size of government and the competence of government

[FDG]

The only way to substantiate any claim is with facts.

We can also apply the principle by Ludwig Von Mises that government have no price discovery mechanism and therefore cannot allocate resources efficiently.

His point was not exactly that; namely, a whole planned economy has no price discovery mechanism, but a government as part of a market economy indeed has a potential "price discovery" mechanism through the market itself. Surely it can distort this price mechanism, as much as a couple of "market failures" may do aswell.

Anyway, an easy way to substantiate your claim would be to assume the absence of economies of scale in government function, coupled with a constrained govt budget and a kind of marginal salary = marginal productivity general equilibrium condition. If that is the case, the "first" government employees will be the best paid and most productive, and a budgetary expansion will necessarily have to cater to less "able" workers. It's kind of heavily theoretical as an argument, I wouldn't bet my money on it, and it's only valid "ceteris paribus" so you won't be able to compare even very similar countries.

Exceptions also exist, there are natural monopolies (where big economies of scale and barriers to entry exist) which are somewhat better administered by politicians because at least they need to take into account their re-election, or more generally by a cooperative structure created by a union of citizens. "Government" is a bit too abstract. I'm a bit of a fan of regionalism, especially since the west *seems* for now to be a relatively war-free environment.

Another way to approach the topic would simply be to assume that there is a bounded and stable number of functions a government should perform. Each heterogeneous individual can perform a maximum number of functions, which varies according to ability (let's assume it's inborn), and needs to be provided with a minimum salary to live off, whatever its level of ability. The minimum salary acts as a fixed cost, thus for a given level of budget and "functions", there will be an inverse U-shaped relationship between the number of govt employees and total effectivness (basically a too low number can't perform all the functions but a too high number requires hiring marginally unskilled workers).

Finally, I'm pretty sure these topics have been explored to death in the economic litearture thus I advise you to look it up on google scholar.