U =M-G/n +log(G) -n/k Where k is a positive constant and G/n is the charge for club membership a)Derive the optimal membership for the club if it maximizes the utility of each member b)Assuming the club choose G optimally given its membership, calculate the loss due to membership of the club with suboptimal size c)Assume that the total population is the size m,with k 2k.Show that there is a continuum of pareto-efficient allocations of population to clubs. d)What club size maximises total utility produced by the club?contrast to the answer in part a