Optimal Transition Dynamics in the Leontief Two-Sector Growth Model With Durable Capital: The Case of Capital Intensive Consumption Goods

Abstract

We present results on undiscounted optimal policies in the Leontief two-sector growth model with durable capital. Unlike the results with a labour intensive consumption goods sector, we show that a monotonic optimal programme is only one special case out of many richer possibilities of transition dynamics. Depending on the initial capital stock, and a key parameter z that could be interpreted as a marginal rate of transformation of capital between today and tomorrow, an optimal programme may converge to a periodtwo cycle; and even when it converges to the golden rule stock, it can do so (damped) cyclically or with a "jump".j ere_461 490..511 JEL Classification Numbers: D90, C62, O21.

Optimal cyclicity and chaos in the 2-sector RSS model: An anything-goes construction

“…11 It is to be noted, however, that the work of Nishimura and Yano, with its powerful geometric conception, has been carried forward in Fujio (2005Fujio ( , 2008Fujio ( , 2009, under the rubric of what we are characterizing the second direction. 12 See paragraph 4 in Boldrin and Deneckere (1990), for example.…”

On the Eventual Periodicity of Piecewise Linear Chaotic Maps

“…In particular, one can ask whether there exists a family of piecewise linear maps that yields under particular parametric assumptions all of the aforementioned results and consolidates them in the sense that (i) the result of [7] holds for a point with a given arbitrary number of periods k and (ii) that of [17] is invariant with respect to perturbations of a particular map within a specified family. This question, of interest c 2017 Australian Mathematical Publishing Association Inc. 0004-9727/2017 $16.00 in itself, is also motivated by issues in economic dynamics where a rationalisation of a particular map as a solution to an optimisation problem is of substantive consequence (see, for example, [2,5,9,17]). We will give a complete answer to this question.…”