Bagels and the law of profit maximisation

Profit maximization is one of the most fundamental assumptions in economics, yet it is rarely testable because of data limitations and the complexity of most firms. New research tests the theory of profit maximization and suggests that one under-appreciated strategy to making profit-maximizing decisions is feedback.

by Chicago Graduate School of Business
Last Updated: 23 Jul 2013

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. The data generated by this business provides an unusual window into the study of profit maximization.

In a 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.

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. 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, the results show that choosing the right price is one of the most challenging tasks for any business. Since payments are made on a trust 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 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.

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.

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. 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 firms 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.

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. 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 firms bottom line.

An Economist Sells Bagels: A Case Study in Profit Maximization.
Steven D. Levett
Chicago Graduate School of Business

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