The New York Times recently announced its intent to start charging some frequent online readers a flat fee.  For visitors that aren’t print subscribers, a certain number of articles per month will be free; once the articles-per–month threshold is reached, a flat fee for unlimited access kicks in.

This is an attempt to extract surplus from those readers who have demonstrated a strong propensity to hit the online edition on a regular basis.  The big unknown of course is how many of the frequent online visitors will maintain their behaviors and pay up, and how many will modify their reading habits to avoid the fee.

This is where a solid understanding of your demand curve, coupled with optimization modeling, can help make difficult pricing decisions.  Understanding how segments support the curve will also help minimize cannibalization of existing products (unless that is a desired effect) and build brand strength, rather than eroding it by creating a “wall of anger” with otherwise loyal customers.

This article caught our attention because of a recent inquiry we had from a manufacturer about challenging legacy pricing structures.  The complicating factor in this case was an absence of reliable historical data we could use to quantify the relationship between changes in price, changes in volume, and the corresponding changes in profit taking unit costs into account.

Working with Professor Wayne Winston from Indiana University, we were able to develop three paths to strengthen our understanding of the relevant demand curves and then solve for proximate optimal pricing.  The common thread among these paths is that they involve a degree of creativity to essentially create the information that is needed to drive advantage through pricing analytics.

Path 1 – Simple Estimation of Demand Curves

Here we leverage two different techniques to estimate demand curves, and then run a series of optimization models to figure optimal prices under different scenarios (recurring fixed rent, outright sale, two-part tariffs, qty discounts, etc.).  The first technique to estimate demand curves uses internal “experts” to estimate volumes (either for a specific customer or a segment of customers) at different price levels based on their experience.  We develop independent estimates across experts and then figure out the best way to represent the collective input from group, be it an average curve or series of scenarios.  We then corroborate the internal expert curves with the limited historical data and, if possible, with an external view from a sample of our clients’ customers.

The second technique involves leveraging what we know about the value of our product to the end customer to derive a demand curve.  We then use this alternate curve to further corroborate the expert demand curve from the first approach.  Once we have a demand curve (or a few demand curve scenarios), we incorporate variable unit cost information from finance, build a profit function ((P-UC)*Qp), and then solve for the P that maximizes profits.  All in all, this is the simplest approach and requires the least amount of input data.  The trade-off is that it is also the least rigorous approach and we attempt to mitigate this with corroborating estimates.

Path 2 –  Discrete Choice Modeling

In this case we build a discrete choice model, again with expert input from internal and external sources, and then solve for optimal prices under different scenarios.  The base case discrete choice model can be extended to account for dynamic competitive responses and solve for equilibrium prices.  Using the discrete choice model involves developing product attribute scenarios (e.g. prices for a machine and a relevant competitive set), having a sample of internal/external experts make choices for each of the scenarios, generating weights, sensitivities, and likelihoods, and then modeling for the optimal prices that drive highest profits (again predicated on internal unit costs).  This approach is more rigorous than Path 1, but the trade-off is that it is difficult and expensive to construct the scenarios and get the data.

Path 3 – Econometric Estimation of Demand Curves

With an econometric approach we construct a multi-variate model to rigorously model the demand curves.  Our thought is to model machine demand as a function of historical macro-economic variables, and other historical variables including the machine price.  This idea was triggered by the recognition that over time machine quantities have varied, even if price hasn’t.  Once you develop a multi-variate equation to model demand, you essentially “fix” the significant independent variables with reliable economic forecasts OR run scenarios with assumptions.  Then based on forecasts or scenarios for the significant independent variables, you solve for the “P” that optimizes the profit function using solver.  This is the most rigorous approach but you can imagine the costs.  A robust historical data set needs to be assembled, variables that reflect on demand developed and tested, and a complex equation estimated.  This is hard and takes time.

There are trade-offs under each approach and we need further dialogue with our client to sort out which approach or combination is most feasible and makes the most sense.  A useful exercise to help sort out the actual path is some top-down modeling of the business value that is “in play” from sharpening up the pricing regime.  If the value at play is large with respect to current revenues and profits, and it can be corroborated with meaningful anecdotes, it will be worth embarking on the more rigorous paths.

Going back to The New York Times, one advantage leadership has is the ability to segment and survey lots of consumers from the millions that read the online edition.  But the question remains: what type of  information can help them really understand their demand curve?

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