By David Cass, Karl Shell
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Additional resources for The Hamiltonian Approach to Dynamic Economics
There is a finite bound B < oo such that every production point (c, z, —k, —/) e T which is replicable or feasible satisfies the boundedness restriction ||(c, z, k)\\ < B. (B) By way of further interpretation, it is interesting to observe that assumptions (T4) and (T6) play a role in our model analogous to that of the Inada conditions in the standard one-good model, and are crucial, for instance, in establishing the existence of stationary points which exhibit intertemporal consumption efficiency (modified golden rule paths).
An alternative method of relating these two models is simply to convert consumption-optimal growth into production-maximal growth. This can be accomplished by treating both cumulated utility output and primary factor input (the latter conceived as a stock yielding service flows) as produced stocks, an approach nicely elaborated by several authors, 12 We have in mind here the infinite horizon version of the production-maximal growth model, as analyzed, for instance, by Furuya and Inada . Also, our assumptions about technology would have to be modified somewhat in order to be consistent with the discussion below.
Must obey dynamical laws derived from a convex-concave Hamiltonian function. Thus, for example, our results are immediately applicable to a fairly general version of the neoclassical investment model. On a broader tack, we also believe that our duality emphasis may be quite useful in investigating the various existence problems which are deliberately sidestepped in the present paper. For instance, the existence of solutions to the particular differential equations (or differential correspondences) we define as representing optimal growth would follow from a duality theorem for concave programming in some appropriate infinite-dimensional space.
The Hamiltonian Approach to Dynamic Economics by David Cass, Karl Shell