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: 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.

KEY POINT #1 INDIVIDUAL DEMAND CURVES SLOPE DOWN…. THE LAW OF DEMAND! As we raise price, consumers will respond by purchasing less. 4

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 5

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 6

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 7

Elasticity of demand Price elasticity is a factor in calculating MR. Definition: price elasticity of demand (e) (%  in Q 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. 8

Price change between month 1 and month 2 Definition: Elasticity= [(q 2 -q 1 )/(q 1 +q 2 )]  [(p 2 -p 1 )/(p 1 +p 2 )]. 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? 9

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. 10

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; 11

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). 12

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? 13

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! 14

Example Suppose you have the following data: Elasticity=–2 Average Price =$10 Marginal Cost= $8 Should we raise the price? How do you know? 15

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.” 17

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FORECASTING TREND 19

Quadratic Trend 20

Quadratic Trend: Parabolic 21

Quadratic Trend 22

Quadratic trend 23

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 24

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. 25

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: 26

Pure seasonality (s=4, relative weights, 10, 5, 8, 25) 27

Forecasting seasonality 28

Seasonality and trend 29

To create seasonal dummies variables in Eviews, use the command The first seasonal dummy variable is created: genr IMPORTANT: If you include all “s” seasonal dummy variable in your model, you must eliminate the constant from your regression model 30

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. 31

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. 32

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. 33

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). 34