This paper considers the modeling and analysis of continuous time stochastic growth optimization in a mean field game setting. The individual capital stock evolution is determined by production, consumption and stochastic depreciation. We adopt a Cobb-Douglas production function and HARA utility combining own consumption and relative consumption with respect to the population average. The use of relative consumption reflects human psychology of satisfaction, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the ratio type interaction in the utility structure, our performance estimate depends on large deviation techniques.