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MathGroup Archive 2006

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optimise / minimize with constraints (dummy question)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67424] optimise / minimize with constraints (dummy question)
  • From: Kuehn <fideliuskuehn at hotmail.com>
  • Date: Fri, 23 Jun 2006 04:31:41 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I am currenty writing my thesis in behavioural economics, please don't laugh about the possibly stupid question i have. 
I am trying to minimise a cost function in a principal-agent model subject to 2 constraints. 
Purely intuitively i plug in 

Minimize[(1-\[Beta])x+\[Beta]z+(1-\[Delta])x+\[Delta]z, {(1-\[Beta]) Sqrt[x]+ \[Beta] Sqrt[z]-az> Sqrt[x], (1-\[Beta]) Sqrt[x]+ \[Beta] Sqrt[z]-az>(1-\[Delta]) Sqrt[x]+ \[Delta] Sqrt[z]-dz},{x,z}]

into Mathematica but it does not give any output (for you surely "not suprisingly" :) )

Could anyone tell me what 
1.is wrong with either my model setup (how can i alter it to receive a optimal (x and z) dependent on (a or d)??
2.whether mathematica is any help at all in this problem.

Here again the setup written in the "spoken way":
Min costs function: (1-Beta)x+Beta z+(1-Delta)x+Delta z
subject to 1: (1-Beta)sqrtx+Beta sqrtz-az>sqrtx
subject to 2: (1-Beta)sqrtx+Beta sqrtz-az>(1-Delta)sqrtx+Delta sqrtz-dz

It would be amazingly great if someone could give me a hint, i am fiddling for this for days and need someone who knows how to optimise...
Thanks so much in advance!


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