Exercise 5.11. Consider a two-period economy consisting of two types of households. NA households have the utility function u ¡ ci 1 ¢ + βAu ¡ ci 2 ¢ , where ci 1 and ci 2 denotes the consumption of household i into two periods. The remaining NB households have the utility function u ¡ ci 1 ¢ + βBu ¡ ci 2 ¢ , with βB < βA. Each group, respectively, has income yA and yB at date 1, and can save this to the second date at some exogenously given gross interest rate R. Show that for general u (·), this economy does not admit a representative household.