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Managerial Economics and Organizational Architecture, Chapter 4
Demand
The willingness and ability to buy
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
Demandlearning objectives
Students should be able to• Describe and apply demand
function and demand curve• Distinguish between change in
quantity demanded and change in demand
• Calculate and interpret demand elasticity
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
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
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
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.
(Interpret each term of the above equation.)
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Managerial Economics and Organizational Architecture, Chapter 4
Variable values
Suppose the variables have the following values:
P = $30Ps = $50
Pr = $40
I = $50,000
How many tickets will PTC sell?
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
The demand curve
Substitute variable values (except for P) into the equation and simplify:
P = 60 - 0.15Q
This is the equation for the demand curve.
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Managerial Economics and Organizational Architecture, Chapter 4
Graphing the demand curve
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
Demand elasticity
The price elasticity of demand is given by
[Note: the convention used here is to express the elasticity as a negative quantity so that, when calculated, the result is a positive number]
P
Q
%
%
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
Calculating elasticityarc price elasticity
• Information requirements:• Quantity demanded before and after the
price change• Q1
• Q2
• Price before and after the price change• P1
• P2
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
Calculating elasticityarc price elasticity
)(
)(
2)(
2)(
21
21
21
21
PPPQQQ
PPP
QQQ
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
Arc price elasticityexample
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
Calculating elasticitypoint price elasticity
Information requirements
• Demand curve equation:Q=a+bP, b=Q/P, b<0
• Current price and quantity P Q
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
Calculating elasticitypoint price elasticity
Q
Pb
Q
P
P
Q
PPQ
Q
P
Q
%
%
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
Point price elasticityexample
If the demand equation is Q=400-6.67P, P=35*, and Q=167, then elasticity is
*This price is midway between the two prices in the arc elasticity calculation.
4.1)167/35)(67.6(
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Managerial Economics and Organizational Architecture, Chapter 4
Range of price elasticities
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
Determinants of price elasticity
• Availability of substitutes– few substitutes for milk– many substitutes for milk at the supermarket
• Size of good in consumer budget– consider salt versus a Lexus
• Time period for consumer adjustment– given enough time, how do we adjust to higher
fuel prices?
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
Price changes and total revenue
PTC’s total revenue is TR=PQ The inverse demand curve is P=60-.15Q Substituting, TR=(60-.15Q)Q=60Q-.15Q2 From this we can derive marginal revenue
(MR=TR/Q=60-.30Q)
(Well, OK, we did use a little calculus for that last step. Trust us.)
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Managerial Economics and Organizational Architecture, Chapter 4
Elasticity, prices, and total revenue
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
Demand, total revenue, & marginal revenuelinear demand curve
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
Other demand influences
• Complements versus substitutes– Cross price elasticity of demand
21
21
yy
y
xx
x
xy
PP
PQQQ
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
Other demand influences
• Income– Normal goods– Inferior goods
• Income elasticity
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Managerial Economics and Organizational Architecture, Chapter 4
Product life cycle
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Managerial Economics and Organizational Architecture, Chapter 4
Omitted variables problem
1998 1999 2000
Income (I) $3,000 $4,000 $3,500
Advertising (A) 2 3 2.5
Price (P) 10 10 10
Sales (S) 236 284 260
True demand S=120-2P+8A+0.04I
Estimated demand S=140+48A
McGraw-Hill/Irwin
Managerial Economics and Organizational Architecture, Chapter 4
Estimating demandthe identification problem
McGraw-Hill/Irwin