A non-invariance result for the spatial AK model
Decisions in Economics and Finance(2023)
摘要
This paper deals with the positivity condition of an infinite-dimensional
evolutionary equation, associated with a control problem for the optimal
consumption over space. We consider a spatial growth model for capital, with
production generating endogenous growth and technology of the form AK. We show
that for certain initial data, even in the case of heterogeneous spatial
distribution of technology and population, the solution to an auxiliary control
problem that is commonly used as a candidate for the original problem is not
admissible. In particular, we show that initial conditions that are
non-negative, under the auxiliary optimal consumption strategy, may lead to
negative capital allocations over time.
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关键词
Optimal control in infinite dimension,State constraints,AK model of economic growth,Evolution equations,Invariance in Banach spaces,R1,O4,C61,49K20,93C20,58J70
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