Every product or service sold by a firm has a unique demand curve—a relationship between how much customers want a thing and how much they’re willing to pay for it. And for many firms, “it is hard to know what exactly it looks like,” says Suraj Malladi, an assistant professor of managerial economics and decision sciences at Kellogg.
Firms often learn by trying different prices over time. Experimenting with prices is like turning a dial. The lower the price is, the higher is the demand. Make your product more expensive, and demand will fall. Finding the right price is merely a matter of setting the dial where this balance is most profitable.
But for many firms, the process by which they search for the right price matters. Learning the shape of a demand curve is like stepping through a bumpy landscape in the dark. If a company is slow to change its prices, it’ll pay the cost of setting a suboptimal price—and it cannot afford to stumble around forever.
One common approach to pricing that firms take is starting low and slowly raising prices over time. Firms that do this often express that lowering prices is unlikely to generate enough extra demand to make the move worth their while. Yet they also hesitate to increase prices too quickly out of fear of losing customers.
“In other words, firms act as if their demand curve is ‘kinked’: dropping prices would barely stimulate demand, but raising prices would rapidly drop demand,” Malladi says.
Malladi developed a simple economic model that shows why firms might behave this way and how this approach can drive up prices over time. The model is no crystal ball that captures every aspect of price setting in reality, but it provides an explanation for a widespread practice.
The findings also help connect the dots between what business students learn in the classroom and how firms actually behave. “Students often ask, ‘How do firms set prices when they don’t know their demand?’” he says. One answer is that they can experiment with prices over time and maybe converge closer to an optimal price. But with his model, Malladi aspires to say more about what this process of experimentation looks like.
The price is right?
Malladi models a setting where a firm tries out different prices, and he makes some simplifying assumptions. First, demand curves in the model are persistent—that is, their shape doesn’t change over time. “We take the perspective of a firm whose demand is fairly stable over time, like a local salon or restaurant.”
Next, the firm doesn’t know much about its demand at the start. Consider a firm selling a new kind of cereal. It knows that there are some limits to how elastic or inelastic demand for cereal is. But beyond that, it doesn’t know too much else about its demand curve.
The model also assumes that a firm conducts its 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 get to experiment with pricing once or twice a year, they’d better choose wisely how they do it.
“That’s a high-stakes, low-velocity decision,” says Malladi. “It’s not just important that I find a good price eventually—I need to do well along the way.”
Not all companies need to do this kind of sequential price experimentation. A department store chain, for example, can try different prices in different stores and then choose a price that nets the highest profits. “But many businesses set uniform prices and change them infrequently,” Malladi adds. “For those businesses, it is important to think carefully about the order in which you change prices.”
Playing it safe
To capture the uncertainty firms face and their caution in changing prices, Malladi set up the model so that a firm maximizes its guaranteed profits rather than average profits.
“For every [pricing] plan, I can ask myself, How bad could it be? For what kind of demand curves would this plan return low profits?” he explains. “Then I choose the plan where the profits I stand to make even in the worst-case scenario are not so bad.”
Malladi finds that, without knowing the demand, the strategy with the best profit guarantee initially sets prices low and then ratchets them up gradually over time. Moreover, for this strategy, the firm behaves as if its demand curve is kinked at the current price and sales, even if it is not kinked in reality.
The reasoning is intuitive. As long as the firm “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.” But before making a price hike, the firm considers the possibility that demand is very elastic in that region, so it raises prices conservatively.
Then the firm would repeat the process with a slightly higher price, while learning a little bit more about the shape of its demand at each step. Eventually, the price increases become smaller, and the process comes to a halt.
Proof positive
That approach might sound elementary, but it’s not the only conceivable price-optimizing strategy companies use. Alternatively, a firm might start by setting high prices and dropping them over time, or ping-ponging between low and high prices in order to find a happy medium.
Malladi’s model, however, proves that under the conservative approach, prices inevitably move upward, and so do profits. “And this is the only strategy that gives the firm the highest guaranteed profits,” he says.
What’s more, in order to implement this strategy, it isn’t necessary to analyze previous price experiments or to forecast future sales. All that’s needed to choose the next price are the most recent price and sales data. “In that sense, it’s really simple policy,” Malladi says.
Because the model doesn’t account for all the factors that go into pricing—like promotional sales, or undercutting a competitor, or adjusting to changing demand—it can’t explain every pricing strategy. But it does provide an explanation for why many companies prefer to learn about demand by raising prices. It also suggests why heuristics that resemble Malladi’s model—like startup incubator Y Combinator’s 10/5/20 rule, where companies set the initial price of a product to 10 percent of its real value and then raise the price in 5 percent increments over time until demand drops by 20 percent—may be effective.
“Venture capitalists and management-consulting firms give advice on how firms should be changing their prices around, and the message is often ‘raise prices.’ The model gives one economic justification for why they might suggest that,” Malladi says.