Foldes, Lucien (2014) The optimal consumption function in a Brownian model of accumulation part B: existence of solutions of boundary value problems. Systemic Risk Centre Discussion Papers (25). Systemic Risk Centre, The London School of Economics and Political Science, London, UK.
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Abstract
In Part A of the present study, subtitled 'The Consumption Function as Solution of a Boundary Value Problem' Discussion Paper No. TE/96/297, STICERD, London School of Economics, we formulated a Brownian model of accumulation and derived sufficient conditions for optimality of a plan generated by a logarithmic consumption function, i.e. a relation expressing log-consumption as a time-invariant, deterministic function H(z) of log-capital z (both variables being measured in 'intensive' units). Writing h(z) = H'(z), J(z) = exp{H(z)-z}, the conditions require that the pair (h,J) satisfy a certain non-linear, non-autonomous (but asymptotically autonomous) system of o.d.e.s (F,G) of the form h'(z) = F(h,J,z), J'(z) = G(h,J) = (h-1)J for real z, and that h(z) and J(z) converge to certain limiting values (depending on parameters) as z tends to + or - infinity. The present paper, which is self-contained mathematically, analyses this system and shows that the resulting two-point boundary value problem has a (unique) solution for each range of parameter values considered. This solution may be characterised as the connection between saddle points of the autonomous systems obtained from (F,G) as z tends to + or - infinity.
| Item Type: | Monograph (Discussion Paper) |
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| Official URL: | http://www.systemicrisk.ac.uk/ |
| Additional Information: | © 2014 The Author |
| Divisions: | Systemic Risk Centre |
| Subjects: | H Social Sciences > HG Finance |
| JEL classification: | D - Microeconomics > D9 - Intertemporal Choice and Growth > D90 - General E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E13 - Neoclassical O - Economic Development, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O41 - One, Two, and Multisector Growth Models |
| Date Deposited: | 16 Feb 2015 15:09 |
| Last Modified: | 13 Sep 2024 20:29 |
| Projects: | ES/K002309/1 |
| Funders: | Economic and Social Research Council |
| URI: | http://eprints.lse.ac.uk/id/eprint/60956 |
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