In its certainty equivalence form, consumption is proportional to the sum of human and non-human wealth. With labor income uncertainty the proportionality takes the form of homogeneity of consumption with respect to the two components of wealth. In this paper we analyze the stochastic properties of labor income which yield the homogeneity property as the utility maximizing solution. A sufficient condition is derived on the Way in which a certain income shift (in time series analysis) or difference (in cross section comparison) preserves the homogeneity result. Application of this condition to some geometric processes and normal distribution of income is made. For other income processes the response of consumption to a certain income movement may be larger, which appears as excess sensitivity.