How can I solve the following non-linear equations numerically?

c == c * (pi / beta * R) ^ (1/sigma) ;
pi * (pi - 1) == beta * pi * (pi - 1) + (v / alpha * gamma) * (c + g) ^ ((1 + eps) / alpha) + ((1 - v) / gamma) * (c + g) * c ^ (-sigma) ;

All variables are specified, and I am interested in the value of c for varying values of pi. The idea here is to solve these equations to find the effect of the steady state inflation on the steady state consumption. How do I solve this? It would be nice to specify an interval for pi and see the effects on c and visualise this in a graph.

Thanks in advance!

Answer 1

[Walter Roberson]

For the first of those equations to be true, either c = 0 or pi = beta/R; if pi = beta/R then (pi / beta * R) is 1, and you arrive at c = c * 1^(1/sigma) which is c = c

Either way, c is independent of pi.