here is the question

8. Consider an N-consumer, M-good economy in which each consumer J = 1, ..., N has en- dowment w = (wi, ..., wMy) and utility function u' (r) over consumption bundles r = (I1 , ..., I'M). (a) Consider allocations (pl*, ...,(*) that maximise the sum of all the consumers' utilities, that is, which are a solution to N max (x],...,IN)ERMN + J=1 Lu'(x') subject to Ex! = >w! for all i = 1, ., M. J=1 J=1 Show that allocations (al*, ..., (*) are Pareto-efficient. to (b) From now on, suppose that N = M = 2 and that the consumers have Cobb-Douglas utility functions. Solve for the Pareto-efficient allocations from (a) in this case. (c) Find Pareto-efficient allocations that do not maximise the sum of consumers' utilities. Interpret the differences with your answer from (a). Is it not the case that comparing utilities across consumers is a crazy thing to do