We invent Implicit Marshallian demands, which combine desirable features of Hicksian and Marshallian demands. We propose and estimate the Exact Affine Stone Index (EASI) implicit Marshallian demand system. Like the Almost Ideal Demand (AID) system, EASI budget shares are linear in parameters given real expenditures. However, unlike the AID, EASI demands can have any rank and its Engel curves can have any shape over real expenditures. EASI error terms equal random utility parameters to account for unobserved preference heterogeneity. EASI demand functions can be estimated using GMM or three stage least squares, and, like AID, an approximate EASI model can be estimated by linear regression. (JEL D11, D12)

Significant departures from log normality are observed in income data, in violation of Gibrat’s law. We show empirically that the distribution of consumption expenditures across households is, within cohorts, closer to log normal than the distribution of income. We explain this empirical result by showing that the logic of Gibrat’s law applies not to total income, but to permanent income and to marginal utility.