A scientific approach to managing competition - The Industrial Physicist

An interesting use of the Volterra-Lotka model, applied to the competition (or lack thereof) between ballpoints and fountain pens. Quoting directly from the article by Theodore Modis in The Industrial Physicist:

Battle of the pens
The struggle between fountain pens and ballpoint pens had a different ending (Figure 1, left). The substitution of ballpoint pens for fountain pens as writing instruments went through three distinct stages. Before the appearance of ballpoint pens, fountainpen sales grew undisturbed to fill the writing- instrument market. They were following an S-shaped curve when the ballpoint technology appeared in 1951. As ballpoint sales picked up, those of fountain pens declined in the period 1951 to 1973. Fountain pens staged a counterattack by radically dropping prices. But that effort failed. Fountain pens kept losing market share and embarked on an extinction course. By 1973, their average price had dropped to as low as 72 cents, to no avail.

Eventually, however, the prices of fountain pens began rising. The fountain pen underwent what Darwin would have described as a character displacement to the luxury niche of the executive pen market. In the early 1970s, the strategy of fountain pens became a retreat into noncompetition. By 1988, the price of some fountain pens in the United States had climbed to $400. The Volterra-Lotka model indicates that today the two species no longer interact but each follows a simple S-shaped growth pattern. As a consequence, fountain pens have secured a healthy and profitable market niche. Had they persisted in their competition with ballpoint pens, they would have perished.