> Although I contend that the two really aren't that different as government spending is just the aggregate of individual spending on government itself.
America has a progressive tax system, so this sort of aggregation argument is over-simplistic.
> You are suggesting that subsidizing something can make the sum total of all spending on that thing go down?
Yes, absolutely. Even operating from your premises, spending more can decrease costs.
In the case of no/low-interest loans, as long as the cost of defaults doesn't exceed the amount saved in interest paid to banks, everyone is spending less money on education.
Combining no/low-interest loans with increased state funding for education significantly decreases the risk of default.
So the "right answer" to minimizing spending is just a matter of simply arithmetic:
C_f = Cost of state Funding
C_d = Cost of Defaults
B_i = Total money saved on interest payments (let's assume 5% rate with 20k load, probably higher if the entire market is unsubsidized)
Then we want to maximize B_i - C_d + C_f.
Since we have some amount of state funding and some subsidized loans, it's entirely plausible that increasing C_f could decrease C_d, because the loans are smaller and therefore risk of default is lower. Furthermore, decreasing C_d increases B_i since higher-interest unsubsidized loans will meet the new demand.
Of course, there's a degenerate optimization: you can always just have zero subsidies. Most first world countries rightly give a shit about educating the non-independently-wealthy.
But also:
* I don't think "minimize cost" is a wise philosophy wrt education. Nations that do this tend to be sucky places to live/work.
* America has a progressive tax system, so the aggregate reasoning of your first response is at least disingenuous.