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Lecture 4: Topic #1
Simple Pricing
and demand
Review
Background: consumer surplus
and demand curves (cont.)
• Hot dog consumer
• Values first dog at $5, next at $4 . . . fifth at $1
• Note that if hot dogs price is $3, consumer will
purchase 3 hot dogs
Background: aggregate demand
• Aggregate Demand: the buying behavior of a group of consumers; a
total of all the individual demand curves.
• To construct demand, sort by value.
Price
$7.00
$6.00
$5.00
$4.00
$3.00
$2.00
$1.00
Quantity
1
2
3
4
5
6
7
Revenue
$7.00
$12.00
$15.00
$16.00
$15.00
$12.00
$7.00
Marginal
Revenue
$7.00
$5.00
$3.00
$1.00
-$1.00
-$3.00
-$5.00
$8.00
• Discussion: Why do aggregate demand curves slope downward?
$6.00
• How to estimate?
Price
• Role of heterogeneity?
$4.00
$2.00
Example: finding the optimal price
•
Start from the top
•
If MR > MC, reduce price (sell one more unit)
•
Continue until the next price cut (additional sale) until MR<MC
How do we estimate MR?
• Price elasticity is a factor in calculating MR.
• Definition: price elasticity of demand (e)
• (%change in quantity demanded)  (%change in price)
• If |e| is less than one, demand is said to be inelastic.
• If |e| is greater than one, demand is said to be elastic.
Elasticity and pricing
• MR>MC is equivalent to
• P(1-1/|e|)>MC
• P>MC/(1-1/|e|)
• (P-MC)/P>1/|e|
• Discussion: e= –2, p=$10, mc= $8, should you raise
prices?
• Discussion: mark-up of 3-liter Coke is 2.7%. Should
you raise the price?
• Discussion: Sales people MR>0 vs. marketing MR>MC.
Alternate introductory anecdote
• In 1994, the peso devalued by 40% in Mexico
• Interest rates and unemployment shot up
• Overall economy slowed dramatically and consumer income fell
• Concurrently, demand for Sara Lee hot dogs declined
• This surprised managers because they thought demand would
hold steady, or even increase, since hot dogs were more of a
consumer staple than a luxury item.
• Surveys revealed the decline was mostly confined to premium
hot dogs
• And, consumers were using creative substitutes
• Lower priced brands did take off but were priced too low.
• Failure to understand demand and to price accordingly was
costly
Lecture 4: Topic #2
FORECASTING ANALYSIS
Why learn forecasting?
• As we have just seen, profitability relies crucially on
understanding demand, revenues, and costs. This is
true not just for today, but the future as well.
• Example: American Airlines hires forecasters to provide
projections of demand for flights
• In industries where storing inventories can be costly,
forecasting sales is crucial.
• Firms need to make staffing decisions based on
expected revenues and growth.
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Forecasting methods
 Simple:
 Averages: The sample mean of the data
 Weights distant observations the same as recent ones
 Naïve: Forecasts of the future value is the most recently
observed value
 Moving averages
 For some value m, the average of the most recent m
observations.
 Exponential smoothing
 Weights more recent observations more heavily that distant
observations
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Exponential smoothing
 Suppose we have T observations of some series yt.
t 1
ˆ t  a  (1  a ) s y t  s
y
s 0
 The parameter a is called the smoothing parameter.
Example, with a=0.50

ˆ 2  0.50 * y1  0.50y1
y
ˆ 3  0.50( y 2  0.50y1 )  0.50y 2  0.25 y1
y
 More recent observations are weighted more. Can be
adjusted to accommodate seasonality and trend.
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More advanced modeling
 The Box-Jenkins methodology
 Assumes a mathematical model can be written to
approximate the data.
 Forecasted values are then the expected value of the
model based on available information.
 Explicitly accommodates:
 Trend
 Seasonality
 Cyclical variation
 Can be extended to allow variables to be related to other
variables.
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Box-Jenkins procedure
 Check to see if the data is stationary. Does the data
have trend or seasonality? If so, include seasonal/trend
variables in your model. If necessary accommodate
breaks by limiting your sample or including variables to
account for the changing behavior.
 Make appropriate guesses for the best fitting model.
 Estimate several models. Use your best judgement to
choose the most appropriate one.
 Perform diagnostic to ensure that your model has
accounted for all correlation in the residuals.