### The Power of the Soup Nazi

Welcome back loyal readers. Having spent much of the last month sending out job applications, it’s time I took a break. That means taking the time to notice economic quirks in my daily life and writing about them.

While flipping through channels over Thanksgiving break, I came across an episode of Seinfeld that caught my attention: the Soup Nazi. For those unfamiliar with the episode, the Soup Nazi is the owner and operator of the most popular soup counter on the upper-west side of

The episode begins with Jerry and George explaining the Soup Nazi phenomenon to Elaine. Doubting the strictness of the hyperbolically monikered soup genius, Elaine openly flaunts the rules, resulting in an abrupt “No soup for you! Come back, one year!” from the Soup Nazi. This exchange sets up the two strong-willed characters as adversaries for the remainder of the episode.

Elaine gets her chance to settle the score when an armoire given by the Soup Nazi to his favorite customer Kramer ends up in Elaine’s apartment. The Soup Nazi had apparently left handwritten copies of his recipes in the bottom drawer. Upon discovering the recipes, Elaine becomes increasingly excited at her opportunity for revenge, telling Jerry “I could give these to every restaurant in town. I could have 'em published! I could…I could drop fliers from a plane above the city.”

It is at this point that the episode takes a most disappointing turn as Jerry tries to dissuade Elaine from bringing down her nemesis saying “I don't want you causing any trouble down at that soup stand. I happen to love that soup.” But if all he cares about is the soup, why would he care who makes it? If anything, letting the recipes out would improve the situation for Jerry as a consumer. You see, the Soup Nazi, by virtue of having the best soup around, enjoys a certain monopoly power. Economists recognize monopoly power as a means for certain retailers to raise prices, reduce access to the product, and skimp on services, all to the detriment of the consumer. In this case, the Soup Nazi wields his monopoly power with long lines and by enforcing an authoritarian code of conduct. But if the soup recipes were made widely available, lines would be reduced and codes of conduct relaxed as other retailers compete for customers. The soup Nazi could then change his ways and compete for customers with the rest or resist such changes and be put out of business. He loses something either way while Jerry and the rest of the soup fanatics gain.

The writers of Seinfeld show a complete lack of economic insight regarding the demise of the Soup Nazi. Even at the episode’s end, as the Soup Nazi rations the last of his stock before going out of business, Newman laments the last of the soup. But why should this be the last of the soup? As I just explained, availability of the soup should be expected to increase as other retailers duplicate the recipes of the Soup Nazi.

This simple bit of economic logic was not lost on the writers of the Simpsons who consider an analogous situation in the episode “Flaming Moe’s.” In this episode, Homer shares his secret recipe for a cocktail called the Flaming Homer with Moe, owner of the local bar. Moe’s business takes off when he begins serving the irresistible cocktail under the name Flaming Moe. Soon Aerosmith is playing there every night and Homer can’t even find a seat at the bar. Homer becomes consumed with jealousy and eventually reveals the secret ingredient to everyone in the bar.

Can you guess what happens next? The scene that follows shows every other storefront along the main strip advertising the Flaming Moe. This is good for consumers as Moe, exercising monopoly power, had been successful charging high prices and restricting access to his product. Once the secret got out, anyone could produce it and so his power as a monopolist was lost. This is precisely what should have happened at the end of the Soup Nazi episode. Realizing the inevitability of this outcome, it makes no sense for Jerry to try and prevent Elaine from making the recipes public. This is not to say that revealing another party’s proprietary information is in any way ethical. Enforcement of property rights is a necessary component of the legal system in any society that hopes to reward technical innovations and artistic creativity by its citizens. (Editor’s note: The irony of having said this while also providing links to youtube clips has not been lost on the author.) But anyone familiar with the show should know that Jerry and his friends are guided only by self interest. And in this case, self interest dictates that Jerry allow the recipes to be made public.

As an addendum, I just saw the movie Mean Girls and noticed a mistake in the math. In the Mathletes competition toward the end, the competitors were asked to solve the following equation: lim x->0 [ln(1-x)*sin(x)/(1-cos^2(x))]. That is the limit of a fraction as x goes to zero in both the numerator and the denominator. The girl from the other school said the answer was 1 and was ruled incorrect. Notice that both the numerator, ln(1-x)*sin(x), and the denominator, (1-cos^2(x)), are equal to zero when evaluated at x=0. So what is zero divided by zero? Recall what your high school teacher taught you: "any number divided by zero is 'undefined.'" Applying that very lesson, Lindsay Lohan's character responds, "the limit does not exist," and wins the competition. While her answer was consistent with what most of us were taught, it is in fact wrong.

When adults use calculus to solve problems, it is not enough to say that 0/0 is 'undefined.' 'Undefined' didn't put a man on the moon. 'Undefined' is just another way of saying, "I don't know." To know what 0/0 is, you have to know the speed at which both the numerator and the denominator go to zero. Think about this problem: lim x-> [c/x], where c is an arbitrary non-negative constant. As x goes to zero, the ratio c/x goes to infinity. Since zero is a non-negative constant, we might reasonably conclude that 0/0 is infinity. Now think about this problem: lim x-> [x/c], for any c as before. As x goes to zero, the ratio x/c goes to zero, so we can reasonably conclude that 0/0 is zero. Last, consider this problem: lim x-> [x/x]. Since the ratio is equal to 1 for every value of x, we can reasonably conclude that 0/0 is 1. The point is, 0/0 can be zero, infinity, or some constant (1 being an example), all depending upon which gets to zero faster, the numerator or the denomenator.

l'Hospital's rule formalizes this argument and shows that for any N(x) and D(x) such that lim x->0 N(x) = 0 and lim x->0 D(x) = 0, lim x->0 [N(x)/D(x)] = lim x->0 [N'(x)/D'(x)]. In the Mean Girls problem, N(x) = ln(1-x)*sin(x) and D(x) = 1- cos^2(x). Taking derivatives of both numerator and denominator, we have that lim x->0 [N'(x)/D'(x)]= 0/0, so we're back where we started! Not to worry, we can simply apply l'Hospital's rule to again so that lim x->0 [N'(x)/D'(x)] = lim x->0 [N''(x)/D''(x)], which is equal to -2/2, or -1. So both girls were in fact wrong.