Answer all questions. [25 marks] Jane maintains her satisfaction by consuming two goods weekly: X and Y. Her utility function is given as U(x, y) - 2xy; x > 0, y > 0, where x represents the amount of good X and y represents the amount of good Y. She has a weekly income of $72. The price of good X $9 per unit, and the price of good Y is $1 per unit. (a) Write an equation for Jane's budget line. [1 mark] (b) Find Jane's marginal utility of consuming an additional unit of good X and the marginal utility of consuming an additional unit of good Y. [2 marks] (c) Find Jane's optimal consumption bundle and determine the amount of satisfaction she is deriving from that optimal consumption bundle. Show your answers in a diagram, with among of good X on x-axis and amount of good Y on y-axis. Label your diagram fully. [6 marks] (d) Assuming now that the price of good X falls by $5 per unit. Comment how this change affect Jane's optimal bundle and her satisfaction level. Also, show all the changes in a diagram and show all your workings clearly. Remember to label your diagram fully. [7 marks] (e) (i) Find the numerical values of the income and substitution effects on consumption of good X that has been brought about by the fall in the price of good X above in (d). Show these effects clearly on a diagram. Also, comment on what kind of good is good X [6 marks] (ii) Determine the money income level that Jane needs to be as well off as before the change in the price of good X. Explain your answer. [3 marks]