2. [This question shows that our marginal utility calculations for consumer behav ior essentially do not depend on which utility we use to represent preferences, even though the marginal utilities themselves do.] Suppose a : X > IR. is differentiable at. some :1? E X : with strictly positive marginal utilities. Let f : IR > R be a function with strictly positive derivative; let 1] := f on. (In particulaL u and 11 represent the same preferences because f is strictly increasing.) (a) Show by example that. the marginal utility for good 1 could be different under a and under it. (b) Show that the ratio %}r~%% is the same for utility 11 as it is for utility u