How to set a profit maximising price with just two data points

How to set a profit maximising price with just two data points

Pricing as a marketing function

Marketing is the business discipline that exists to create customers and increase profits. Ultimately, for marketing to justify its existence, it needs to consistently add new profits that exceed the costs incurred in creating them.

Given this simple definition and financial imperative, many marketing departments are predominantly focused on short term sales activation activities. Generating leads by running ads, developing promotions, creating campaigns, producing collateral and the like. This is not a criticism. Every marketing department must do this and do it well.

A less common approach is for marketing to also invest time in value creation in addition to sales activation. They focus on customer outcomes and will make time to develop the product and offer to improve the value they create for customers.

More uncommon still is the strategic marketing approach. These marketing departments are also responsible for value capture. Optimising price to find the right balance between sales volume and profit margin. They excel equally at sales activation, value creation and value capture.

It’s the final element that this article addresses. How to set profit maximising price.

The one price theory

If you know your contribution margin and understand your price response curve, which is how your sales volume is affected by price changes, then only one price will maximise your profit contribution. These are the two data points the title alluded to. I will get to how you find these data in a moment but, for now, let’s look at the theory.


The contribution margin (CM) is the selling price of a product minus its variable costs. If a product sells for $10 and has variable costs of $6 then the CM is $4. Each product sold contributes $4 to the overhead and, once the overhead is covered, to the bottom-line profit. Dividing the CM by the selling price expresses the margin as a % of sales. In our case, $4 divided by $10 gives 0.4 which is a CM% of 40%. So, 40% of the sales revenue contributes to the overhead and ultimately the net profit.

The price response curve is the line that represents the inverse relationship between price and total unit sales. Higher price generally means lower unit sales and vice versa. The line is plotted on a two-dimensional chart. Price is shown on the X-axis and units sold is plotted on the Y-axis. This gives the curve a downward sloping aspect.

Plotting the data

The chart below shows the price response curve (a straight line for this simple example – more on that later) that shows the expected level of sales at each price point. The vertical dotted line represents the variable costs per unit sold. Together with the baseline of the chart, these two lines create a triangle between points A, B and C. It’s within this triangle that our optimum contribution is found.

No alt text provided for this image

The way to find this price is to recognise that profit is a function of price multiplied by volume which means that it can be represented in this chart by a solid rectangle. The larger area of the rectangle the bigger the profit. Therefore, the mathematical challenge becomes ‘what is the largest rectangle I can fit inside the triangle A-B-C.

No alt text provided for this image

You solve these sorts of problems with derivatives, but you don’t need to as I have developed a tool that does exactly this. You enter the current price and unit sales, the contribution margin, a suggested price increase (or decrease), and the expected reduction (or increase) in unit sales. It looks like this.

No alt text provided for this image

The results from these inputs suggest that a price increase of 14.5% would lead to a reduction in unit sales of around 23%, a drop in revenue of around 12% but an increase in profit of around 10%. This is the optimal solution, all things being equal. Which at this point, they almost certainly are not.

The results will vary considerably as the inputs are altered. The effect of the price response curve (price sensitivity) and the amount of contribution margin can have a dramatic effect on the profit maximising price.

Understanding how the two variables of contribution margin and price response curve work together is critical when you optimise your pricing. However, the simplistic approach we have taken so far is only useful for understanding the theory and setting a baseline for further exploration. In the real world, we have to go a little deeper.

 From simplicity to reality   

Nobody is going to make a significant price move based on this elementary approach alone. Like most simple ideas there are other factors to consider. The following are the three most important.

1 – Price isn’t the only factor driving demand 

In well-functioning commodity markets, price and demand are inextricably linked. Individual suppliers don’t get to set the price – that is done by a highly efficient market. For most products though, price is just one of many factors driving demand.

Your positioning and brand building, your sales force effectiveness, your promotional and advertising efforts, the activity of your principal competitors all affect the demand for your product. The price must be seen in the context of a complex multi-factorial problem rather than a stand-alone element.

2 – Price response curves are not linear

A linear response curve would imply that the relationship between a price change and volume change is constant. Every dollar increase in price would lead to 100 fewer units sold, for example. This means that the price elasticity, which is a measure of % change in demand as a ratio of % change in price, will be different at different price points.

If we hold the price elasticity constant, then the demand curve takes on the properties of a power curve. A linear curve and power curve are shown below for the same single data point. Both approaches can give inaccurate forecasts at extreme price movements. But note how both would give similar forecasts based on a reasonable price change of a few % points. This is why linear demand curves are still very useful in the real world.

No alt text provided for this image

To construct a true price response curve, you need to fit a line to observed data. Take the five data points below. The charts show the relationship to a linear and power curve. Both are pretty accurate. The final chart uses polynomials to draw a line that best explains the relationship between price and volume. Whether you prioritise accuracy or simplicity is a judgement call. The tools will optimise based on any price response curve you decide to select.

No alt text provided for this image

3 – Price response curves are not fixed

Your market may be expanding or contracting. The demand for your product could grow or fall without any change in your price or other marketing activity. You must factor in the big picture when making pricing decisions.

Most importantly, if you make a significant price move you should expect a response from your competitors. These sort of response, counter-response price wars typically go through a few cycles before they reach a new equilibrium. Predicting how these will play out is another thing the tool can help you with but that is another topic for another day.

Pricing does not stand alone

The one price theory is mathematically sound. If you have two data points – the shape of your price response curve and the contribution margin of your product then only one price will maximise your contribution and therefore your profit when every other factor is held constant.

Given the caveats we have outlined it must be used in the context of an integrated commercial execution plan. Only when you are confident that all other aspects of the marketing and sales efforts have been optimised will the one price theory give you a tool to confidently maximise profit.

Pricing is too often created by finance based on a targeted return of investment, or similar, and marketing’s job is to sell what they are given. Unfortunately, there is a perception that giving marketing price discretion will simply lead to margin erosion as they overuse the price lever at the expense of other tools.

With sufficient rigour, supported by a dynamic and flexible commercial execution toolkit, marketing is best placed to make the right pricing decision. Give them the tools and they will do the job – sales activation, value creation and value capture.

Leave a reply

Your email address will not be published. Required fields are marked *