This paper analyzes the dependence of average consumption on the saving rate in a one-sector neoclassical Solow growth model with production shocks and stochastic rates of population growth and depreciation where arbitrary ergodic processes are considered. The long-run behavior of the stochastic capital intensity and hence average consumption is uniquely determined by a random fixed point which depends continuously on the saving rate. We prove existence of a golden rule saving rate maximizing average consumption per capita. A dynamic inefficiency result is given to ascertain the importance of the golden rule for the stochastic Solow model. The cases of Cobb-Douglas and CES production function are analyzed numerically, revealing that shocks to either parameter can lead to higher average consumption at the golden rule saving rate.