Solving the Life-Cycle Model with Labour Income Uncertainty: Some Implications of Income Volatility for Consumption Plan

We derive a generalised version of the Ramsey-type consumption function when labour income is assumed to follow the standard geometric Brownian motion, and show how the propensity to consume might depend on its drift and diffusion parameters. This enables us to explain the circumstance in which precautionary savings can arise when a risk averse consumer faces income uncertainty, and to resolve the main consumption puzzles: excess smoothness and excess sensitivity of consumption relative to income and its insensitivity to the real interest rate. Our results also show how labour income uncertainty could explain the existence of a subsistence level of consumption and, in that context, shed light on Kuznets’ paradox regarding constancy of the average propensity to consume in the long run. Finally, we find that using the subjective rate of time preference as the sole measure of a consumer’s impatience to consume could be misleading when the path of labour income is volatile.