Producer Theory and Profit Maximization...where exactly are opportunity costs accounted for within the general equilibrium framework? This question was posed to me by one of my first year undergraduates this year (in a slightly different form!) and I don't think I had a very good answer for him.

As I read through Debreu's axiomatic treatment of profit maximization I find myself asking the same question. Where are opportunity costs taken into account? Are opportunity costs essentially a special type of contingent commodity that exists in perhaps a different time and place with its own price?

This matters because the assumption of additivity and the possibility of inaction implies that the maximum profit of a producer either does not exist or is null. Null profit in equilibrium makes sense to me IF one is talking about economic profits and not accounting profits. Economic profits requires taking opportunity costs into account...

Anyone out there have any thoughts on this one...or is this discussion just too pedantic

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## Wednesday, December 8, 2010

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I was under the impression that accounting profits always = zero in competitive equilbrium, as marginal cost = marginal revenue holds in every industry with free entry to ensure this (etc). Opportunity cost is the net benefit of alternative activity foregone, and with complete markets earning zero accounting profit there is no net benefit in alternative production plans (you already pointed out the finiteness of commodity space). Its fundamental to marginal value theory?

ReplyDeleteOne way to think about it: in Debreu's framework, producers (i.e. firms) do not own any capital, rather they rent capital services from households. So there are no opportunity costs for the firm (aside from the price of capital services, etc.). (Btw, it is not generally true within Debreu's model that firms make zero profits, although it is true if we assume constant returns to scale.)

ReplyDeleteIntuitively, it seems likely that any equilibrium in which households rent capital services to firms can also be supported as an equilibrium in which firms own (and can buy/sell) capital (this is certainly true of simple cases, e.g. the Ramsey/neoclassical growth model). In this case, opportunity costs would be the shadow prices on some of the firms' constraints, and would have some relation to the prices from the equilibrium in which households own capital. I don't know if this suggestion is true, but I'm sure someone either proved or disproved it a long time ago.

Ok, having now thought about both of these comments a bit I have come to the following position. In the Debreu framework economic profits (and costs) and accounting profits (and costs) are the same because with complete markets, complete contracts, etc opportunity costs are always zero. This does not mean that producers will always end up with zero profit because, as Keshav pointed out, one can still get positive profits as long as one does not have constant returns to scale.

ReplyDeleteDon't know if anyone else is finding this useful, but it has helped me to de-conflict various aspects of general equilibrium theory...

I found Keshav's point useful, particularly about the shadow prices. I also found this when I looked for a simple explanation of why profits can exist absent constant returns:

ReplyDeletewww.ellerman.org/Davids-Stuff/The-Firm/ad_mod3.doc

Its pretty interesting - he points out the disagreement between Arrow and McKenzie on the issue which definitely merits further reading.