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 >