The neoclassical model and the firm

It can be argued, with some justification I would say, that the high point of neoclassical economics is Gerard Debreu's "Theory of Value". I have argued before that the firm really doesn't exist in the standard neoclassical model. As Nicoli Foss has noted

"With perfect and costless contracting, it is hard to see room for anything resembling firms (even one-person firms), since consumers could contract directly with owners of factor services and wouldn’t need the services of the intermediaries known as firms".

and as Foss, Lando and Thomsen explain,

"[t]he pure analysis of the market institution leaves almost no room for the firm (Debreu 1959)".

Debreu obviously has a supply side to his model, there are "producers", just not firms,

"[. . . ] when one abstracts from legal forms of organization (corporations, sole proprietorships, partnerships, . . . ) and types of activity (Agriculture, Mining, Construction, Manufacturing, Transportation, Services, . . . ) one obtains the concept of a producer, i.e., an economic agent whose role is to choose (and carry out) a production plan". (Debreu 1959: 37).

Today I cane across a pdf version of Debreu's book and did a searched it for the word "firm". I found only two occurances in the book.

"In so far as Yj represents technological knowledge, it is clear that two production plans separately possible are jointly possible. Alternatively the jth producer can be interpreted as an industry rather than as a firm; then the additivity assumption means that there is free entry for firms into that industry, i.e., no institutional or other barrier to entry."

Interestingly Debreu says that a "producer" can be an industry. The question this raises with me is, Is the non-discussion of firms in the book accidental? Or did Debreu fully reaslise that firms, by any serious definition of the word, didn't exist in the neoclassical model and thus he didn't refer to them. He was content to deal with the abstraction that is a "producer"?