Transcript Managerial Economics

Managerial Economics
ninth edition
Thomas
Maurice
Chapter 7
Demand Estimation &
Forecasting
McGraw-Hill/Irwin
McGraw-Hill/Irwin
Managerial Economics, 9e
Managerial Economics, 9e
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
Managerial Economics
Direct Methods of Demand
Estimation
• Consumer interviews
• Range from stopping shoppers to speak with
them to administering detailed questionnaires
• Potential problems
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7-2
Selection of a representative sample, which is a
sample (usually random) having characteristics
that accurately reflect the population as a whole
Response bias, which is the difference between
responses given by an individual to a hypothetical
question and the action the individual takes when
the situation actually occurs
Inability of the respondent to answer accurately
Managerial Economics
Direct Methods of Demand
Estimation
• Market studies & experiments
• Market studies attempt to hold
everything constant during the study
except the price of the good
• Lab experiments use volunteers to
simulate actual buying conditions
• Field experiments observe actual
behavior of consumers
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Managerial Economics
Empirical Demand Functions
• Demand equations derived from actual
market data
• Useful in making pricing & production
decisions
• In linear form, an empirical demand
function can be specified as
Q  a  bP  cM  dPR
where Q is quantity demanded, P is the price of the good
or service, M is consumer income, & PR is the price of some
related good R
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Managerial Economics
Empirical Demand Functions
Q  a  bP  cM  dPR
• In linear form
• b = Q/P
• c = Q/M
• d = Q/PR
• Expected signs of coefficients
• b is expected to be negative
• c is positive for normal goods; negative for inferior
goods
• d is positive for substitutes; negative for
complements
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Managerial Economics
Empirical Demand Functions
Q  a  bP  cM  dPR
• Estimated elasticities of demand are
computed as
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P
ˆ
Ê  b
Q
M
ˆ
ˆ
EM  c
Q
Ê XR
PR
ˆ
d
Q
Managerial Economics
Nonlinear Empirical Demand
Specification
• When demand is specified in log-linear
form, the demand function can be
written as
b
c d
Q  aP M PR
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To estimate a log-linear demand
function, convert to logarithms
lnQ  lna  b ln P  c ln M  d ln PR
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In this form, elasticities are constant
Ê  bˆ
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Eˆ M  cˆ
Ê XR  dˆ
Managerial Economics
Demand for a Price-Setter
• To estimate demand function for a
price-setting firm:
• Step 1: Specify price-setting firm’s
demand function
• Step 2: Collect data for the variables
in the firm’s demand function
• Step 3: Estimate firm’s demand using
ordinary least-squares regression
(OLS)
7-8
Managerial Economics
Time-Series Forecasts
• A time-series model shows how a timeordered sequence of observations on a
variable is generated
• Simplest form is linear trend forecasting
• Sales in each time period (Qt ) are
assumed to be linearly related to time (t)
Qt  a  bt
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Managerial Economics
Linear Trend Forecasting
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Use regression analysis to estimate
values of a and b
ˆ
Qˆ t  aˆ  bt
• If b > 0, sales are increasing over time
• If b < 0, sales are decreasing over time
• If b = 0, sales are constant over time
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Statistical significance of a trend is
determined by testing b̂ or by examining
the p-value for bˆ
Managerial Economics
A Linear Trend Forecast
(Figure 7.1)
Q
Estimated trend line

Q̂ 2009
12
Q̂ 20047
Sales
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t
2012
2007
2006
2005
2004
2003
2002
2001
2000
1999
Time
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1998
1997
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Managerial Economics
Forecasting Sales for Terminator
Pest Control (Figure 7.2)
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Managerial Economics
Seasonal (or Cyclical) Variation
• Can bias the estimation of parameters
in linear trend forecasting
• To account for such variation, dummy
variables are added to the trend
equation
• Shift trend line up or down depending on the
particular seasonal pattern
• Significance of seasonal behavior
determined by using t-test or p-value for
the estimated coefficient on the dummy
variable
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Managerial Economics
Sales with Seasonal Variation
(Figure 7.3)
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2004
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2005
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2006
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2007
Managerial Economics
Dummy Variables
• To account for N seasonal time
periods
• N – 1 dummy variables are added
• Each dummy variable accounts for
one seasonal time period
• Takes value of 1 for observations that
occur during the season assigned to
that dummy variable
• Takes value of 0 otherwise
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Managerial Economics
Effect of Seasonal Variation
(Figure 7.4)
Qt
Qt = a’ + bt
Sales
Qt = a + bt
a’
c
a
t
Time
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Managerial Economics
Some Final Warnings
• The further into the future a forecast is
made, the wider is the confidence
interval or region of uncertainty
• Model misspecification, either by
excluding an important variable or by
using an inappropriate functional form,
reduces reliability of the forecast
• Forecasts are incapable of predicting
sharp changes that occur because of
structural changes in the market
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