Mark's utility function is given by the following equation U(x, y) = xy2. where x and y are consumed units of good X and Y, respectively. Good X's price is $3, and good Y's price is $6. Mark has $180 to spend. Show all the steps, with definition of every new notation used in the steps. What is Mark's optimal consumption, (x*, y*)? (5 pts.) b) Good Y's price decreases to $3. What is the new final optimal consumption, (XF. VF)? (5 pts.) C) What is the compensating variation for Good Y's price decrease from $6 to $3? (5 pts.) d) What is the equivalent variation for Good Y's price decrease from $6 to $3? (5 pts.) e) Suppose that the price of good X is fixed at $3, and the price of good Y is unknown, Py. Find Mark's uncompensated demand for good Y and draw the uncompensated demand curve (D, ). On the same graph, draw two hicksian demand curves for Y, Hey and HEv, where Hey is the hicksian demand with Mark's utility from consuming (x', y"), and Hey is the other hicksian demand with Mark's utility from consuming (XF, VF) when Py is $3. Make sure to include two coordinates for each of the three demand curves. (10 pts.)