Transcript Demand Objectives - Metropolitan State University

Brickley, Smith, and Zimmerman,
Managerial Economics and
Organizational Architecture, 4th ed.
Chapter 4: Demand
Demand
learning 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
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
Demand Estimation
• Suppose you were asked to estimate the
demand function for a local theater
company
• What variables would you include?
• Price of theater tickets
• Price of symphony tickets
• Price of nearby restaurant meals
• Income
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.
Suppose the variables have the
following values:
P = $30
Ps = $50
Pr = $40
I = $50,000
How many tickets will PTC sell?
Q = 200
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.
Graphing the demand curve
Demand elasticity
The price elasticity of demand is given by
 %Q 
  

 %P 
[Note: the convention used here is to express the elasticity as a
negative quantity so that, when calculated, the result is a
positive number]
Calculating elasticity
• Information requirements:
• Quantity demanded before and after the price
change
• Q1
• Q2
• Price before and after the price change
• P1
• P2
Calculating elasticity
 Q 
 (Q1  Q2 ) 
 Q 


 (Q  Q ) 
2
1
2






 P 
 P 
 ( P1  P2 ) 
 ( P1  P2 ) 


2

Price Elasticity
example
Range of price elasticities
Price Elasticity
• η>1
Elastic demand
• η<1
Inelastic demand
• η=1
Unit elastic demand
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?
Elasticity, prices, and total revenue
(total revenue = P x Q)
Other demand influences
• Complements versus substitutes
– Cross price elasticity of demand
Qx
Qx1  Qx 2
 xy 
Py
Py1  Py 2
Other demand influences
• Income
– Normal goods
– Inferior goods
• Income elasticity of demand
Product life cycle
Demand Estimation
Three general techniques:
• Interviews
• Price Experimentation
• Statistical Analysis
Statistical Analysis
• Correlation is when two variables move
together
• “Move together” does not necessarily mean
the two variables move in the same
direction
• Same direction = positive relationship
• Opposite direction = inverse relationship
Statistical Analysis
Beware of three potential problems:
• Omitted variables
• Multicollinearity
• Identification problem
Omitted variables problem
1998
1999
2000
$3,000
$4,000
$3,500
2
3
2.5
Price (P)
10
10
10
Sales (S)
236
284
260
Income (I)
Advertising (A)
True demand
S=120-2P+8A+0.04I
Estimated demand
S=140+48A
Estimating demand
the identification problem