I'm reading a book where the definition of an equilibrium for a competitive economy is given as in
Kenneth J. Arrow; Gerard Debreu (1954) Existence of an Equilibrium for a Competitive Economy Econometrica, Vol. 22, No. 3. , pp. 265-290.
where the authors define an equilibrium roughly as a price vector $p$ where households maximize utility, firms maximize profit, and consumption of households satisfies the income restraint.
However, it seems to me that the zero profit rule which is often associated with equilibrium in a competitive economy is not assumed (nor implied).
So my question is how does the zero profit rule enter into general equilibrium theory?
Is it imposed as a further assumption and if so are there any seminal papers discussing the role of the zero-profit rule and perhaps like the above article giving conditions for the existence of competitive equilibrium?
Handbook chapters could also be interesting but I am not sure which handbooks one should consult when looking for microeconomic theory and general equilibrium theory.