Lecture 6: Simple pricing review

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Lecture 6 Simple pricing review
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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 gt MC. Increase price
  (reduce quantity) if MR lt MC. The optimal price
  is where MR MC.
• Price elasticity of demand, e ( change in
  quantity demanded) ( change in price)
• If e gt 1, demand is elastic if e lt 1, demand
  is inelastic.
• ?Revenue ?Price ?Quantity
• Elastic Demand (e gt 1) Quantity changes more
  than price.
• Inelastic Demand (e lt 1) Quantity changes less
  than price.

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Summary (cont.)

• MR gt MC implies that (P - MC)/P gt 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
• 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 ?Quantity
  (factor elasticity)(?Factor).
• 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 MRgt0, then total revenue will increase if you
  sell one more. Highest level of MR doesnt mean
  profits are maximized as we saw on our quiz.
• If MRgtMC, 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 MRgtMC.
  PRODUCE AND SELL MORE!!! HOW???? DECREASE PRICE
• WHEN MRltMC. 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.

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Price change between month 1 and month 2

• Definition Elasticity
• (q2-q1)/(q1q2) ? (p2-p1)/(p1p2).
• 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.

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Example Grocery Store (MidSouth in 1999).

• 3-Liter Coke Promotion (Instituted to meet
  Wal-Mart 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).

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If you want, Ill show you the math

• Proposition MR Avg(P)(1-1/e)
• If egt1, MRgt0.
• If elt1, MRlt0.
• 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

• MRgtMC
• gt avg(P)1-1/egtMC
• gtavg(P)-avg(P)/egtMC
• gtavg(P)-MCgtavg(P)/e
• gtavg(P)-MC/avg(P)gt1/e
• The firms actual mark-up exceeds the desired
  markup!
• It should lower price!

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Example

• Suppose you have the following data
• Elasticity2
• Average Price 10
• Marginal Cost 8
• Should we raise the price? How do you know?

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Lecture 6 Topic 2Forecasting trend and
seasonality
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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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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_at_trend1

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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, s12, weekly data, s52.
• 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.
• There will be s seasonal dummy variables. The
  pure seasonal dummy variable model without trend

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Pure seasonality (s4, 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 _at_seas().
• The first seasonal dummy variable is created
• genr s1_at_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
• 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.
• SIClog(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).