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Optimal size of firms

I have read Brearley and Myers. I have read a lot of books on enterprise and busines. I have read quite a bit of economics. In none of those places have I previously come across an analysis of what makes an optimal size of a firm.

I remember years ago reading something about the ease of communication and enforcing laws being a determinant of the size of countries or empires. Obviously there are problems with this when we look back on the Roman and British Empires, and think about the internet and modern communications.

On the face of it, with the market and prices being such perfect instruments for organising economic activity, it is not clear that firms are needed at all. Scott Adams of Dilbert fame has a large brand that has no employees, and I am fairly sure that Scott works at his PC in his dressing gown. How come the bosses of IBM and and Exxon do not do this?

The answer is to do with transaction costs: the price of using the price mechanism. It may be perfect, but it is not free! The argument is that the explicit arms-length contract that would have to be entered into to make someone a reasonable substitute for an employee is so complicated and costly that you really wouldn't want to bother unless the job was very simple (like operating the works canteen, or doing the cleaning).

I buy the general argument, but I'd like some numbers. I was reading a book, 'The Origin and Evolution of New Businesses' by Amar Bhidé. It simply observed that Oscar Mayer, the leading restaurant vendor of hot dogs in the US was a tiny fraction of the size of MacDonalds (and had a much smaller proportion of the market for hot dog vending market). This it put down to the influence of the founder, Ray Croc, suggesting at the very least, very slow convergence to equilibrium in these kind of markets.

This is one of those questions that business-school types seem to be uncurious about. Maybe it genuinely is a question that is not worth asking, but it would be nice for someone clearly to articulate why.

References

Wikipedia article on this topic, references Coase, who had the seminal insight.

Econtalk discussion of this with Mike Munger - highly recommended.

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