# American Institute of Mathematical Sciences

2013, 3(1): 63-76. doi: 10.3934/naco.2013.3.63

## Instability and growth due to adjustment costs

 1 University of Vienna, Brünnerstr. 72, 1210 Vienna, Austria, Austria

Received  September 2011 Revised  November 2012 Published  January 2013

This paper provides a new and surprising reason for growth, namely costs. More precisely, adding adjustment costs of the control to a one-dimensional, strictly concave optimal control problem does not affect the steady state(s). Then, sufficiently high adjustment costs turn an interior and saddle-point stable steady state of the original, one-state variable model into a source that can lead to unbounded growth. Given a version of the open economy Ramsey model, the initial conditions determine whether unbounded growth or impoverishment results. Related to this threshold property, the strict concave two-state variable control model allows for thresholds even if it has a unique and stable steady state.
Citation: Franz Wirl, Andreas J. Novak. Instability and growth due to adjustment costs. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 63-76. doi: 10.3934/naco.2013.3.63
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