As Krugman put it on his blog “most of what I and many others do is sorta-kinda neoclassical because it takes the maximization-and-equilibrium world as a starting point ...”.
Here, one has the fatal methodological blunder in a nutshell. By taking these green-cheese assumptions as hardcore premises (Weintraub, 1985, p. 147) neoclassicals simply cannot handle increasing returns — which are the very characteristic of industrialization since Adam Smith’s pin factory.
“A competitive equilibrium is not possible at a point of increasing returns to scale because no one wants to be the firm (negative profits). A competitive equilibrium is not possible at a point of decreasing returns to scale because everyone wants to be the firm (positive profits). General equilibrium theory for a competitive capitalist economy only works in the special case of constant returns to scale where (by assumption) no one cares who acts as the firm (zero profits).” (Ellerman, 1986, p. 70)
In order to get out of this homemade analytical trap the sorta-kinda maximization-and-equilibrium premises have to be dropped and replaced (2011). Neoclassicals cannot do this because it amounts to self-annihilation.
Ellerman, D. P. (1986). Property Appropriation and Economic Theory. In P. Mirowski (Ed.), The Reconstruction of Economic Theory, 41–92. Boston, Dordrecht, Lancaster: Kluwer-Nijhoff.
Kakarot-Handtke, E. (2011). Increasing Returns and Stability. SSRN Working Paper Series, 1921267: 1–19. URL
Weintraub, E. R. (1985). Joan Robinson’s Critique of Equilibrium: An Appraisal. American Economic Review, Papers and Proceedings, 75(2): 146–149. URL
You say “I don’t find [increasing returns] particularly problematic”. This, perhaps, is due to a lack of deeper understanding.
“So, Brian, what are you working on these days?” Arthur had given him the two-word answer just to get started: “Increasing returns.” And the economics department chairman, ..., had stared at him with a kind of deadpan look. “But — we know increasing returns don’t exist.” “Besides,” jumped in Rothenberg with a grin, “if they did, we’d have to outlaw them!” And then they'd laughed. (Waldrop, 1993, p. 18)
“The whole [invisible hand] theory is at risk if there are increasing returns which are ‘large relative to the size of the economy’. ... It arises from the fact that, even if firms continued to act as price takers, there may exist no equilibrium prices.” (Hahn, 1984, p. 116)
Neoclassical economics, i.e. sorta-kinda maximization-and-equilibrium, is dead and buried. The same holds for Post Keynesianism (2011). What is needed is a paradigm shift. Because this is clearly beyond the capabilities of Neoclassicals and Post Keynesians (2013) they are asked to retire without further self-debunking.
Hahn, F. H. (1984). Equilibrium and Macroeconomics. Cambridge: MIT Press.
Kakarot-Handtke, E. (2011). Why Post Keynesianism is Not Yet a Science. SSRN Working Paper Series, 1966438: 1–20. URL
Kakarot-Handtke, E. (2013). Confused Confusers: How to Stop Thinking Like an Economist and Start Thinking Like a Scientist. SSRN Working Paper Series, 2207598: 1–16. URL
Waldrop, M. M. (1993). Complexity. London: Viking.
Immediately following Still behind the curve.