The larger point is that the goals of providing the best education possible and making the most money possible do not directly coincide. A utopian public school will invest all of its money in such a way that it will be able to provide all students with the best education possible. A utopian for-profit school cannot do this because doing so would yield no profit. Instead, it would maximize profit by attracting as many students as possible with the fewest expenditures possible.
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
The only way for a for-profit school to provide a higher quality of education is for its combined efficiencies to be much higher than the combined efficiencies of a regular public school, because there is a negative term for expenditures in the metric being optimized, whereas there is not for regular public schools. I have not seen enough data to know whether or not this occurs. Furthermore, I don't trust the metrics that we do use because they rely on tests that are easy for schools to game and are too easy to pass. And then there's the issue of what standards to use when evaluating the effectiveness of a school (absolute, statewide relative, or local relative). Not to mention that this only covers schools that don't target specific groups of students, in which case the process of evaluation changes substantially.
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