A Simple Mapping from MPCs to MPXs

Standard consumption models assume a notional consumption flow that does not distinguish between nondurable and durable consumption. Such notional-consumption models generate notional marginal propensities to consume (MPC). By contrast, empirical work and policy discussions often highlight marginal propensities for expenditure (MPX), which incorporate spending on a durable stock. We compare the notional-consumption model to an isomorphic model with a durable stock, and map notional MPCs into MPXs. The mapping is especially simple for a one-period horizon: MPX = (1 - s + s/(r+d)) x MPC, with durable share s, real interest rate r, and durable depreciation rate d.