I was trying to think about why certain people say that regulations are bad for the economy, and why others say that regulations are a necessary evil.

I found that it was pretty clear that very few people, within the general spectrum of American political views regarding the economy, believe that regulations are a “positive good” for the economy.

I tried to come up with a mathematical concept that could effectively capture the essence of what a “regulation” is in the economy, and I used the Lagrangian multiplier, and treated national economic output (GDP), which is a function of *k* capital variables, *l* labor variables, and *r* resource variables; So the GDP function is a function of k+l+r variables.

I treated each government regulation as a single constraint function that would be a function of *at most* k+l+r variables, but possibly even just one of them, this function being set to a constant. It is also possible that a constraint function could range over an interval, in which case the regulation would be modeled as an inequality constraint, rather than an equality constraint in the previous case. If there are *c* constraints, then there are a total of c equality and inequality constraints. It’s somewhat obvious that inequality constraints/interval constraints are “less constraining” than an equality constraint; i.e. a mandated wage is a stricter regulation than a minimum wage or wage interval.

Under certain conditions, an optimum (a maximum GDP) will exist, and be unique. Since an unconstrained maximum is greater than (more optimal) than a constrained maximum, the difference becoming larger as more regulations (constraints) are added to the economic system, it has thus been shown that regulations make us poorer than what we would be without them. If the Lagrangian multiplier model of constrained optimization is mathematically rigorous (which it is), and government regulation of the economy can be treated as a constraint (which I’m not sure is even valid), and we want to maximize the GDP given those constraints, then the constraints would lead to total output lying inside the *production possibilities frontier,* (the maximum production being the optimum, or “full employment” given the constraints you have). The production possibilities frontier or full employment could be approached with less regulations.

Is this model valid/invalid?