We investigate an assignment market in which multiple objects are assigned, together with associated payments, to a group of agents with unit demand preferences. Preferences over bundles, the pairs of (object, payment), accommodate income e¤ects. Among all (Walrasian) equilibria in such a market, there is one supported by the coordinate-wise minimum prices, the minimum price equilibrium (MPE). We propose a price adjustment process, "the Serial Vickrey process,"that …nds an MPE in a …nite number of steps. The Serial Vickrey process introduces objects one by one, and on the basis of the structural properties of MPE, the "Serial Vickrey sub-process"sequentially …nds an MPE for k + 1 objects by using an MPE for k objects. In the Serial Vickrey process, instead of revealing the whole preference, each agent only reports …nitely many "indi¤erence prices."We also discuss the application of the Serial Vickrey process to calibrate agents' utility functions in the quantitative analysis of housing market research in the assignment model.