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Managerial Economics and Organizational Architecture, Chapter 4
Demand
The willingness and ability to buy
Managerial Economics and Organizational Architecture, Chapter 4
Demandlearning objectives
Students should be able toDescribe and apply demand function and demand curveDistinguish between change in quantity demanded and change in demandCalculate and interpret demand elasticity
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
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.)
Managerial Economics and Organizational Architecture, Chapter 4
Variable values
Suppose the variables have the following values:
P = $30
Ps = $50
Pr = $40I = $50,000
How many tickets will PTC sell?
Managerial Economics and Organizational Architecture, Chapter 4
The demand curve
Substituting variable values (except for P) into the equation and simplifying:
P = 60 - 0.15Q
which is the equation for the demand curve.
Managerial Economics and Organizational Architecture, Chapter 4
Graphing the demand curve
Managerial Economics and Organizational Architecture, Chapter 4
Demand elasticity
The elasticity of demand is given by
⎟⎠
⎞⎜⎝
⎛ΔΔ
−=P
Q
%
%η
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
Managerial Economics and Organizational Architecture, Chapter 4
Calculating elasticityarc price elasticity
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
+Δ+Δ
−=
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
+Δ
+Δ
−=
)(
)(
2)(
2)(
21
21
21
21
PPPQQQ
PPP
QQQ
η
Managerial Economics and Organizational Architecture, Chapter 4
Arc price elasticityexample
Managerial Economics and Organizational Architecture, Chapter 4
Calculating elasticitypoint price elasticity
Information requirements
Demand curve equation:Q=a-bP, b=ΔQ/ΔP
Current price and quantity P Q
Managerial Economics and Organizational Architecture, Chapter 4
Calculating elasticitypoint price elasticity
⎟⎟⎠
⎞⎜⎜⎝
⎛×−=⎟⎟
⎠
⎞⎜⎜⎝
⎛×
ΔΔ
−=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
Δ
Δ
−=⎟⎠
⎞⎜⎝
⎛ΔΔ
−=
Q
Pb
Q
P
P
Q
PPQ
Q
P
Q
%
%η
Managerial Economics and Organizational Architecture, Chapter 4
Point price elasticityexample
If the demand equation is Q=20-4P, P=14, and Q=27, then elasticity is
07.2)27/14)(4( −=−=η
Managerial Economics and Organizational Architecture, Chapter 4
Range of price elasticities
Managerial Economics and Organizational Architecture, Chapter 4
Determinants of price elasticity
Availability of substitutes– few substitutes for milk– lots of 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?
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=ΔTR/ΔQ=60-.30Q)
(Well, OK, we did use a little calculus for that last step. Trust us.)
Managerial Economics and Organizational Architecture, Chapter 4
Elasticity, prices, and total revenue
Managerial Economics and Organizational Architecture, Chapter 4
Demand, total revenue, & marginal revenue
linear demand curve
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
+Δ+
Δ
=η
Managerial Economics and Organizational Architecture, Chapter 4
Other demand influences
Income– Normal goods– Inferior goods
Income elasticity
Managerial Economics and Organizational Architecture, Chapter 4
Product life cycle
Managerial Economics and Organizational Architecture, Chapter 4
Estimating demandthe identification problem