Prove that when indirect utility functions of all consumers i = 1, .... , n have the Gorman form:

v_i(p; w) = a_i(p) + b(p)w_i

and the social welfare function is utilitarian:

W (u_i, ...., u_n) = (from i to n) u_i

then for any wealth distribution aggregate demand can always be viewed as being generated by a normative representative consumer.