Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2005
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2005

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Newbie with simple questions (take 2)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62325] Re: Newbie with simple questions (take 2)
  • From: misha <iamisha1 at comcast.net>
  • Date: Sun, 20 Nov 2005 04:50:29 -0500 (EST)
  • References: <dlp37m$1hp$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I've narrowed my question down quite a bit...

Why can't I use superscripts?

I initially tried q(superscript 2, subscript h) and q(superscript h, 
subscript l) and got error messages.  Then I tried q(superscript h, 
subscript 2) and q(superscript l, subscript 2), but this didn't seem to 
help.  It seems that Mathematica interprets superscripts as exponents. 
Is there a way around this?

In any case, I did the following and got some satisfying results:
Solve[{D[(a-x-z-c)x==0, x], D[(a-y-z-d)y==0, y], D[t(a-x-z-g)z + 
(1-t)(a-y-z-g)z==0, z]}, {x,y,z}]

So the question regarding solving FOCs and simultaneous equations no 
longer needs answering, but I am very open to suggestions regarding such 
problems!

In short, my question boils down to naming variables and using 
superscripts in doing so.

Thank you!

Misha

misha wrote:

> I am a new user (errr..purchaser) of Mathematica, but I have not been 
> able to find answers to these (probably) simple questions with 
> Mathematica?s help browser.  I am trying to use Mathematica to solve a 
> simple system of simultaneous equations.  I suppose I could use it to 
> solve the first order conditions (FOCs), but I?m having enough problems 
> as it is.  I have more ambitious goals than this, but I thought this 
> would be an easy place to start.
> 
> By the way, can anyone recommend a book heavy in examples for a 
> beginning user such as myself?
> 
> Here is the complete problem:
> 
> P(Q) = a - Q (inverse demand curve)
> 
> Q = q1 + q2 (Cournot) duopoly
> 
> C1(q1) = c*q1 (firm 1?s commonly known cost function, with constant 
> marginal cost, c)
> 
> C2 =  cL*q2 with probability t
>        cH*q2 with probability 1 - t
> 
> (firm 2?s cost functions for constant marginal costs cL < cH, known to 
> firm 2 but unknown with certainty to firm 1)
> 
> If Firm 2 has constant marginal cost cH, firm 2 chooses q2 to solve
> 
> max{[(a - q1* - q2) - cH]*q2}
> 
> If Firm 2 has constant marginal cost cL, then firm 2 chooses q2 to solve
> 
> max{[(a - q1* - q2) - cL]*q2}
> 
> The resulting FOCs are:
> 
> <<the asterisk denotes ?optimal? and the cH in parentheses denotes that 
> it is a function of cH>>
> 
> q2*(cH) = (1/2)*(a - q1* - cH)
> 
> q2*(cL) = (1/2)*(a - q1* - cL)
> 
> Similarly, Firm 1 chooses q1 to solve
> 
> max{t[(a - q1 - q2*(cH)) - c]*q1 + (1 - t)[(a - q1 - q2*(cL)) - c]*q1},
> 
> which yields FOC:
> 
> q1* = (1/2)*[t(a - q2*(cH) - c) + (1 - t)(a - q2*(cL) - c)]
> 
> So I want to use Mathematica to do the tedious algebra to get me the 
> following:
> 
> q2*(cH) = (a - 2cH + c)/3 + (1 - t)(cH - cL)/6
> 
> q2*(cL) = (a - 2cL + c)/3 - t(cH - cL)/6
> 
> q1* = (a - 2c + tcH + (1 - t)cL)/3
> 


  • Prev by Date: Re: Confusing results with N[expr]?
  • Next by Date: Re: Types in Mathematica
  • Previous by thread: Newbie with simple questions (take 2)
  • Next by thread: Re: Newbie with simple questions (take 2)