ABSTRACT
Note that the Muellbaucr's PIG LOG and PIGL sy:;tems are generated as speeial cases of (i) or (ii), with R = 2 (hence rank 2). PIG LOG is a special case of (i) with Kt = land Kz = 0. PIGL is a special case of (ii) with pz = 0. Similarly, the Gorman polar form (quasi-homotheticity) is a special case of (ii) with /~ = 2 (rank 2), Pi = -l, and P2 = 0. The rank-3 quadratic expenditure system is obtained by setting PI = -], P2 = 0, P3 = l in (ii). Homotheticity is rank L with Pl = l in (ii). In fact, virtually all consumer demand systems that have been estimated belong to the class of rank-2 demand systems satisfying the conditions of Gorman's theorem. Section IV contains more on rank-2 (and rank-3) demand systems. The kf:y point here, however, is that exact aggregation is considerably more general thau the existence of a representative agent; the latter is but one way of demand systems that can be consistently aggregated.
