Firms, we may be sure, do not exist in anything like complete service to the profit motive. At any given moment, the most economical thing for a firm to do is liquidate: firms are never more profitable than when going out of business because they no longer incur the costs of replenishing their factors of production. When a firm has more assets than can be maintained at a profit, the firm becomes vulnerable to at least partial liquidation by hostile takeover — one process by which the firm's sector becomes more efficient.

Firms are much more in the business of staying in business, of putting capital to work maintaining stocks of productive assets, of gaining the best return from those stocks under the market conditions of the moment, of providing for the material comfort of top management, and of extending the life of the firm so as to be in business when opportunities for extraordinary profits occur.

The particular activities required to stay in business depend naturally on the business one is in. Specific outputs dictate specific forms of competition for markets:

To the extent that a product is intrinsically uniform, e.g. crude oil, it is natural that the competition should take place in terms of efficiency, i.e. price. Where such competitions have actually occurred, they have quickly eventuated in monopolies such as Standard Oil.
When markets are new, as was the case for automobiles early in the 20th Century, or for computers late in the 20th Century, the exact nature of the product that best serves the market is still open to definition. In these instances, competition operates through product differentiation, and competitors abound. As markets mature and products become uniform, the criteria of efficiency assert themselves, and competitors are reduced toward a monopoly situation.
For individual firms, the outcome of pure competition is uncertain and severe; thus competition tends to be mitigated by those who manage firms on behalf of the second and third generation heirs of industrial pioneers. Professional managers are most likely to compete through some form of product differentiation (artificially induced, if necessary) while colluding on matters such as price and market share. Thus the economic efficiency subsumed in production theory is only vaguely and irregularly apparent in the behaviors of firms; and the inference of production tradeoffs through the lens of marginalism is understandably aqueous. If firms generally do not, in and of themselves, exhibit discernable production functions, then we have no basis for abstracting sectors by somehow ‘adding up the production parameters for the sectors’ constituent firms.

Sectors’ behaviors, on the other hand, might be directly abstracted in terms of a tendency to operate where their marginal revenues equal their marginal costs. These behaviors would be the creature of no more than capitalists balancing the global investment portfolio, rather than of atomistic firms seeking survival:

When capital is withdrawn from a comparatively less profitable sector, the firms in that sector must operate with fewer assets. Asset reduction can take place by closing down inefficient operations or entire corporations. This translates operations to a more efficient range of the sector’s production function.
A conspicuously profitable sector, by contrast, will attract capital away from other sectors. This makes firms outside the conspicuous sector more efficient, while those firms within the sector receiving additional capital will become less efficient.
In either case, capital is seen to flow so as to unify all returns at the sectoral level of focus, where production functions emerge as realistic summa of observable tendencies:
Increased demand can be met by more efficient, but idle, new productive capacity that is usually ready to be brought online because industrial engineers generally allow for growth when designing facilities with the newest technology;
less efficient, idle old capital can always be brought back online if a product’s price increases; and
Other things equal, decreases in price or demand will present the obverse of these effects.
Being composed of many firms, a sector has broad and immediate latitude as to its volume of output; and we have every reason to expect this latitude will be exercised to adjust a sector’s application of assets toward efficiency as prices change.

In sum, we expect to find sectors in continual progress toward efficiency because capital placement is always operating to make any sector as efficient as the most efficient sector. This tendency should be in evidence even though the various sectors are comprised by products and markets that vary widely as to their operations, product maturities, and forms of competition. Though capital placements would certainly be distributed unevenly among the firms composing a sector, their varied effects on the operating efficiencies of these firms need not be made visible by a multi-sectoral model.