a) Assume that the utility function and marginal utility for A and B are as follow: U (A, B) = 3A + 5B with MUA = 6A and MUB = 5. i) Determine whether the assumption of 'more is better' satisfied for both goods. (2 marks) ii) Show the MRSA, B for this utility function. What does the MRSA, B tell us? (3 marks) iii) Find out whether the MRSA, B is diminishing, constant or increasing as the consumer substitutes A for B along an indifference curve. (2 marks) iv) Determine whether the indifference curves corresponding to this utility function are convex to the origin, concave to the origin or straight lines. Justify your rationale. (3 marks) b) Sincere is joining a competition performance. He needs to select the prize that lies at the Container A. The competition's host told him, there is a 50 percent chance to have a worth S10,000 treasure and a 50 percent chance to have nothing. Before the container is opened, the competition's host give Sincere an option for selling to him what is in the container for S6000 if he pays him $3000 for this option. i) If Sincere cares the expected dollar values of various outcomes only, will he purchase this option? (5 marks) ii) How does Sincere's degree of risk aversion affecting his willingness to purchase this option? (5 marks)