Companies often learn by testing different prices over time. Experimenting with prices is like turning a dial. The lower the price, the higher the demand. Make your product more expensive and demand will decrease. Finding the right price is just a matter of setting the dial where that balance is most profitable.
But for many companies, the process by which they find the right price matters. Learning the shape of a demand curve is like walking through a bumpy landscape in the dark. If a firm is slow to change its prices, it will pay the cost of setting a suboptimal price—and it cannot afford to flounder forever.
A common approach to pricing that businesses take is to start low and slowly increase prices over time. Companies that do this often express that the price cut is unlikely to generate enough additional demand to make the move worthwhile. However, they are also reluctant to raise prices too quickly for fear of losing customers.
“In other words, firms act as if the demand curve is ‘skewed’: falling prices will barely stimulate demand, but rising prices will quickly reduce demand,” says Malladi.
Malladi developed a simple economic model that shows why companies might behave this way and how this approach can increase prices over time. The model is not a crystal ball that captures every aspect of price regulation in reality, but it does provide an explanation for a widespread practice.
The findings also help connect the dots between what business students learn in the classroom and how companies actually behave. “Students often ask, ‘How do businesses set prices when they don’t know their demand?’ he says. One answer is that they can experiment with the values over time and perhaps converge closer to an optimal value. But with his model, Malladi aspires to say more about what this process of experimentation looks like.
Is the price right?
Malladi models an environment where a firm tries different prices and makes some simplifying assumptions. First, the demand curves in the model are persistent—that is, their shape does not change over time. “We take the perspective of a company whose demand is fairly stable over time, like a local salon or restaurant.”
Then the company doesn’t know much about its demand at first. Consider a company that sells a new type of cereal. He knows that there are limits to how elastic or inelastic the demand for cereals is. But beyond that, it doesn’t know much else about the demand curve.
The model also assumes that a firm conducts the pricing experiments sequentially. A beverage company selling a new drink may sign contracts with distributors that fix prices for months at a time. If they only experiment with pricing once or twice a year, they better choose wisely how they do it.
“This is a high-stakes, low-velocity decision,” says Malladi. “It’s not just important that I get a good price in the end – I have to do well along the way.”
Not all companies need to do this kind of sequential price experimentation. A department store chain, for example, might test different prices in different stores and then choose a price that yields the highest profits. “But many businesses set flat prices and rarely change them,” adds Malladi. “For these businesses, it’s important to think carefully about the order in which you change prices.”
Playing it safe
To capture the uncertainty that firms face and their reluctance to change prices, Malladi created the model so that a firm maximizes its guaranteed profits rather than average profits.
“For each [pricing] design, I wonder, how bad could it be? For what kind of demand curves would this plan yield low profits?’ explains. “Then I choose the plan where the profits I expect to make even in the worst case scenario are not that bad.”
Malladi finds that, without knowing demand, the strategy with the best guarantee of profit initially sets prices low and then gradually raises them over time. Furthermore, for this strategy, the firm behaves as if the demand curve is kinked at the current price and sales, even if it is not actually kinked.
The reasoning is intuitive. As long as the company “assumes the worst” about potential demand and sets prices accordingly, “only good surprises are possible,” he says. “For example, if I thought I’d only sell 10,000 units and priced them accordingly, but I actually sold 20,000—great! That makes it more attractive now to raise the price.” However, before raising prices, the company considers the possibility that demand is very elastic in this area, so it raises prices conservatively.
The firm would then repeat the process at a slightly higher price, learning a little more about the shape of demand at each step. Eventually, the price increases become smaller and the process stops.
Proof positive
This approach may sound rudimentary, but it’s not the only potential price optimization strategy companies are using. Alternatively, a business can start by setting high prices and dropping them over time, or ping-pong between low and high prices to find a happy medium.
Malladi’s model, however, proves that with the conservative approach, prices inevitably move up, and so do profits. “And that’s the only strategy that gives the company the highest guaranteed profits,” he says.
Moreover, to implement this strategy, it is not necessary to analyze past price experiments or predict future sales. All you need to pick the next price is the latest price and sales data. “In that sense, it’s very simple politics,” says Malladi.
Because the model does not take into account all factors that affect pricing—such as promotional sales, a competitor’s price reduction, or adjusting to changing demand—it cannot explain every pricing strategy. But it does provide an explanation for why many firms prefer to learn about demand by raising prices. It also suggests why heuristics similar to Malladi’s model—like startup incubator Y Combinator’s 10/5/20 rule, where companies set the initial price of a product at 10 percent of its true value and then raise the price in 5 percent increments over time until demand drops by 20 percent—can be effective.
“Venture capitalists and management consultancies give advice on how companies should change their prices, and the message is often ‘raise prices.’ The model gives an economic justification for why they might recommend it,” says Malladi.
