Many businesses focus on driving volume or reducing costs, rather than increasing price, under the mistaken belief that they have greater control over volume and costs than price. Yet, a 1 percent increase in price (holding volume fixed) has a greater impact on operating profit than a 1 percent increase in volume or a 1 percent decrease in cost. By not seizing the initiative on price, businesses abrogate decisions about price to competitors, customers, and the channel. A careful analysis and understanding of those same actors could help them price in a more profitable manner – hence, this book, which is designed to communicate the fundamental principles of pricing.

There is a science to pricing rooted in economic theory. Under a set of assumptions about consumer and market behavior, we can derive prescriptive pricing rules. These rules provide guidelines and help in understanding how prices will and should change when the underlying environment changes. As nothing straight ever came from the crooked timber of humanity, there is also an art to pricing as well. How products and services are positioned and communicated to consumers can affect their price perception. Even objectively identical products are able to command different prices.

The first step in formulating a pricing strategy is to understand the behavior of buyers. We start with the assumption that buyers are rational, suggesting that mad dogs and Englishmen are not the only ones who go out into the noonday sun.

Auctions are a venerable selling institution, in use since the time of Herodotus. The word comes from the Latin auctus, meaning to increase. An obscure term for auction, one guaranteed to impress friends and neighbors, is the Latin word subhastare. It is the conjunction of sub, meaning “under,” and hasta, meaning “spear.” After a military victory, a Roman soldier would plant his spear in the ground to mark the location of his spoils. Later, he would put these goods up for sale by auction.

Perhaps the most engaging tale about auctions is the sale of the Roman Empire to the highest bidder. It is described in Edward Gibbon's account of the decline and fall of the same.

In 193 a.d. the Praetorian guard3 murdered the emperor Pertinax. Sulpicianus, father-in-law to Pertinax, offered the Praetorians 5,000 drachmas per guard to be emperor. Realizing they were onto a good thing, the guard announced that the empire was available for sale to the highest bidder. Didius Julianus outbid all comers and became emperor for the price of 6,250 drachmas per guard. The description by Gibbon is worth a read:

The goal of this chapter is to convey the main principles of pricing in competitive environments. We approach them through a series of of thought experiments. The advantage of these experiments is that every variable within them can be controlled. This allows one to precisely isolate how each aspect of the competitive environment affects prices. The result will be a clearer and deeper understanding of pricing in competitive environments than any collection of anecdotes or string of ‘just so’ stories is able to deliver. To apply the lessons of this chapter, one must know some basic facts about the industry one is in – specifically, entry costs, exit costs, structure of demand, number, concentration and the distribution of rivals' sizes.

The Pricing Dilemma

Imagine two firms selling identical widgets to a market of 100 individuals. Each buyer is interested in purchasing at most one widget, and the RP of each buyer is $3. Each buyer will buy from the seller that offers them the largest surplus. Because the products are identical (in the eyes of each buyer), each buyer will purchase from the lowest-priced seller. In the event that both firms set equal prices (and so yield the same surplus to all buyers), the buyers divide equally between the two firms.

The production cost for each firm is $1 a widget. Production is instantaneous and defect-free, so neither firm needs to worry about inventory, returns, and the other complications of real life. Production capacity is unlimited for both firms.

The word game in game theory is not limited to parlor games, such as bridge or Scrabble. It applies to all situations in which two or more agents are in competition with one another, such as a negotiation between labor and management or a price war between rival firms.

Let us begin with a simple situation to provide a flavor of what is to come.

John is currently the monopoly supplier of SOMA. Oskar is thinking of entering the SOMA business. What Oskar decides depends on how John will react to his entering the market. Will John lower prices to ruin Oskar, or will he maintain his current prices?

Oskar expects to be $50 million ahead if he enters the market and John accommodates his entry. If John decides to retaliate by lowering prices, Oskar will lose $100 million in total.

Oskar believes that John stands to make $500 million as a monopolist. This amount will be reduced to $400 million if John accommodates Oskar's entry. If John lowers prices in retaliation, he loses $200 million.

John has just announced that should Oskar enter the market, he will start a price war by lowering prices. Assuming that Oskar cannot afford to lose $100 million, should he enter the SOMA industry?

If Oskar believes John's threat, the answer is, of course, no. But why should Oskar believe this? Notice the following: if Oskar enters, which action gives John the higher profit? Accommodating Oskar's entry. He wins $400 million rather than lose $200 million.

In this chapter, we examine the issues associated with setting the same posted price for all buyers. The first is the trade-off between margin and volume. A high price means a high margin but a low sales volume. A low price means a low margin but a large sales volume. Somewhere between the two is a “sweet spot,” and it is natural to ask what that sweet spot depends on.

To think about the trade-off between margin and volume, it will be useful to ignore competition. Therefore, as we change our price we assume that the competition will not respond by changing its price, its offering, or both. Furthermore, to keep the arithmetic simple, we assume that the consumer surplus from buying a competitor's product is always zero. What is restrictive about this assumption is that the consumer surplus never changes. In effect, the competition does not lower its prices in response to us raising ours, or configuring its product differently. The economics shorthand for this assumption is that the firm setting prices is a monopoly. We will adopt this shorthand in the text that follows. The assumption, though drastic, allows us to focus on the interaction between the seller and buyers to the exclusion of other issues. (The consequences of dropping this assumption are examined in Chapter 7).

If one takes the rational buyer model seriously, the most important challenge for the seller is determining how a buyer will respond to a price. For this reason, we begin this chapter with a laundry list of methods for estimating how buyers will respond to price.

1. Managerial judgment. A simple way is to use the accumulated knowledge of product managers, salespeople, and members of the product engineering team to arrive at a demand curve for the product or service. Subjects are given a product book that provides information on items such as product sales and product price, as well as competitive sales and competitive prices. After digesting this information, the subjects are asked how much, in percentage terms, sales are likely to change for an X percent price increase where X is incremented in some fashion, say 2 percent, 4 percent, and so on, up to 10 percent, followed by the same questions for an X percent price decrease. Subjects should be asked to think about competitive response during the exercise, so the obtained demand curve reflects a realistic state of the world. For each price response, the subjects should identify a source-of-volume model, which is a way to describe how the composition of buyers (those who buy from this seller, those who buy from the competition, and those who currently buy from no one) changes as a function of a price change.

It is not uncommon for different customers to value the same product differently. This difference in valuation allows one to earn a greater profit by matching the price to a customer's RP – in other words, selling the same product or service to different buyers at different prices. In many cases, some modification of the product or service is needed to be able to charge different prices. The practice is called price discrimination. To see why the practice is more profitable than charging a uniform price, an example is helpful.

Example 14 Recall the monopolist from Example 3 in Chapter 4. The demand for the monopolist's product is described by the demand curve 9 – p. Such a curve can arise in the following way: Suppose there is one customer with a R P of 8, another with a RP of 7, and so on. When the monopolist was restricted to charging a single price, we determined that the price should be $5 a unit, yielding a profit of $16. Suppose the monopolist could get away with charging a different price to each buyer, say, $7 to the buyer with a R P of $8, $6 to the buyer with a RP of $7, and so on until the buyer with a R P of $2. The profit would be 6 + 5 + 4 + 3 + 1 = 19. □

To price effectively, one must account for the specifics of the industry, such as regulation and supply and demand; specific aspects of the product market, such as competition, customer value, costs and channel issues; and, finally transaction-specific elements, such as discounts, allowances, payment terms, rebates, and the like. In other words, one needs sound industry knowledge, sound product market knowledge, and sound transaction specific knowledge to price effectively. As Sherlock Holmes notes: “Data, data, data. I cannot make bricks without clay.”

Each chapter in this book provides key information that helps in pricing effectively. Two important principles underlie effective pricing. First, one must have some knowledge of price response or the demand curve for the product (or service). From the demand curve, one can obtain an estimate of price elasticity. Chapter 3 discusses several ways of getting at price response, ranging from managerial judgment to use of analogous products, benchmarking, focus groups, surveys, experimentation, using regression analysis on historical data, and EVC to conjoint analysis. The bottom line is that you cannot price with confidence if you do not know how your customers will respond to price.

The second important principle is to understand the value that customers place on your product. Value is connected implicitly to price elasticity because the demand curve is a representation of customer willingness to pay. However, you should be trying to influence customer valuation and, thus, customer response to price.

To begin, we consider the simplest nontrivial pricing problem.

The Ultimatum

The world contains just two people: a buyer and a seller. The seller has a book that she values at zero that she wishes to sell to the buyer. It is the only book of its kind in the world and the buyer is fully aware of its contents and condition. The buyer values the book at $10, neither more nor less. Each is aware of how the other values the book. The seller has one chance to set a price. Once the price is fixed, the buyer has one chance to buy at the price posted or to decline. No other inducements, counteroffers, or promises are permitted. What price should the seller set to maximize her revenue?

The usual mysteries that cloud a pricing situation have been stripped away. There is no uncertainty about the nature or quality of the product. The value of the product to the buyer is known, as is the seller's opportunity cost. There are only one seller and one buyer. The dance between seller and buyer is limited to a single take-it-or-leave-it offer.

It is clear that the chosen price should not exceed $10, the value of the book to the buyer. Thus, the only question is just how close to $10 the seller can set the price and have the buyer accept.