Maximizing the Bagel Dollar

Economics textbooks tend to use simple businesses to illustrate economic theory. For instance, Greg Mankiw’s Principles of Economics uses a bagel shop to illustrate how production costs change as bagel sales increase or decrease. And when it comes to maximizing profits, the standard texts tell us that businesses should price at or above marginal cost.

In a new paper, Freakonomics author Steve Levitt follows up on his study of an innovative bagel business. The business worked on an "honor system." Its owner, Paul F., would leave bagels in a basket at workplaces everyday and ask those who took bagels to leave a payment. It turns out that many workplaces were quite honest and the business has thrived for over 20 years.

In the new paper, Levitt takes the wealth of data from the bagel business and uses it to see whether Paul maximizes profits. Paul's business is ideal: he sells only bagels and donuts, his costs are well known, he understands the demand curve he faces (Paul can see how many bagels and donuts are left unsold each day), and Paul himself was once an economist. If there ever was a business that would be profit maximizing, it's Paul's.

When demand jumps around from day to day, maximizing profits involves doing two things.

• Get Quantities Right: The first thing a firm must do is make sure that, for the price they are charging, the quantity of bagels matches that demand at that price. It is easy to see that mistakes could lead to stock-outs (shortages) or left-overs (surpluses) [the RED arrows in the figure] Both are costly in terms of lost sales or over-production.

• Get Prices Right: The second thing a profit maximizing firm needs to do is get the prices right. The price should be set so that quantity demanded at that price equates marginal revenue with marginal cost. Pricing too low or too high [the PURPLE arrows in the figure] leads lost profits for the firm.

Levitt shows that Paul gets quantities right (for both bagels and donuts, there are very few stock-outs or left-overs), but he often gets prices wrong. Paul systematically prices donuts and bagels too low. Indeed, his prices are so low, they fall on the inelastic section of Paul's demand curve--Paul could actually increase total revenue by increasing his prices. Hence, his prices are at a point like P in the figure. At point P, marginal revenue is negative (below the x-axis); so increasing price and reducing sales will raise revenue.

Levitt argues that this might be an issue for many businesses like Paul’s. What Paul gets to see from day-to-day is how well he is doing getting quantities right; since his price doesn’t change, however, he doesn’t see how well he is doing getting prices right. So if he is wrong, he never knows it.

1. Economists believe that firms do not systematically forgo profits because they will experiment with price and quantity changes. Why do you think a bagel business might be reluctant to experiment with price changes?

2. Levitt considers whether pricing is a longer-run decision for the firm and so it may be that Ben was pricing with regard to long-run price elasticity of demand rather than short-run price elasticity of demand. It turns out that even on a longer-run basis, demand was inelastic at Paul’s pricing. Why is it important to distinguish between long and short-run price elasticity when evaluating whether a firm is maximizing profits?

3. Can you think of other examples of businesses that might be systematically pricing too low or too high?

Joshua Gans is Professor of Economics at the Melbourne Business School, University of Melbourne. He has co-authored the Pacific Rim Edition of Mankiw's Principles of Economics and his own text, Core Economics for Managers (Thomson, 2005). He maintains his own blog at coreecon.blogspot.com.