We analyze the implications of different welfare criteria on economic and population growth in the case of stochastic population change. Edgeworth (1925) argues that total utilitarianism leads to a lower economic performance and a larger population size than average utilitarianism. Following works show that while his intuition holds in a static framework, the result is unclear in a dynamic setting of endogenous growth. We show that if population dynamics is stochastic, Edgeworth's conjecture may or may not hold. In particular, which utilitarian criterion implies larger economic and population growth rates depends on the value of the inverse of the intertemporal elasticity of substitution, the features of the random process driving demographic change and the magnitude of the (linear) dilution coefficient. We also characterize the size of the range of parameter values supporting Edgeworth's conjecture; such a range is wide if the dilution parameter is large enough while it is particularly narrow (but still non-empty) if the parameter is small.