Firms in a post-Keynesian model be like: 
(Pulling from "Introduction to Post-Keynesian Economics by Marc Lavoie")
Firms here are not assumed to be profit-maximizing, but rather want to ensure their own survival. So, they want to gather economic power, to keep out new firms and control markets.
Firms here are not assumed to be profit-maximizing, but rather want to ensure their own survival. So, they want to gather economic power, to keep out new firms and control markets.
That means they need to grow. Firms that don't keep up with the growth of the market will be overtaken and fail. Growth, of course, requires capital expenditures and R&D. Yet how can firms get the funds required for that spending? It's simple: with profits.
Lenders and firms both want to limit their risks here (firms don't want to default because it threatens their survival). So, more profits means more money can be borrowed for investments, which means more growth.
In naive neoclassical models, the assumption of decreasing returns to scale (AKA increasing marginal costs) limits the size of firms. But empirically, this doesn't seem to hold in most industries.
Instead, what limits firms here is that while they want growth, they need enough profits to finance that growth, and don't want to take on too much risk.
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