The reason economists use mathematics is typically misunderstood. It has little to do with sophistication, complexity, or a claim to higher truth. Math essentially plays two roles
in economics, neither of which is cause for glory: clarity and consistency. First, math ensures that the elements of a model—the assumptions, behavioral mechanisms, and main results— are stated clearly and are transparent. Once a model is stated in mathematical form, what it says or does is obvious to all who can read it. This clarity is of great value and is not adequately appreciated. We still have endless debates today about what Karl Marx, John Maynard Keynes, or Joseph Schumpeter really meant. Even though all three are giants of the economics profession, they formulated their models largely (but not exclusively) in verbal form. By contrast, no ink has ever been spilled over what Paul Samuelson, Joe Stiglitz, or Ken Arrow had in mind when they developed the theories that won them their
Nobel. Mathematical models require that all the t’s be crossed and the i’s be dotted.