We introduce the logistic model of consumption growth, which captures a negative feedback loop preventing an unlimited growth of consumption due to finite biophysical resources of our planet. This simple dynamic model allows for derivation of the expression describing the declining long-term tail of a social discount curve. The latter plays a critical role in, e.g., climate finance with benefits on current investments deferred to centuries from now. The growth rate of consumption is irregularly evolving in time, which makes estimation of an expected term-structure of consumption growth and associated social discount rates a challenging task. Nonetheless, observations show that the problem at hand is perturbative with the small parameter being the product of an average strength of fluctuations in the growth rate and its autocorrelation time. This fact permits utilization of the cumulant expansion method to derive remarkably simple expressions for the term-structure of expected consumption growth and associated discount rates in the bounded economy. Comparison with empirical data shows that the dynamic effect related to the planetary resource constrains could become a dominant mechanism responsible for a declining long-term tail of a social discount curve at the time horizon estimated here as about100 years from now (the lower boundary). The derived results can help to shape a more realistic long-term social discounting policy. Furthermore, with the obvious redefinition of the key parameters of the model, obtained results are directly applicable for description of expected long-term population growth in stochastic environments.