A theory of unbounded endogenous growth, partial optimal equilibrium models, and their applications
In light of recent development in endogenous growth models, this dissertation advocates an infinite time horizon, fully endogenous, and equilibrium optimal growth model. The proposed endogenous growth model possesses not only complete endogeneity but also the capacity of unbounded per capita growth, which the traditional neoclassical growth model lacks. This endogenous growth model still maintains the conventional neoclassical constant returns to scale characteristic. Not as in several other major endogenous growth models, no externality and increasing return to scale are needed for infinite growth. While it has certain similarities with historic Neumann expansion model, it is justified on contemporary notions such as human capital, knowledge, endogenous technological progress and so on. Specified with Ramsey optimal growth model, it produces an optimal structure equilibrium that does not have the stability problem as the neoclassical steady state equilibrium may have. Having the capability of endogenous and infinite growth, many long term large social-economic issues facing human economy and society, for example, education, population growth, economic equality, environment etc. can be discussed in the context of economic growth. Further mathematical study expands the generality to a class of general optimal control models that allow unbounded growth. A set of unified necessary and sufficient (if and only if) conditions for the infinite continuous time optimal control problem are provided to show that not only all the classical sufficiency theorems can derived from this set of N-S conditions but also inseparability of the transversality conditions. An existence theorem for the fast-discounting problems provides a more complete mathematical foundation for the class of optimal control models. Asserting every system has its systematic flaws, a set of four systematic methods are proposed to model the systematic flaws under equilibrium optimization--conditional optimization, additional constraints, by product externality, and external process. A direct application of these methods is in public economics. It provides a unique perspective in describing public goods in a dynamic optimal control model vis-a-vis in a growth model. Finally, another sector agent representing a different economic mechanism is introduced to optimize the same economy. A theory of public provision as addition to the private provision in a mixed economy is formulated. Furthermore, differences in efficiencies and preferences between public and private provisions are considered. A theory of bureaucratic inefficiency and preferences in relation to the public provision is derived. This dissertation emphasizes the philosophical underpinning and generalization of modeling methods.
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