power point slides for lecture #5 (ppt file)
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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.
10
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
11
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.
12
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.
13
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.