New PDF release: The Hamiltonian Approach to Dynamic Economics

By David Cass, Karl Shell

ISBN-10: 012163650X

ISBN-13: 9780121636500

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Extra resources for The Hamiltonian Approach to Dynamic Economics

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5 Note that, though T is not compact, from assumptions (T2), (T6), and (T7), a cross-section like {(c\ z\—k\ —/'): (c\z\ —k\ —V)eT and (k\ /') = (k, /)} is compact. , when {k9 /) > 0; see Footnote 7 below. 40 Property (H3). CASS AND SHELL H is nondecreasing in p and /. Property (H4). , q), and concave and linear homogeneous in (A:, /). And, most important, Property (H5). , q) = (c, z),6 and, at least for (k, I) > 0, dH(p, q, k, l)/d(k, I) = (r, w). 7 Thus, the generalized gradients of H with respect to (p, q) are static profit-maximizing outputs (and conversely), while, for all practical purposes, the generalized gradients of H with respect to (k, I) are competitive input rents (and conversely).

This assumption is made so that we can sensibly talk about stationary points. An essentially equivalent assumption would be that, however many, all primary factors grow asymptotically at the same constant rate (the "natural" growth rate). 9 Since an output price system "convexifies" just the production possibility sets derived from a nonconvex technology, in that case one can only recover the union of the convex hulls of cross sections of the representation Γ, or its "northeast" boundary, from the representation H.

Terminal capital stocks as well as intermediate utility output). In this connection, it should also be mentioned that our simplifying assumptions (Al) and (A3) play a role in this particular duality theorem similar to that of Slater's condition in the more familiar duality theorem for concave programming in Euclidean w-dimensional space, and can be weakened accordingly. COMPETITIVE DYNAMICAL SYSTEMS 45 where k* are the golden rule capital stocks, and Q* the current investment goods prices (in terms of utility output) which support their maintenance.

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The Hamiltonian Approach to Dynamic Economics by David Cass, Karl Shell


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