Suppose society wants to spend one extra dollar for education. Where should it go? Pre-K underprivileged kids? Subsidies for elite business schools? Somewhere in the vast spectrum in between?
In order to make the problem concrete, initially assume the objective function is the present value of GDP summed over the long (infinite) term with discounting. Because it's long term, even things like humanities education may yield economic benefit.
In this form, the problem is a "pure" financial function of "Dollar in; dollar out", albeit an extremely difficult one. No need to argue over ideologies and philosophy. What is the optimum? Does anyone remotely have a clue of what the answer might be?
Having solved this problem (ha!), one can then use it as a starting point for considering social costs and benefits not counted in GDP: re-enter those ideologies and philosophies and maybe social policies like enforcing equal opportunity (though inequality has an economic cost as well, so it may already be captured). Or, consider a completely orthogonal means of wealth redistribution (e.g., taxation) leaving education to function at the macroeconomic optimum. Or, if we have a quantifiable measure of these social benefits and costs, simply add that value in.
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