3. Donald and Ronald are two multimillionaire twin brothers who are a little insane about their card collections, which they like to show to all guests at the parties hosted in their mansion. Donald's preferences for \"obscure actors and actresses\" cards (good :22) and \"noisy pop singers\" cards (good y) are reprasented by the utility function u(:c, y) = 2:312. Suppose that the unit price of both cards is 1 dollar. Their income to spend on this sick hobby is 6 million dollars for each. (a) Solve for Donald's optimal choice. (b) Suppose p, rises to 2 dollars. Mat is his new optimal consumption plan? How much would he have to increase his income in order to remain indifferent to the original situation? ((1) Ronald's preferences are represented by v(x,y) = Ina: + 2ln 3;. Answer parts (a) and (b) for Ronald. Comment. (d) In fact, generalizing the conclusion from part (c), suppose that a consumer's utility function is u, and that f is an order-preserving transformation of 1:. Using the chain rule of differentiation, can you prove that, at any bundle, the MRS of the transformed utility function u) is the same as that of the original function u? (0) Finally, using the Lagrange function method, what is Donald's marginal utility of in- come at the optimum, A', in the initial situation? What about in the nal situation