This is such a stupid post, I literally laughed when I read it. Not only is it stupid and misses the point, it bleeds "Look at me I have an undergraduate degree in economics, LOOK AT ME!". Just because you can name drop doesn't mean you have a good grasp of what you are talking about.You are using the standard monopoly theory of Cournot, a theory about 200 years old. Modern microeconomic theory has evolved past it, though it is still taught. Also, this theory doesn't assume that public monopolies would be benevolent.
You are assuming that: Private monopolies and public monopolies have perfect information (wrong in practice), that they can only set 1 price (also wrong) and that private monopolies maximize profits (true), while public monopolies practice marginal cost pricing (untrue). Public monopolies are as selfish as private monopolies, and they don't have any incentives to reduce costs (they can operate with losses and the government pays them back with money from taxes).
Modern game theory shows that mutually beneficial trade doesn't takes place when information is imperfect. To maximize efficiency, you need to maximize the utilization of dispersed information. If monopolies had perfect information, they could simply discriminate prices and achieve perfect efficiency to maximize profits. The core problem of economics is information, as Hayek perceived in 1937.
You are using the standard assumption of the naive interventionist: that the government is benevolent and omniscient. The concept that government is omniscient was refuted (as if it needed to be refuted!) by Hayek (nobel prize in 1974) and the concept that governments are benevolent (that they maximize public good) was refuted by the Public Choice theory, whose master is James Buchanan, nobel prize in 1986. You also should evolve your defense of government intervention beyond the microeconomics 101, or become a liberal, like me.
At no point did Samuel assume perfect information, or that a monopoly can only set one price. That's what the Cournot model assumes (which is actually a model of duopoly, not monopoly, but the issue is similar enough to illustrate a point), but the Cournot model is just a model used to simplify reality. Even without these assumptions being 100% accurate, you can discover something important using models, and in the case of Cournot the lesson is that firms with market power (monopolies or duopolists or whatever) cut back on supply to raise prices and profits. Even without perfect information or a single price, that conclusion is still valid: private monopolies supply less and have higher prices. You don't even need an econ degree to understand that much, it's pretty clear from any look at monopolies in any economy.
The reason why Cournot and Bertrand models of duopoly are still taught in universities is because they still provide roughly accurate representations of how monopolies will act. If they weren't roughly accurate models, they wouldn't be taught.
You also don't have to assume that a government monopoly prices precisely at marginal cost. All you have to assume is that they price CLOSER TO marginal cost (or closer to the socially optimal price) than a private monopoly would, WHICH THEY DO! This isn't a controversial position in economics at all (which is why econ textbooks still recommend government intervention in natural monopolies), and Public Choice theory doesn't refute this conclusion in the slightest. The basic insight from Public Choice theory in this regard is that you can't treat an organization of any sort as benevolent, but must identify their interests which they will pursue. In the case of government monopolies, it's true that they aren't benevolent and will pursue their own interests, but in most cases in developed economies their own interests (generally appeasing their government overlords) still encourages them to produce much closer to the socially optimal output than private monopolies.
For someone obviously trying so hard to present themselves as well-read in economic literature, I really recommend you go back over your basics, because you've clearly missed the point of learning models like the Cournot or Bertrand model. I suggest you evolve your criticism of government intervention to be based on substance, rather than dropping names then misrepresenting the econ literature you're name-dropping.You also should evolve your defense of government intervention beyond the microeconomics 101, or become a liberal, like me.
If this were true, then there would be no such thing as mutually beneficial trade, because there is no such thing as perfect information. I understand that English may be your second language, but I recommend you do more either more proof reading or thinking before posting.Modern game theory shows that mutually beneficial trade doesn't takes place when information is imperfect.
PS: It's a bit ironic to have Paul Samuelson as your avatar and then say that Krugman is full of bullshit, considering that the two economists are/were on pretty much the exact same page on most issues, particularly Keynesian macroeconomics.