In an episode of the 1990s sitcom “Seinfeld,” Jerry’s zany neighbor Kramer asked for help lugging his purchases from the Price Club to his New York City apartment. Jerry takes one look at his bulk buys, including a 10-pound package of cocktail meatballs, and says, “What, are you out of your mind? … You will never be able to finish all this stuff.” Kramer responds: “$17.50. You can’t beat that.”

Even before Costco’s warehouse stores made quantity discounts fashionable, consumers have been trained to expect that if they pay one price to purchase one item, they often can get a price break when they buy two or more of the same item. But that also presents a conundrum to businesses: How much of a discount should companies give if they don’t have any history of bulk sales of that product or service? What is the best price that will make customers buy more than one item and still yield maximum profitability?

That is the subject of “A Conjoint Model of Quantity Discounts” by Raghuram Iyengar, a marketing professor at Wharton, and Kamel Jedidi, a marketing professor at Columbia University. They took the traditional conjoint analysis model, which looks at how consumers arrive at a decision to purchase after considering the features of a product or service, and modified it to include the effect of quantity on such a decision. By doing so, they came up with a way for businesses to arrive at the best price for quantity discounts without the cost and hassle of launching trial-and-error pricing plans. “Unraveling how much people are willing to pay is at the heart of designing optimal price quantity discount,” Iyengar says.

The logic behind offering bulk discounts is simple: Customers’ enjoyment of the subsequent units of the same item diminishes, and thus they are willing to pay less for them. For instance, Disney charges adults $79 each for a one-day admission to its theme park and $243 for 10 consecutive days. If there were no bulk discount, 10 days of admission would cost $790. Disney slashed the price by 69% for people who are willing to spend 10 days at the park.

Why? Disney believes enjoyment of the park will steadily decline the longer the visitors stay there, the researchers note. After all, the teacup ride is only fun the first three times — you get tired of it after a while. To entice people to stay longer at the park so Disney can keep making money off them, the company had to offer a bulk discounted rate. But how can Disney be sure that the $243 price for a 10-day ticket would maximize its profits? Why not $450 or even $650, which still represents substantial discounts from $790? The researchers argue that Disney figured out that $243 was the optimal price to entice a family to stay and still allow the company to make money, given competition and other factors. “It’s in Disney’s interest to understand how much people are willing to pay to stay an additional day and to price it exactly that way,” Iyengar says.

His and Jedidi’s research is intended to help companies arrive at this “sweet spot” price. To illustrate how their model works, Iyengar and Jedidi applied their mathematical formula to the online movie rental business. They chose this market because consumers are familiar with the product as well as the rental plans of the industry’s two major players, Netflix and Blockbuster. The authors created a fictitious company called, and came up with a scenario in which the business would try to break into the market with pricing plans aimed at capturing market share. They modeled two scenarios for the new company’s DVD rental plans: one that assumes no competition and another that does.

First, the authors surveyed 250 consumers to collect data for their model. They presented the participants with several plans, pitting MovieMail against Netflix and Blockbuster. The rental plans featured different levels of pricing depending on the number of movies a customer wanted to take out at a time, as well as the availability of high-definition Blu-Ray movies. The researchers told participants that MovieMail is a new company that operates just like Netflix and Blockbuster Online, offering the same movie selection, search capabilities and delivery time.

The survey presented consumers with several combinations of rental plans, and they were asked to choose one or none of the DVD proposals offered. The depth of the bulk discounts varied, as the authors attempted to determine the optimum price consumers would bear. In one scenario, participants had to make one of four choices: MovieMail’s $15.99 a month plan to rent two DVDs at a time, whether in standard or Blu-Ray format; Netflix’s $17.99 a month three-DVD plan without the option for Blu-Ray; Blockbuster’s $33.99 a month plan for six DVDs with Blu-Ray, or pass on the plans altogether. The authors also asked participants about their actual DVD rental habits. From this, they found out that their sample was statistically representative of the market.

Iyengar and Jedidi ultimately discovered that what consumers were willing to pay declines after renting the first DVD and takes a steep plunge after the second. They calculated the exact values of a customer’s marginal willingness to pay, which they plugged into their formula to come up with the best pricing. “The critical information for designing such a quantity discount scheme is knowledge of consumers’ willingness to pay for successive units of a product or service,” Iyengar and Jedidi write in their paper.

According to the researchers, Netflix, Blockbuster and, theoretically, MovieMail must offer drastic discounts to keep customers interested in rental plans offering two or more DVDs. If not, consumers won’t bite. “Consumers’ willingness to pay is the maximum price value that makes one indifferent between buying and not buying,” Jedidi notes.

The survey showed that brand name also had an impact on pricing. Netflix had superior brand equity while consumers valued Blockbuster about the same as a relative unknown, in this case MovieMail. As such, consumers were willing to pay a premium for Netflix. The availability of Blu-Ray movies also affects a consumer’s choice of provider. Iyengar and Jedidi’s test showed that consumers were willing to pay around $1.00 a month more on average for Netflix than Blockbuster and MovieMail, and about 65 cents more to have Blu-Ray as an option.

For a one-DVD plan with Blu-Ray, for instance, consumers surveyed would pay $12.47 a month on average to Netflix, but only $11.35 to Blockbuster and $11.37 to MovieMail for the same plan. Without the Blu-Ray option, they were willing to pay Netflix $11.78, Blockbuster $10.73 and MovieMail $10.74. Netflix actually charges $2 more per month for one-DVD plan customers to get Blu-Ray movies but Blockbuster does not, perhaps a strategy to offset its weaker brand name in the DVD rental market, the researchers suggest.

The Power of Price

The authors next examined consumer demand. They separated the test subjects into four groups based on how much they would be willing to spend, recognizing that not all customers are the same because some would potentially be worth more to the company than others. Iyengar and Jedidi note that consumers wanted to compare the prices of different plans before choosing one or none.

According to the researchers, the study results for Netflix indicated that 10.7% of customers potentially would be worth $68.99 each to the company per month because they were willing to shell out the most for a DVD rental plan. This group was therefore considered the company’s most valuable customers. Another 19.1% — those who were light DVD renters but willing to pay more per unit — were worth $27.81 per month. A third of Netflix’s customers were heavy renters but not willing to pay much for each successive movie taken out. They yielded an average value of $26.71 per month. The least attractive — and largest — group of customers at 36.9% would pay even less for a rental plan and represented a per-month value of $16.93 per consumer. Such analysis of segmented results will help companies tailor special offers and plans to different customers, the authors point out.

Iyengar and Jedidi also used consumer demand data to determine that a 1% price increase by Netflix would cause a 1.15% drop in demand for one-DVD-out-at-a-time rental plans. The decline in demand would accelerate with rental plans for more DVDs. But if Blockbuster sets the same price hikes, the researchers say, demand would drop by an even higher percentage — leading to the conclusion that Blockbuster customers are more price-conscious than Netflix subscribers. Such analysis will help a company figure out the depth of the quantity discount it should offer to be successful, they note.

Given these insights, Iyengar and Jedidi began crafting pricing plans for the fictional MovieMail. Initially, their plans assumed no competition in the market to set a kind of benchmark. Later on, they factored in the effect of competition.

The authors assumed that MovieMail incurs the same marginal costs as Netflix — $1.22 per rented DVD for mailing, packaging and royalty fees. They also noted that customers rent 4.9 DVDs on average per month under a one-DVD plan and up to 13.8 DVDs for a four-DVD plan, according to survey results. These quantities, together with marginal costs, gave Iyengar and Jedidi an idea of how much it would cost MovieMail to distribute movies.

Then Iyengar and Jedidi tried to determine the highest price MovieMail customers would bear to yield the largest profit, without competition from rival providers.

Based on results from the survey, they predict that MovieMail stood to maximize profit if it charged $13 a month for a one-DVD plan, and that 91 out of the 250 potential customers surveyed would sign up. That would yield a market penetration of 36.4%, meaning slightly more than a third of consumers would sign up for a DVD rental plan. MovieMail’s profit would be $638.82 from those 91 customers, after subtracting marginal costs. The optimal price for a two-DVD plan would be $23 a month while the profit maximizing price for three DVDs is $31.

Then Iyengar and Jedidi created a second set of pricing plans that reflected competition from Netflix and Blockbuster. Their model assumed that consumers know MovieMail is entering the market and that its DVDs are readily available. It also assumed that customers won’t incur any costs to switch to MovieMail and that Netflix and Blockbuster won’t respond with special deals and other incentives to counteract a rival’s entry into the market. Currently, Netflix and Blockbuster charge $8.99 a month for one-DVD-out-at-a-time plan, $13.99 for two DVDs and $16.99 for three. Netflix also offers a four-DVD plan at $23.99 a month. Among respondents, Netflix enjoyed a 73.2% share of the market while Blockbuster had 25.2% and 1.6% rented from other providers.

Using the authors’ conjoint model, MovieMail’s best move would be to offer cheaper plans than Netflix or Blockbuster. Their mathematical formula yielded $8.22 as the best monthly price for a one-DVD plan, $12.69 for two DVDs and $16.40 and $21.82 for three- and four-DVD plans, respectively. The savings over both Netflix and Blockbuster would be enough to garner MovieMail a 33% overall market share. Netflix’s share would fall to 49% and Blockbuster to 18%.

So even without testing the market with trial pricing plans, the researchers were able to calculate the likely optimal price for MovieMail’s DVD rental service. Iyengar and Jedidi contend that using a mathematical formula offers companies a money-saving shortcut to determining the best way to employ quantity discounts. Businesses can use data culled from market research and plug the values into the researchers’ model to arrive at the “sweet spot” price. “Companies can test and learn over time,” Jedidi notes. “However, an important value that we add here is to design quantity discounts for new products.”