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August 4th, 2011, 02:39 PM  #1 
Newbie Joined: Aug 2011 Posts: 4 Thanks: 0  is there an analytical solution to (x+a)^g(xa)^g=p*a*x
Hello guys, I'm working on an economics model where a worker has a concave incentive contract and a production function y=x+mu where x is the effort provided and mu is an error term. Anyway, when I want to calculate the worker's optimal level of effort I end up with something like: (x+a)^g(xa)^g=p*a*x with g<1 and x>0, p>0, a>0. When I assign values to the parameters a,g and p I obtain a graphical solution. Nevertheless, I would need an analytical one to use in a further step of the model. I'm struggling with that since two days and I start to fear that there is no analytical solution. Am I right? Do you have any suggestion? Thanks, Giancarlo 
August 4th, 2011, 06:29 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: is there an analytical solution to (x+a)^g(xa)^g=p*a*x
I don't see an analytical solution either. I don't suppose an approximate solution would help? You could do a series expansion if it would.

August 8th, 2011, 10:19 AM  #3  
Newbie Joined: Aug 2011 Posts: 4 Thanks: 0  Re: is there an analytical solution to (x+a)^g(xa)^g=p*a*x Quote:
 
August 8th, 2011, 01:20 PM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: is there an analytical solution to (x+a)^g(xa)^g=p*a*x 
August 8th, 2011, 02:12 PM  #5  
Newbie Joined: Aug 2011 Posts: 4 Thanks: 0  Re: is there an analytical solution to (x+a)^g(xa)^g=p*a*x Quote:
 
August 8th, 2011, 03:23 PM  #6  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: is there an analytical solution to (x+a)^g(xa)^g=p*a*x Quote:
 
August 9th, 2011, 10:20 AM  #7  
Newbie Joined: Aug 2011 Posts: 4 Thanks: 0  Re: is there an analytical solution to (x+a)^g(xa)^g=p*a*x Quote:
 
August 9th, 2011, 11:37 AM  #8 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: is there an analytical solution to (x+a)^g(xa)^g=p*a*x
Wish I could be more helpful...!


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