The Price Response Function

Overview

The price response function is a function that specifies the level of consumer demand for a given product at a given price. It may be referred to by other names, such as the demand function. Typically, demand is given the label q, and price is given the label p, so that the function becomes

{% q(p) %}

That is, demand is a function of p. This simple function actually hides many facts that must be kept in mind when modeling the demand function.

• First, the demand function must be specified for a given period. That is, demand can only occur over time, so that the number of products purchased over a month is much greater than over a single week.
• Second, the demand function will probably depend on a number of other factors besides just price. For instance, there may be seasonality to demand. Likewise, the price of competitive products may also be a factor
• The demand function specifies an expected demand only. It should be fairly obvious that the demand for any period is not fixed, but random to some degree. The function therefore cannot predict the demand exactly, the best we can do is to estimate the expected value of the demand.

Estimating the Price Response Function

There are generally two strategies to fitting a function to price response data.

• Fitting an Assumed Functional Form - first assume the form of the function and then fit the function to available data. For a list of commonly used functions, please see pricing functions.
• Measuring Local Price Sensitivity - only try to measure the change in demand for small changes in the price. In such as scenario, the process of choosing a price function is simplified, due to Taylors Theorem. The theorem guarantees that we approximate any function reasonably well in a small neighborhood of a point by using a linear function. This means that we can get alot of mileage out of just measuring the slope of the demand curve. (see price sensitivity below)

Differentiated Pricing

A differentiated priciing strategy is a pricing plan which charges different prices for the same product. This can be done based on customer type (for example, senior discounts), or for quantity of product sold. (i.e. the more bought the less charged).

Differentiated pricing requires a more complex analysis than the basic demand curve, and often requires a more complete picture of the customer, such as may be achieved through modeling the customer. (see below)

Modeling the Customer

The foregoing price analytics model pricing in something of a reduced form. That is, a functional form of the price curve is estimated and then fit, without first trying to build an underlying model that explains the price sensitivity. In order to get deeper insight in a firms price curves, marketers often try to model the customer that drives the demand curve. Understanding the customer helps to create additional flexibility in pricing, such as using a differentiated pricing strategy.

Supply Demand Trends over Time

Once a snapshot of the demand/price dynamics has been constructed, it may be useful to forecast how those relationships will change over time. Understanding the trends that affect your products demand is helpful for creating forward looking strategic plans.

Time series analysis is the standard framework for modeling date based data. In terms of creating marketing forecasts, many trends can be understood as being driven by underlying demographics.

Behavioural Factors Affecting Purchases

behavioural pricing

Bayesianism in Pricing

One of the biggest challenges in pricing is the lack of data necessary to measure the demand curve. Ideally, a firm would like to run an experiment where it changes its price to various price points and measures the response. This is not generally a viable plan, although companies can try to approximate this by running different price points in different test markets.

When there is not enough data to fit a model well, firms must find ways to create a model that utitilizes the data that is available while still recognizing its limitations. One form of statistical that deals with integrating new data with prior expectations in a precise fashion is bayesianism.