When I tried your code, I got the following error message:
Solve::nsmet: This system cannot be solved with the methods available to Solve. >>
The first and second equations can be solved for c1 and c2, respectively. The above error message is due to the third equation x3==0. Try
x3 = PowerExpand[x3]
before calling Solve assuming that \ is less than 1. Solve will then be able to solve the equations. The result is, unfortunately, not so illuminating. After some arithmetic, the third equation can be turned into the form
\[Lambda] (c3^(1/(1-\[Alpha])-\[Theta]) r (1-\[Alpha])^(\[Alpha]/(1-\[Alpha]))-A \[Theta] (1-\[Tau])) == 0
which gives a better looking solution.