Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/192656 
Year of Publication: 
2012
Series/Report no.: 
Discussion Papers No. 674
Publisher: 
Statistics Norway, Research Department, Oslo
Abstract: 
We bridge mathematical number theory with that of optimal control and show that a generalised Fibonacci sequence enters the control function of finite horizon dynamic optimisation problems with one state and one control variable. In particular, we show that the recursive expression describing the first-order approximation of the control function can be written in terms of a generalised Fibonacci sequence when restricting the final state to equal the steady state of the system. Further, by deriving the solution to this sequence, we are able to write the first-order approximation of optimal control explicitly. Our procedure is illustrated in an example often referred to as the Brock-Mirman economic growth model.
Subjects: 
Fibonacci sequence
Golden ratio
Mathematical number theory
Optimal control.
JEL: 
C6
Document Type: 
Working Paper

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