Modeling of Ability, Effort, and now, `Effort Capacity' : A Candidate General Equilibrium Structure

Every fixed point has representation as, u=g(u), equivalently g(u)=h[g(u)]. Let all times t have parameterization as `commencement of period t'. This study arrives at a Fixed Point Theorem (FPT) between ability (η), effort (e), and `Capacity for Effort (ξ)'. Let e=g(ξ) and η=h[g(ξ)]. The FPT establishes existence of the `transitive' fixed points, h[g(ξ_{t})]=g(ξ_{t})=ξ_{t} and establishes the path, ξ_{t}=e_{t}=e_{t+1} to be the equilibrium path for effort. Importantly, absent introduction of ξ, there does not exist any fixed point between η and e that is robust to parameterization of general equilibrium. Clearly, the relation between ξ and e mirrors the dependence of kinetic energy (effort) on existence of potential energy (capacity for effort). With the FPT in tow, whereas `off equilibrium' behavior is parameterized by e_{t+1}≠e_{t}, there exist conditions that facilitate rationality or irrationality of the off-equilibrium path. Rather then, searches for fixed points, u=g(u), the FPT facilitates attempts at parameterization of conditions, such as, `contract terms that fail incentive compatibility criterions', or specific formulations of, information asymmetry, moral hazard or free rider problems, etc. that induce rationality or irrationality of choice of, e_{t}=g(ξ_{t})≠ξ_{t} or e_{t}≠e_{t+1} from economic agents. The FPT facilitates, in addition, exogeneity of specification of `reference points' in studies of `reference-dependent' expectations formation. Section 2 of the study provides formal theoretical illustrations of applications of the FPT