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. Discussion: Why do aggregate demand curves slope downward? Role of heterogeneity? How to estimate?

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.

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 10

Exponential smoothing Suppose we have T observations of some series y t. The parameter  is called the smoothing parameter. Example, with  =0.50 More recent observations are weighted more. Can be adjusted to accommodate seasonality and trend. 11

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. 12

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. 13