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Lecture 6: Simple pricing
review
Summary of main points
• Aggregate demand or market demand is the total number of units
that will be purchased by a group of consumers at a given price.
• Pricing is an extent decision. Reduce price (increase quantity) if MR
> MC. Increase price (reduce quantity) if MR < MC. The optimal
price is where MR = MC.
• Price elasticity of demand, e = (% change in quantity demanded)
÷ (% change in price)
• If |e| > 1, demand is elastic; if |e| < 1, demand is inelastic.
• %ΔRevenue ≈ %ΔPrice + %ΔQuantity
• Elastic Demand (|e| > 1): Quantity changes more than price.
• Inelastic Demand (|e| < 1): Quantity changes less than price.
Summary (cont.)
• MR > MC implies that (P - MC)/P > 1/|e|; in words, if the actual
markup is bigger than the desired markup, reduce price
•
•
Equivalently, sell more
Four factors make demand more elastic:
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•
•
•
Products with close substitutes (or distant complements) have more
elastic demand.
Demand for brands is more elastic than industry demand.
In the long run, demand becomes more elastic.
As price increases, demand becomes more elastic.
• Income elasticity, cross-price elasticity, and advertising
elasticity are measures of how changes in these other factors
affect demand.
• It is possible to use elasticity to forecast changes in demand:
%ΔQuantity ≈ (factor elasticity)*(%ΔFactor).
• Stay-even analysis can be used to determine the volume
required to offset a change in costs or prices.
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KEY POINT #1
 INDIVIDUAL DEMAND CURVES SLOPE
DOWN…. THE LAW OF DEMAND!
 As we raise price, consumers will
respond by purchasing less.
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Pricing trade-off
• Pricing is an extent decision
• Profit= Total Revenue – Total Cost
• Demand curves turn pricing decisions into
quantity decisions: “what price should I charge?”
is equivalent to “how much should I sell?”
• Fundamental tradeoff:
• Lower price sell more, but earn less on each unit
sold
• Higher price sell less, but earn more on each unit
sold
• Tradeoff created by downward sloping demand
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Pricing
• Marginal analysis finds the profit increasing solution to
the pricing tradeoff.
• It tells you only whether to raise or lower price, not by
how much.
• Definition: marginal revenue (MR) is change in total
revenue from selling extra unit.
• If MR>0, then total revenue will increase if you sell one
more. Highest level of MR doesn’t mean profits are
maximized as we saw on our quiz.
• If MR>MC, then total profits will increase if you sell one
more.
• We already know: Profits are maximized when MR = MC
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KEY POINT #2
 MARGINAL ANALYSIS TELLS US THAT
WHEN MR>MC…. PRODUCE AND SELL
MORE!!! HOW???? DECREASE PRICE
 WHEN MR<MC…. WE ARE PRODUCING
AND SELLING TOO MUCH…. SELL
LESS!!! HOW??? INCREASE PRICE
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Elasticity of demand
• Price elasticity is a factor in calculating MR.
• Definition: price elasticity of demand (e)
• (%D in Qd)  (%D 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.
Price change between month 1
and month 2
• Definition: Elasticity=
[(q2-q1)/(q1+q2)]  [(p2-p1)/(p1+p2)].
• Note, by the law of demand, elasticity of price
change should be negative.
• Example: On a promotion week for Vlasic, the price
of Vlasic pickles dropped by 25% and quantity
increased by 300%.
• Is the price elasticity of demand -12?
• HINT: could something other than price be changing?
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KEY POINT #3
 WHEN DEMAND IS ELASTIC, RAISING
THE PRICE WILL REDUCE REVENUE.
 WHEN DEMAND IS INELASTIC, RAISING
THE PRICE WILL RAISE REVENUE!!
 Note: Remember revenue is only one
side of the coin. We would need to
know something about costs to
determine if profit are maximized.
Example: Grocery Store
(MidSouth in 1999).
 3-Liter Coke Promotion (Instituted to meet WalMart promotion)
• Compute price elasticity of 3 liter coke; cross price
elasticity of 2 liter coke with respect to 3 liter price;
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Revenue:
 Demand for 3-liters was very elastic. Please calculate
the revenue that resulted from the price decrease.
 Did revenue increase or decrease?
 Should increase as we already discussed.
 We can show the %change in revenue is equal to the
%change in price + % change in quantity.
 Since prices and quantities move in opposite directions,
total revenue changes will determined by which changes by
more (in absolute value).
If you want, I’ll show you the
math
• Proposition: MR = Avg(P)(1-1/|e|)
• If |e|>1, MR>0.
• If |e|<1, MR<0.
• Discussion: If demand for Nike sneakers is inelastic,
should Nike raise or lower price?
• Discussion: If demand for Nike sneakers is elastic,
should Nike raise or lower price?
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Example
 MR>MC




=> avg(P)[1-1/|e|]>MC
=>avg(P)-avg(P)/|e|>MC
=>avg(P)-MC>avg(P)/|e|
=>[avg(P)-MC]/avg(P)>1/|e|
 The firm’s actual mark-up exceeds the desired markup!
 It should lower price!
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Example
 Suppose you have the following data:
 Elasticity=–2
 Average Price =$10
 Marginal Cost= $8
 Should we raise the price? How do you know?
Lecture 6: Topic #2
Forecasting trend and
seasonality
Features common to firm level
time series data
 Trend
 The series appears to be dependent on time. There are
several types of trend that are possible
 Linear trend
 Quadratic trend
 Exponential trend
 Seasonality
 Patterns that repeat themselves over time. Typically
occurs at the same time every year (retail sales during
December), but irregular types of seasonality are also
possible (Presidential election years).
 Other types of “cyclical variation.”
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y
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-10
0
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time
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FORECASTING TREND
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Quadratic Trend
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Quadratic Trend: Parabolic
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Quadratic Trend
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Quadratic trend
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Modeling trend in EViews
 Inspect the data
 Does the data appear to have a trend?
 Is it linear? Is it quadratic?
 If the data appears to grow exponentially (population, money
supply, or perhaps even your firms sales) it may make sense to
take the natural log of the variable. To do so in Eviews, we use
the command “log.”
 To create a linear time trend variable, suppose you call
it ‘t’ use the following syntax in Eviews:
 genr t=@trend+1
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Seasonality
 In addition to trend, there may appear to be a seasonal
component to your data.
 Suppose you have ‘s’ observations of your data series in
one year. For example, for monthly data, s=12, weekly
data, s=52.
 Often times, the data will depend on the specific season
we happen to be in.
 Retail sales during Christmas
 Egg coloring during Easter
 Political ads during Presidential election years.
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Modelling seasonality
 There are a number of ways to deal with seasonality.
Likely the easiest is the use of deterministic seasonality.
1 if the t - th obs occurs in season " i" 
Di,t  

0
otherwise


 There will be “s” seasonal dummy variables. The pure

seasonal dummy variable model without trend:
yt b1D1,t b2 D2,t b3 D3,t  ....bs Ds,t  et
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Pure seasonality (s=4, relative
weights, 10, 5, 8, 25)
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Forecasting seasonality
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Seasonality and trend
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 To create seasonal dummies variables in Eviews, use the
command “@seas().”
 The first seasonal dummy variable is created:
 genr s1=@seas(1).
 IMPORTANT: If you include all “s” seasonal dummy variable
in your model, you must eliminate the constant from your
regression model
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Putting it all together
 Often, seasonality and trend will account for a massive
portion of the variance in the data. Even after
accounting for these components, “something appears
to be missing.”
 In time series forecasting, the most powerful methods
involve the use of ARMA components.
 To determine if autoregressive-moving average
components are present, we look at the correlogram of
the residuals.
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The full model
 The model with seasonality, quadratic trend, and ARMA
components can be written:
y t  b1D1,t  ... bsDs,t a1 t a 2 t 2  ut ,
ut  1ut1   2 ut2  ...  p ut p  ...
et  1et1  ...  q etq
 Ummmm, say what????

 The autoregressive components allow us to control for the
fact that data is directly related to itself over time.
 The moving average components, which are often less
important, can be used in instances where past errors are
expected to be useful in forecasting.
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Model selection
 Autocorrelation (AC) can be used to choose a model.
The autocorrelations measure any correlation or
persistence. For ARMA(p,q) models, autocorrelations
begin behaving like an AR(p) process after lag q.
 Partial autocorrelations (PAC) only analyze direct
correlations. For ARMA(p,q) processes, PACs begin
behaving like an MA(q) process after lag p.
 For AR(p) process, the autocorrelation is never
theoretically zero, but PAC cuts off after lag p.
 For MA(q) process, the PAC is never theoretically zero,
but AC cuts off after lag q.
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Model selection
 An important statistic that can used in choosing a model
is the Schwarz Bayesian Information Criteria. It rewards
models that reduce the sum of squared errors, while
penalizing models with too many regressors.
 SIC=log(SSE/T)+(k/T)log(T), where k is the number of
regressors.
 The first part is our reward for reducing the sum of
squared errors. The second part is our penalty for
adding regressors. We prefer smaller numbers to larger
number (-17 is smaller than -10).