"When prices are too high accompanied by poor quality with continued renewal of contracts, we know somebody has someone in their pocket. "

The catch to this is that real schools do not invest perfectly and thus introduce a series of efficiency variables, which include efficiency of expenditures and efficiency of what I will refer to as mechanisms (incl. curriculum, teaching methods, etc.), among other things. Charter schools should be able to run more efficiently than regular schools, seeing as dealing with the MEA necessarily forces regular schools to spend inefficiently and charter schools have more control over their curriculum. This allows us to create a series of general equations that summarize the situation.

Regular public schools and non-profit charter schools seek to optimize Q:

Q = f(E, n1, n2, n3)

For-Profit Charters seek to optimize P:

P = I(m) - E
m(Q, a(E), b, n3)

All listed functions have a positive correlation with component variables

List of variables (all are functions)
Q = Quality of education (yields a value between 0 and 1)
P = Profit
I = Income
E = Expenditures (a multivariate function and separable variable)
n1 = Efficiency of expenditures
n2 = Efficiency of mechanisms
n3 = other efficiencies
m = Number of students
a = attractiveness of school for non-educational reasons
b = uncontrollable variable
f = educational effectiveness of function

Transformational variables not listed can be included within