Modeling requires the restatement of the issue using symbols or numbers built into equations. If the analysis can restate an issue using equations, then it does not simply employ one new tool but unlocks the vast and expanding toolset of mathematical methods. However, this leading tool of law and economics may be a skill or mindset that seems inaccessible to a neophyte. Some of the mathematical tools that take advantage of modeling form the subject of later chapters. This chapter introduces the language and methodology of modeling and two powerful mathematical methods, the optimization by solving derivatives and the prediction of the path of gradual change by differential equations.

Even modeling can be introduced with Meinhard v. Salmon. Salmon received a lucrative offer from Gerry, a business acquaintance. The offer could have expanded Salmon's business. Unbeknownst to Gerry, Salmon's business, which was the reason for their acquaintance, had a secret partner, Meinhard. If Gerry knew that Salmon operated in two capacities, as an individual and as a member of a partnership, then Gerry may have specified which of the two he selected as the recipient of his offer. Meinhard, the invisible partner, claimed the offer should be treated as made to the partnership. The litigation that Meinhard started eventually reached the highest court of the jurisdiction and the famous American judge, Benjamin Cardozo, and his colleague Andrews, who is almost equally famous for his vocal dissenting opinions. Previously established law did not answer the question directly.