techniques interviews
surveys, focus groups, questionnaires
price experimentation
track changes in sales when prices change
statistical analysis
must account for omitted variables and other issues
4-23

24. Omitted Variables Problem
1998
1999
2000
Income (I)
$3,000
$4,000
$3,500
Advertising (A) 2 3
2.5
Price (P) 10
Sales (S)
236
284
260
True demand
S=120-2P+8A+0.04I
Estimated demand
S=140+48A
4-24

25. Estimating Demand The Identification Problem$
Three different
equilibriums are not
mapping out the demand
curve S1
Price (in dollars) S2 P1 D1 P2 D2 S3 P3 D3
Estimated demand Q Q1 Q2 Q3
Quantity
4-25