The effect of interest rates on consumption in an income fluctuation problem

We examine the effect of a change in interest rates on an agent's consumption and savings decisions when her income is fluctuating. In each period, a long-lived agent decides how much to save (i.e., invest in a risky bond) and how much to consume while her income and the rate of return on her savings are uncertain and depend on the state of the economy. We show that under the concavity of the consumption function, a condition that ensures that the substitution effect dominates the income effect, lower interest rates encourage the agent's consumption across all states.