Re: st: Optimize

[Yuval Arbel <yuval.arbel@gmail.com>]

Since I saw Muhammad is an Economist, I have one conceptual remark:

Note, that both the total cost (TC) and output (X) are endogenous
variables in the classical economics model of producer behavior.
Consequently, MC should be derived as a function of output and input
prices per unit, and not of quantities (otherwise the simultaneous
relations produces biased and inconsistent estimators).


On Mon, Jul 23, 2012 at 9:52 PM, Austin Nichols <austinnichols@gmail.com> wrote:
> Matthew Baker <matthew.baker@hunter.cuny.edu>:
> That code minimizes the first derivative, according to the OP. I think
> the OP wants to find the minimum of the cubic given, which means
> setting the quadratic to zero in the case of an interior solution
> (i.e. just use the quadratic formula, not Mata). But there are no
> interior solutions for a cubic with positive coefs, so the OP needs to
> substitute in any constraints holding with equality.  Or perhaps I am
> misunderstanding the desideratum here.
>
> On Mon, Jul 23, 2012 at 2:30 PM, Matthew Baker
> <matthew.baker@hunter.cuny.edu> wrote:
>> Mohamud --
>>
>> I think there are a few things wrong with the code that you presented
>> below. For one, I think you want the arguments of your void function
>> to be (todo,x,crit,g,H) - otherwise, as written, you are not returning
>> anything to the evaluator! Moreover, your objective function omits a
>> few operators so I think it should be (3*x^2+2*x+1)^2.
>>
>> Given those few changes, a simplified version of your code that might
>> get closer to what you want is something like:
>>
>> /* begin example */
>> clear all
>> mata:
>> void q(todo,x,crit,g,H)
>> {
>>  crit=(3*x^2+2*x+1)^2
>> }
>> real matrix grid(n1,n2)
>> {
>>  real matrix sol
>>  real scalar i,p
>>  sol=J(0,2,0)
>>  for (i=n1; i<=n2; i++) {
>>  init=i
>>  S=optimize_init()
>>  optimize_init_evaluator(S, &q())
>>  optimize_init_which(S,"min")
>>  optimize_init_evaluatortype(S,"d0")
>>  optimize_init_params(S,init)
>>  p=round(optimize(S),10e-8)
>>  sol=sol \ (i,p)
>>  }
>>  return(sol)
>>  }
>> grid(-10,10)
>> end
>> /* end example */
>>
>> Hope that helps!
>>
>> Matt Baker
>>
>>
>> On Mon, Jul 23, 2012 at 11:45 AM, Mohamud Hussein
>> <Mohamud.Hussein@fera.gsi.gov.uk> wrote:
>>> Thanks Austin.
>>>
>>> I used code below as suggested but had no luck yet. I am sure it has something to do with my complete lack of knowledge in mata language.
>>>
>>> I attach my data. I would be grateful if you can check for me where I am getting it wrong.
>>>
>>> Many thanks,
>>> Mohamud
>>>
>>> ==
>>>
>>> void q(todo,x,y,g,H)
>>> {
>>>  crit=(3x^2+2x+1)^2
>>> }
>>> sol=J(1,0,0)
>>> void grid(n1,n2)
>>> {
>>>  external sol, p
>>>  for (i=n1; i<=n2; i++) {
>>>   init=i
>>>  S=optimize_init()
>>>  optimize_init_evaluator(S, &q())
>>>  optimize_init_which(S,"min")
>>>  optimize_init_evaluatortype(S,"d0")
>>>  optimize_init_params(S,init)
>>>  p=round(optimize(S),10e-4)
>>>  if (!anyof(sol, p)) {
>>>   sol=(sol,p)
>>>   }
>>>  }
>>>  sol
>>> }
>>> grid(-10,10)
>>>
>>> ==
>>>
>>>
>>> -----Original Message-----
>>> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Austin Nichols
>>> Sent: 23 July 2012 15:26
>>> To: statalist@hsphsun2.harvard.edu
>>> Subject: Re: st: Optimize
>>>
>>> Mohamud Hussein <Mohamud.Hussein@fera.gsi.gov.uk>:
>>> Looks like you are trying to maximize the unbounded quadratic rather
>>> than find its zeros.  Use a root finder instead e.g.
>>> http://www.stata.com/statalist/archive/2007-12/msg00551.html
>>> http://www.stata.com/statalist/archive/2009-01/msg01140.html
>>> but note first that the particular example you gave has no zeros (so
>>> no interior solution).
>>>
>>> On Sun, Jul 22, 2012 at 9:59 AM, Mohamud Hussein
>>> <Mohamud.Hussein@fera.gsi.gov.uk> wrote:
>>>> Hi there,
>>>>
>>>> I am trying to run a model for a marginal cost curve equation based on the traditional cubic total cost curve function (i.e. y= x^3+X^2+X+c) using Stata's optimize() command. The goal is to estimate the value of x which minimises y subject to a number of constraints.
>>>>
>>>> When I tried to specify the marginal cost curve function in mata directly as y=3x^2+2x+1 (i.e. first derivative of the total cost equation) I got the following message:
>>>>
>>>> Iteration 0:   f(p) =          1  (not concave)
>>>> Iteration 1:   f(p) =  7.911e+71  (not concave)
>>>> Iteration 2:   f(p) =  1.95e+169  (not concave)
>>>> Iteration 3:   f(p) =  8.32e+250  (not concave)
>>>> Iteration 4:   f(p) =  1.62e+288  (not concave)
>>>> Iteration 5:   f(p) =  2.34e+306
>>>> Hessian is not negative semidefinite
>>>>
>>>> I have never used Stata's mata programming language before and am not quite sure of what do here? Grateful if someone can help me on this.
>>>>
>>>> Thanks,
>>>> Mohamud
>>>
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>>
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-- 
Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street,
Haifa 33031, Israel
e-mail1: yuval.arbel@carmel.ac.il
e-mail2: yuval.arbel@gmail.com

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