The following Julia code is one step in value function iteration. I was trying to understand why we can rescale the profits in calculating the value function (for a general equilibrium model). In the code below, kst.share is the capital share, alpha is the power of production function $k^\alpha$. The code then obtains a skale:
konst = ((1.0-kst.share)*theta/kst.wage)^(1.0 /(1.0-(1.0-kst.share)*theta));
alpha = kst.share*theta/(1.0 -(1.0 -kst.share)*theta);
skale = konst^((1.0 -kst.share)*theta) - konst*kst.wage;
This skale is then applied to the production function $skale*z[iz]*k[ik]^\alpha$. I was wondering if anyone knows why we can do this, and why exactly konst and alpha are set the value in the code above.