Standard production functions are Cobb-Douglas, CES, Leontief.
The most exotic production function I have seen is the Ethier production function.
I am wondering whether there is a book/list of other exotic production functions. i.e. production functions with heterogeneous capital, integrals, etc.
I could not find it doing a google scholar search.
Belo (2010) uses a production function $$ Y_{j,t} = \epsilon_{j,t} F^j(K_{j,t}) $$ where a competitive producer $j$ is allowed to choose the state-contingent productivity level $\epsilon_{j,t}$, subject to the constraint set defined by the following analytically tractable CES aggregator: $$ E_t\left[ \left( \frac{\epsilon_{j,t+1}}{\Theta_{j, t+1}}\right)^\alpha \right]^{1/\alpha} \leq 1. $$ In Cochrane's 2016 essay, "Macro-Finance", Cochrane mentions this specification as a potentially important ingredient for understanding the interaction of macroeconomics and financial markets:
The second ingredient, I think, is to enrich the production technology so that consumer investors can shape the riskiness of the technological opportunities they face. Belo (2010) and Jermann (2013) have recently explored specifications of technology that allow such choices.
