= Merton consumption constant
{c}
{title2=$\gamma_M=[\rho-(1-R)(r+\kappa^2/(2R))]/R$}
In the infinite-horizon <Merton consumption-investment problem> with <constant relative risk aversion utility>, this is the optimal ratio of <consumption> to wealth. A finite value requires $\gamma_M>0$. The <state-price budget constraint> then fixes consumption's multiplier because $\mathbb E[\xi_t(ye^{\rho t}\xi_t)^{-1/R}]=y^{-1/R}e^{-\gamma_Mt}$, whose time integral is $y^{-1/R}/\gamma_M$. When this integral diverges, the value is $+\infty$ for $0<R<1$ and $-\infty$ for $R>1$.
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