Which of the following conditions are required for the set of consumers to exhibit parallel, straight…

In microeconomic aggregation theory, a set of consumers exhibits parallel, straight wealth expansion paths (Engel curves with identical slopes) at any price vector P—ensuring that aggregate demand depends only on aggregate wealth—if and only if consumers' preferences admit indirect utility functions of the Gorman polar form, v_i(p, w_i) = a_i(p) + b(p)w_i (Statement A). The two classic preference families that satisfy the Gorman polar form are: (D) all consumers have identical preferences that are homothetic (where a_i(p) = 0 and b(p) is common to all consumers), and (E) all consumers have preferences that are quasilinear with respect to the same numeraire good. Statements B (heterogeneous preferences in general) and C (equal wealth distribution) do not generate parallel linear wealth expansion paths. Therefore, (A, D and E Only) is correct.