Wealth-to-satisfaction reduction
= Wealth-to-satisfaction reduction
{title2=$V(\xi,w)=\xi^{1-R}v(w/\xi)$}
For <CRRA utility> of a <consumption satisfaction stock>, jointly scaling initial <portfolio wealth>, <consumption satisfaction> and controls gives <homogeneity> of degree $1-R$. The <value function> therefore depends on one dimensionless ratio after factoring out $\xi^{1-R}$. The effective <consumption> coefficient becomes $\xi^{-R}[(1-R)v-(x+1)v']$.