For the last 20 years, an economist with graduate training from Massachusetts Institute of Technology has made a business of delivering donuts and bagels to Washington DC–area businesses. Individuals buy these goods on the honor system, depositing payment in a lockbox. The data generated by this business provides an unusual window into the study of profit maximization.

In the recent study “An Economist Sells Bagels: A Case Study in Profit Maximization,” University of Chicago professor Steven D. Levitt analyzes the extent to which the decisions of the bagel and donut delivery business are consistent with profit maximizing choices.

In order to set prices, a firm needs to know its marginal cost of producing the good, as well as the “elasticity of demand”—how responsive customers will be to changes in prices. There are basic tenets of pricing that every firm should adhere to, including: not setting prices below marginal cost (the cost of producing a product); not choosing a price at which demand is inelastic (which implies that a price increase will raise profits for certain); or stopping production when marginal revenue exceeds marginal cost. Despite these clear economic predictions, direct attempts to test profit maximization are quite rare. In practice, real-world firms are typically very complex, produce multiple goods, and detailed information on marginal cost is rarely available. These factors combine to make it almost impossible to make an accurate assessment of whether a firm is profit maximizing.

There are several reasons why the bagel and donut delivery business would be a leading candidate to maximize profits. First, the service the firm provides is very simple—with only one line of business and two products,marginal cost is easily observed. Second, the firm gets frequent and detailed signals of demand—each day, for each customer, the owner chooses the quantities of bagels and donuts to deliver; later that day, the owner observes the amount of goods that go uneaten and the revenue collected. Third, the owner has studied economics and has 20 years of experience as a professional economist.

“The owner of the business knows the formulas that we teach in microeconomics courses,” says Levitt. “This was an opportunity to go into the field and ask: Does this business owner make decisions consistent with the models that we teach?”

Detailed data, combined with the straightforward nature of this company’s business provide an unusually direct opportunity to test for the firm’s profit maximizing behavior along two important dimensions of decision making: the choice of quantity and the choice of price.

Levitt used 13 years of data that had been collected by the business owner, representing more than 80,000 deliveries. He finds that the company is extremely adept at determining the quantity of bagels and donuts to deliver to a particular company on a given day at a given price.

“Using rules of thumb that are informed by economics and his own intuition, the owner has managed to get very close to profit maximization in regards to choosing quantities,” says Levitt. “It’s a phenomenal display of how an intelligent person with good feedback can perform exactly like the basic economic model would predict.”

However, the firm sets its prices far too low. Levitt’s conservative estimates suggest that the firm sacrificed 30 percent of its potential profit through mispricing.

That the firm does a poor job of pricing, but an excellent job of choosing the quantity to deliver each day, is not that surprising when one considers the information available to the decision maker. Whereas the firm receives daily feedback regarding the quantity demanded by each customer, the daily activities of the firm yield little useful information for determining optimal price.

“Setting prices is a fundamental business decision,” says Levitt. “Yet,my results show that choosing the right price is one of the most challenging tasks for any business.”

The Business
The economist’s bagel and donut delivery business began in 1984.Eachmorning, the owner purchases bagels, cream cheese, and donuts wholesale. The goods are left in a central area at local businesses with a sign stating prices and with a wooden lockbox. Later that day, a company employee returns to collect money and any uneaten bagels and donuts. Since the company does not charge for this service, revenues are generated only by payments. In an average week, the company delivers more than 3,000 bagels and 1,500 donuts to approximately 125 clients.

The company founder provided Levitt with detailed records of the firm’s operations: the amount of goods delivered; the amount of money collected that day; and the number of goods that go uneaten. All information is reported separately for each client, each day. Data includes both the posted prices that customers are charged as well as the wholesale cost of bagels, cream cheese, and donuts.

The data covers the period January 1993 to December 2005. The posted price for bagels increased three times over the course of the sample. Initially, the owner set the price at 60 cents. That price jumped to 75 cents in August 1993, 85 cents in August 1998, and $1 in May 2003. The price of donuts was 50 cents for almost the entire time period, increasing to 60 cents in March 2005.

Since payments are made on the honor system, the firm’s revenue is less than the posted price. Some customers pay less than the posted price, or not at all. On average, the payment rate (defined as actual revenue divided by expected revenue if the posted price were paid for each good consumed) is slightly below 90 percent in the data.

“The business owner knows everything he needs to know to make optimal choices about prices and quantities,” says Levitt.

Modeling Profit Maximization
“On a daily basis, the real choice the owner makes is about the quantity to deliver,” notes Levitt. “Since he only increased prices three times over the whole sample, he basically acts like the price is fixed.”

Using econometric models, Levitt analyzed the optimal quantity of goods that should be delivered to each customer. First, Levitt estimated the optimal quantity to deliver based on a particular price for only one good. The optimal quantity estimates were determined by the posted price of a bagel, the degree of underpayment on the honor system, the marginal cost, and the observed probability that all the bagels delivered are eaten. Levitt analyzed the degree to which the firm’s actions, on average over the course of a year, correspond to the predictions.

The results demonstrate that the firm’s quantity choice closely corresponds with predictions of the model. If the business owner had used Levitt’s model, he would have only increased his total profits by $200 annually.

The optimal quantity decision becomes more difficult when two products are delivered. The concerns include whether the supply of bagels and donuts at a particular location will run out, and the degree to which the firm steals business from itself by offering similar goods.

The firm shows substantial skill in altering its behavior over time to achieve the profit maximizing delivery quantities. Levitt’s regression model adds only trivially to the firm’s existing practices.

In contrast to the quantities supplied, which vary for each customer on a delivery-by-delivery basis, there is little price variation. There are only four price changes over the entire sample (three price changes for bagels, one for donuts). After each of the price increases, both the quantity delivered and consumed of the goods fell, and the payment rate declined. These declines, however, were not enough to offset the increased revenue due to the higher price. Profits rose substantially after each price increase.

Indeed, after every price increase, the firm’s revenue increased, implying that the firm was operating on what is known as the inelastic portion of the demand curve. If the firm is on an inelastic part of the demand curve, when it raises price by 10 percent, the quantity sold falls by less than 10 percent. Consequently, the firms total revenues rise, but since it is producing fewer of the good, its costs must fall. Higher revenues, combined with lower costs,mean more profits.

Levitt explains: “One of the things you are taught in a first year MBA microeconomics course is never to price on the inelastic part of the demand curve, yet, over the entire period, the owner violated this basic rule of pricing. This one decision about what price to charge cost the business owner 30 percent of profits, even though he did everything else right.”

The Importance of Feedback
“Businesses are likely to do well on decisions where immediate and informative feedback is available,” says Levitt.

There are many aspects of business that have immediate feedback elements, such as inventory management and quality control. Firms are likely to perform well on dimensions for which there is frequent and informative feedback regarding profits, but without that feedback, they will likely deviate from ideal profit maximizing behavior.

In regards to prices, a firm has no direct mechanism for learning whether it is pricing correctly. The pattern of real-time adjustments in production rates coupled with much less frequent changes in prices observed in this case study appears to be common practice among firms.

“Ideally, the owner would find the optimal price by charging different customers different prices and observing whether profits increase,” says Levitt. “Absent that kind of feedback, it is difficult—if not impossible—to determine whether you have found the right prices. One approach, rarely utilized by firms, are randomized field experiments. I think these are the way of the future. But even if a firm is not willing to go that far, building in other mechanisms for providing timely and reliable feedback in these areas is likely to prove highly beneficial to a firm’s bottom line.”

 

"An Economist Sells Bagels: A Case Study in Profit Maximization." Steven D. Levett.