Welcome to Pricing 102

Pricing in traditional economics 101 introductions gets difficult very quickly with the addition of competition and further products. Models as those from Cournot or Stackelberg are elegant and beautiful, but also difficult to understand and not very useful for real-life pricing challenges. Therefore, we use our Virtual Customers for an easy and transparent introduction into pricing.

Welcome to buynomics’ Pricing 102!

The Lemonade Stand

In this first introductory pricing journey, we want to help Lisa, the owner of a lemonade stand, who is in the business to make money, price her products in an increasingly complex market as her product range increases and competitors enter her market. This pricing journey consists of 10 steps. Each poses a new pricing challenge, and we want to use buynomics’ Virtual Customer technology to help Lisa make the right pricing decision – and show you how we get there.

Day 1 - How to price the first product?

We start this journey with only Lisa’s Lemonade stand, without competition, selling one product, a 0.4l cup of lemonade. Her unit cost is €1.00, and there is a total daily demand in her street for 1,000 cups of lemonade (yes, it’s a very busy street!). Customers’ average willingness-to-pay is €2.00, and the price elasticity of demand at a price of €2.00 is -2.

The math on the first day is still so simple, that we can compute the profit optimal price. With only one product, in the profit optimum we have

elasticity · margin = -1.

Therefore, with an elasticity of -2 and a margin of 50%, €2.00 is the profit optimum with sales of about 500 cups of lemonade and a total profit for Lisa of about €500.

See how the Virtual Customers react to price changes and how this affects sales, revenue, and profit.

Day 2 - How to adjust the price after a cost increase?

Despite a good first day, the second day starts with some bad news for Lisa. Her costs for the lemonade have increased by 20% so that her unit cost is now at €1.20. Just like the day before, the total daily demand is again 1,000 cups per day, customers’ average willingness-to-pay is €2.00, and the price elasticity of demand at a price of €2.00 is -2.

In the one-product case, the impact of the cost increase can still be estimated easily. For example, under linear demand, to stay in the profit optimum, you need to pass on half of the cost increase to your customers:

price increase = cost increase / 2.

Therefore, with a cost increase of €0.20, the profit optimal price increases by €0.10 from €2.00 to €2.10 with sales of about 450 cups of lemonade and a total profit for Lisa of about €405. Note that the price elasticity of demand has changed with the price increase to €2.10 and is now – 2.3.

For a more precise depiction of the dynamics of the price change, see how our Virtual Customers reacted – and how this affects sales, revenue, and profit.

Day 3 - How to price a portfolio of two lemonade sizes?

After two successful days on the street, Lisa realizes that, at the profit optimal price of €2.10, she served only half of the total market demand. So, she decides to extend her offer with a smaller sized cup of 0.2l. For this new 0.2l size, her unit cost is €0.70, for the 0.4l cup’s unit cost stays at €1.20. The total daily demand stays at 1,000 cups per day, split over both sizes. As most customers prefer the larger cup, their average willingness-to-pay (WTP) of €2.00 for the 0.4l cup is significantly higher than their average WTP of €1.00 for 0.2l cup. For the small cup, the price elasticity of demand at a price of €1.00 is -2. For the large cup, it is -2 at a price of €2.00.

How should Lisa price her lemonade to optimize her profit?

Even in this simple example, finding the optimal prices analytically, considering the interdependencies between the two products, is very difficult – and we have seen few who have attempted it. Good for Lisa, that she can rely on our Virtual Customers technology to determine her profit optimal prices.

Considering all above inputs, the profit optimal prices are €1.20 for the small (0.2l) cup and €2.20 for the large (0.4l) cup. Note that with the addition of the small cup, the price of the large cup increases from €2.10 to €2.20. With the addition of the small cup, Lisa is able to increase her sales volume from 448 to 525 cups (+17%), her revenue by +5%, and her profit by +9%. Not bad!

How did she determine her prices? See for yourself.

Day 4 - How to price a portfolio of products of different quality?

Lisa’s last change to the portfolio was a great success. She feels, however, that there is more to gain. As only a third of her customers bought the smaller sized cup, she decides to diversify her portfolio differently, not in size but in quality. So, she replaces the smaller 0.2l cup of home-made lemonade with a 0.4l sized cup of regular lemonade, which she bought at the supermarket. The 0.4.l cup of home-made lemonade stays unaltered in her portfolio. For the regular lemonade, her unit cost is €0.80, for the home-made lemonade unit cost stay at €1.20. Customers’ average willingness-to-pay (WTP) remain at €2.00 for the home-made lemonade and are at €1.70 for the regular lemonade. For the home-made lemonade, the price elasticity of demand at a price of €2.00 is -2, and it is also -2 for the regular lemonade, but at a price of €1.70.

How should Lisa price her new portfolio?

Finding the optimum analytically is difficult, so Lisa uses the Virtual Customers technology to determine her profit optimal prices. Quickly, she identifies the profit optimal prices of €1.70 for the regular lemonade and €2.20 for the home-made lemonade. With the replacement of the 0.2l cup of home-made lemonade by a 0.4l cup of regular lemonade, Lisa increased her profit by 26%. Her decision paid off!

How did the Virtual Customers react? See for yourself!

Day 5 - How to price a portfolio consisting of three different products?

Offering a second type of lemonade worked out well for Lisa, so she decided to add one more today. This morning, she bought fresh lemons at the market and now offers freshly squeezed lemonade as her premium product. Its unit cost is €2.00 and the top 20% of customers, sorted by willingness-to-pay (WTP), have a WTP above €3.30. She keeps both previous lemonades (regular and the home-made) in her offer with unit costs of €0.80 and €1.20 and average WTP of €1.80 and €2.00, respectively. The price elasticities of demand for all three lemonades is -2, at a price of €1.80 for the regular, €2.00 for the home-made and €2.50 for the freshly squeezed lemonade.

How should Lisa price the new product? And, should she keep the old prices for the other two?

The Virtual Customers technology has served Lisa well so far, so she uses it again to determine her profit optimal prices. For the new premium product she identifies the profit optimal price at €3.20. Note that prices for both other products rise, for the home-made lemonade from €2.20 to €2.30, and for the regular lemonade from €1.70 to €1.90. With the additional product in her portfolio, Lisa’s profit increased again, this time by 29%.

What did the Virtual Customers buy? See for yourself!

Day 6 - How to price against competition?

Lisa’s success in the past days has not gone unnoticed, and today her neighbor is out on the street, trying his own luck. In his offer, he has a 0.4l cup of organic lemonade. To make matters worse, both, the regular lemonade and the fresh lemons are sold out, so that Lisa can only offer her home-made lemonade. Her unit cost stays at €1.20 and the customers’ average willingness-to-pay (WTP) stays at €2.00. For the neighbor’s organic lemonade, the average WTP is at €2.50. The price elasticities of demand are for both at -2, at a price of €2.00 for the home-made and at a price of €2.50 for the organic lemonade. Her neighbor is convinced that his lemonade is better than Lisa’s and sets his price at €2.50, €0.20 above yesterday’s price of the home-made lemonade.

How should Lisa react to the new competition?

Using the Virtual Customers technology, she finds that leaving at her previous price of €2.30, she would waste 20% of her potential profit, so she reduces her price by €0.40 to the new profit optimal price of €1.90. Her new total profit is €246 – a big cut, yet she did the best she could do. Also, at this price it would not make sense for her neighbor to adapt his price.

For a more detailed view on the dynamics between the competitor’s price and Lisa’s profit, see how the Virtual Customers react and how this impacts sales, revenue and profit.

Day 7 - How to price a portfolio of two different products?

After a relatively bad day for Lisa, she is relieved to see that her neighbour has not set up his stand today. Apparently, he sold more than he had expected and has run out of ingredients - good for Lisa. As the temperatures have risen significantly, Lisa decides to offer cones of home-made ice cream in addition to her home-made lemonade. Her unit cost for the new ice cream is €1.80, for the lemonade it stays at €1.20. Customer’s average willingness-to-pay for the ice cream is at €2.50, for the lemonade, it remains at €2.00. The price elasticities of demand are for both at -2, at a price of €2.00 for the lemonade and at a price of €2.50 for the ice cream.

How should Lisa price her new product? And should she change the price of the lemonade again?

With the help of the Virtual Customers technology, she determines a profit optimal price for the ice cream of €2.90. For the lemonade, the optimal price increases by €0.30 to €2.20.

Note that neither of her two products are at their individual profit optimum, however, the portfolio itself is. Her new profit is €568 – 13% above what she would have made with individually optimized products.

Understand the dynamics between prices of two different products by observing the Virtual Customers reactions to price changes.

Day 8 - How to price a portfolio with a bundle?

With the addition of home-made ice cream to her offerings, Lisa was able to increase the profit of her street stand again. Yesterday, Lisa noticed that, with the alternative of ice cream, many of her customers had a difficult time choosing between her products. So, today, she decides to provide a third option to her customers by offering both products together. For the bundle, her unit cost adds up to €3.00, consisting of €1.80 for the ice cream and €1.20 for the lemonade. Customers’ average willingness-to-pay (WTP) for the individual products stay unchanged, at €2.50 for the ice cream and at €2.00 for the lemonade, so the average WTP for the new bundle is at €4.50. The price elasticity of the ice cream is -2 at a price of €2.50 and for the lemonade it is -2 at a price of €2.00.

How should Lisa price the new bundle?

Relying on the Virtual Customers technology, Lisa effortlessly determines the profit optimal price for the bundle and her individual products. She sets the bundle’s price at €4.90, the ice cream’s price at €3.00 and the

lemonade’s price at €2.30. Her profit is €818 – a remarkable increase of 44% compared to yesterday! Bundling her products paid off!

For a detailed depiction of how bundling can benefit sales, and how being slightly off in the price can dramatically hurt sales, see how our Virtual Customers reacted to different price points.

Day 9 - How to price a portfolio with a bundle against competition?

After two days without competition, Lisa’s neighbor is back on the street again. He stacked up on ingredients and is selling his organic lemonade again. But this time, Lisa is well prepared, as her offer now also includes home-made ice cream. Unit costs of her offers stay as before, €1.80 for the ice cream, €1.20 for the lemonade and €3.00 for the bundle. Customers’ willingness-to-pay (WTP) is also unchanged at €2.50 for the ice cream, at €2.00 for the lemonade and at €4.50 for the bundle. Customers’ average WTP for her neighbor’s organic lemonade is €2.50, again. The price elasticity for Lisa’s ice cream is -2 at a price of €2.50, for her lemonade it is -2 at a price of €2.00 and for the organic lemonade it is -2 at a price of €2.50. Her neighbor made a decent profit

on Day 6, when he set his price at €2.50, so today, he chooses the same price.

Should Lisa react to the competitor with a price change?

prices for her offers, Lisa is left with no choice but to use the Virtual Customers technology. She does not mind, since she now knows she can count on its accuracy. Her profit optimal prices decrease to €4.40 for the bundle, €2.90 for the ice cream and €2.10 for the lemonade. Note that with adapted prices, Lisa’s profit is 8% above what she would have made had she left her prices as before. Also, at these prices, it will not make sense for her neighbor to change his price.

What did the Virtual Customers buy? See for yourself!

By now, the situation has become far too complex to determine optimal prices analytically. In order to optimize

Day 10 - How to price a portfolio against different competitors?

At the end of this introductory pricing journey, Lisa’s situation has become far more complex than she had thought. Across the street, another neighbor has opened his stand to sell ice cream. Unlike Lisa’s, it’s not home-made but from the supermarket, so he sells it much cheaper. Now, Lisa is facing competition from all sides, by a high-quality competitor in the lemonade market and by a low-price competitor in the ice cream market.

Her unit cost for the lemonade, the ice cream and the bundle remain at €1.20, €1.80 and €3.00, respectively. Also, customers’ average willingness-to-pay (WTP) for the home-made lemonade, the home-made ice cream and the organic lemonade stay at €2.00, €2.50 and €2.50,

respectively. For the new, regular ice cream of her neighbor, customers’ average WTP is €1.50. For each product, the price elasticity of demand is -2 - for the home-made lemonade at a price of €2.00, for the home-made ice cream at a price of €2.50, for the organic lemonade also at a price of €2.50 and for the regular ice cream at a price of €1.50. Her new competitor sets a price of €1.30 for his ice cream. With more competition at hand, her old competitor fears he will lose sales and decides to decrease his price to €2.30.

How should Lisa set her prices in this highly competitive market?

After the last 9 days, Lisa is now convinced that the Virtual Customers technology helps her to accurately set the right prices for her products. Under consideration of her costs, the dynamics between her products individually and her competitors’ ones, and customers’ preferences, she has no trouble determining her profit optimal prices. She prices her lemonade at €2.00, her ice cream at €2.80 and the bundle at €4.50. Despite the strong competition, she makes a profit of €518 on the final day.

What did the Virtual Customers buy? See for yourself!

Learnings - What Lisa's street stand teaches us about the real world!

The past 10 days have been very exciting for Lisa. She had a lot of ups and, despite a few downs, it’s fair to say that her street stand was a great success. Overall, she sold 5,771 units of lemonade and ice cream, made a total revenue of €12,671 and a total profit of €5,311. Thanks to the Virtual Customers technology, Lisa had no trouble setting profit optimal prices, even as the market became increasingly complex.

Based on the observations of the dynamics in Lisa’s market, we want to share 4 key learnings. While the specific results of Lisa’s lemonade stand cannot be generalized, we can draw conclusions on the general relevance of measures such as the bundling of products or the entry of a new competitor into the market.

1) Extending a product line can improve profits – but you need to add the right products

It is clear that a differentiated portfolio performs better than a single product; however, it is not so clear, how closely the products within the portfolio should be related. For Lisa, the differentiation with a remotely related product (regular lemonade on Day 4) brought her a revenue increase of 12%** and a profit increase of 30%**. The differentiation with a closely related product (0.2l cup of home-made lemonade on Day 3), on the other hand, only improved her revenue by 5%** and her profit by 9%**. We have seen across industries that when differentiation is done with remotely related products, it’s usually 10-20% more profitable than when it is done with closely related products.

2) Reacting to the competition with price changes is better than maintaining prices

When a competitor enters the market, sales go down. However, it’s not so obvious, how to react best. Without necessarily entering a price war, adjusting prices is an important lever. When the competitor entered Lisa’s market on Day 6, she decreased her price by 17% (to a level where her competitor had no incentive of changing his price). Her profit still decreased by 39% but if she had kept her price at the old level, her profit would have decreased by 51%. Her price change led to a 25% higher profit. We have seen in the past, that this generally holds true among our clients, where the right adjustment of prices usually leads to a 10%-30% higher profit.

3) Adding a new product line can lead to a significant increase in profits

Not all customers are the same, as they differ significantly in their needs and preferences. At one point, however, they are very similar: they like to have a choice. For Lisa, offering this choice with the addition of another product (ice cream) to her existing offer (lemonade) on Day 7, led to a better coverage of her customers’ needs. It increased her revenue by 49%* and her profit by 41%*. Offering an extended product range substantially increases revenue, and usually, as it was the case with Lisa, also increases profits.

4) Bundling is powerful, but difficult

It’s no secret that, if done right, bundling is a powerful pricing tool. For Lisa, bundling her products on Day 8 improved her revenue by 49%*** and her profit by 44%***. However, product bundling is difficult. To work, the bundle’s price needs to be in the right relation to the individual product prices; but, to get that relation right, customers’ preferences must be known and incorporated adequately. To arrive at the right relation, Lisa had to increase the prices of the individual products by 3% and 5%, respectively, and price the bundle 8% below the

sum of both individual prices. Anyone who thinks this complexity can be circumvented by offering only the bundle, will be disappointed. Offering only a bundle instead of the individual products will almost always reduce total profit.

For the price optimization of Lisa’s offer, we used our Virtual Customers technology. By predicting real customers’ buying behavior, it enables large scale optimization of offer and prices. We demonstrated the predictive accuracy and effectiveness of the Virtual Customer technology in numerous AB tests with clients.

Interested in how the Virtual Customers technology can benefit you? Contact us or Request a demo!

Footnote

* Please note that Virtual Customers' purchase decisions are stochastic, and therefore sales volumes will be close to the analytical optimum, but not necessarily identical to it.

** Values are in relation to Day 2, when Lisa only offered one product.

*** Values are in relation to Day 7, when Lisa only offered her products separately.