1. How does rational calculation take place within the firm? Keep in mind that some corporate giants are larger in economic terms than the smaller socialist economies.Rational calculation? Tee hee. Dilbert is successful for a reason. Seriously, business firms are collections of transactions that can be organized more cheaply by command-and-control than by open-market transactions (imagine the drawer of wire selling the drawn wire to another contractor who straightens it and then seeks yet another contractor who cuts it.) But those open market transactions provide sufficient information for the entrepreneur to be able to guess how much brass to purchase for drawing into wire in order to convert into cards of finished pins to sell to various users thereof.
That canard about General Motors being bigger than North Korea is a favorite hobbyhorse of socialists and anti-globalization freakazoids. What distinguishes General Motors from North Korea is that General Motors has price signals to respond to that are absent to the North Korean version of Gosplan. The claim that because a corporation is a large planned economy, a planned economy ought to be practical, is a howling non sequitur. The largest corporation subsumes transactions that are a tiny subset of the transactions of a small open economy.
There is a further pedantic point: in the absence of any prices, does anybody really know what the gross product of a small socialist economy is worth?
2. If one person owned (privately) all the firms in the economy, would rational calculation be possible?No. The image brings to my mind that apocalyptic paragraph in Capital about the dwindling numbers of the magnates of capital, who ultimately become incompatible with their capitalist integument. (Socialism, then, is simply the transfer of ownership of the means of production from their one owner to the workers, who presumably know how the enterprise works and all of a sudden have the usurped surplus value to share among themselves. That's the premise behind Edward Bellamy's Looking Backward.)
But think, instead, about Stuart Saunders, who could not combine two large railroads, or Harold Geneen, who thought that success in managing Latin American telephone utilities conferred ability to bake bread or rent cars at airports, or Jimmy Ling, who thought success in shipbuilding implied a Midas touch at making the steel for the ships. I commend Ravenscraft and Scherer's Mergers, Sell-Offs, and Economic Efficiency (details or compare prices), a case study that discovers much of the merger activity of the early 1980s was diversified companies hiving off divisions that underperformed, sometimes because they proved to be more difficult to manage than other divisions offering products closer to the diversifying firm's original core comparative advantages. Fatal conceits do not lay low only government bureaucrats. The cult of the conglomerate has given way to the cult of the CEO, but the CEO can be mugged by reality too.
(I'm getting a bit ahead of my story here, because I've just argued that a diversified firm is not equivalent to a mutual fund.)
3. If one dictator controlled all the firms in the economy, would rational calculation be possible?No. Neither a comprehensive conglomerate firm nor a comprehensive dictatorship would have sufficient price signals to make choices, unless one goes pomo and defines rational as "whatever the dictator wants." I think that wrecked the early Soviet economy, the Chinese Great Leap Forward, and the Luftwaffe. The value of markets is in giving people information to choose among conflicting claims on goods (why else begin the first price theory class with "allocating scarce resources among competing uses," nicht wahr?) That information is absent to the CEO of Comprehensive Conglomerate as well as to the economic dictator.
4. If institutional investors or a diversified citizenry all owned the so-called "market portfolio" in equal proportions, like the Capital Asset Pricing Model suggests, would rational calculation be possible? [TC: Or is this scenario of "perfect capitalism" not much different from pure communism?]Certainly. Those consumers differ in their desires for goods. The existence of shares suggests those consumers are willing to let entrepreneurs be agents on their behalf. Rewards and punishments for acting on those desires remain, and presumably some of those consumers are acting as entrepreneurs, managers, or workers as well as holding their shares. The question as posed hasn't ruled out sole proprietorships.
There is a somewhat more challenging problem. As firms adapt to price signals or develop new products, must these citizens continuously update their portfolios? Sounds like a worse nightmare than an eternal town meeting, the "perfect democracy" scenario from political theory.