How would I solve this using Mathematica?

Questions
,
1

I have some equations that i want to plug in to see what the outcome is and was wondering if anyone can help,

I have: q1 = 4/3-2/3a-4/3p1+2/3p2

&

q2 = 4/3a-2/3+2/3p1-4/3p2

I am trying to find the inverse demand functions in respects to price.

Any help is appreciated.

2

Use Solve to solve equations.

In[8]:= Solve[{q1 == 4/3 - 2/3 a - 4/3 p1 + 2/3 p2,
  q2 == 4/3 a - 2/3 + 2/3 p1 - 4/3 p2}, {p1, p2}]

Out[8]= {{p1 -> 1/2 (2 - 2 q1 - q2), p2 -> a - q1/2 - q2}}
3

You can also do this easily in Wolfram|Alpha:

http://www.wolframalpha.com/input/?i=Solve+for+p1+and+p2+%7Bq1+%3D+4%2F3-2%2F3a-4%2F3p1%2B2%2F3p2%2C++q2+%3D+4%2F3a-2%2F3%2B2%2F3p1-4%2F3p2%7D

4

On top of that.

Assume that two firms, say firm 1 and firm 2 sell differentiated goods and face the following demand functions:
q1= 4/3 - 2/3a - 4/3p1 + 2/3
q2= 4/3a - 2/3 + 2/3p1 - 4/3p2
where a>1 . In addition assume that firms target own profit maximisation, compete(simultaneously) in quantities and have marginal costs equal to c1= c2=c. Assume that 1>c?0.

question) Derive each firms best response function. Are quantities strategic substitutes or complements?

5

and a further question)

derive the equilibrium in quantities any help would be greatly appreciated.