Mark's utility function is given by the following equation

(, ) = x^2,

where x and y are consumed units of good X and Y, respectively. Good X's price is $6, and good Y's price is $4. Mark has $270 to spend. Show all the steps, with definition of every new notation used in the steps.

a)What is Mark's optimal consumption,(* , * )?

b)Good Y's price decreases to $3. What is the new final optimal consumption,(, )?

c)What is the compensating variation for Good Y's price decrease from $4 to $3?

d)What is the equivalent variation for Good Y's price decrease from $4 to $3?

e)Suppose that the price of good X is fixed at $6, and the price of good Y is unknown,y. Find Mark's

uncompensated demand for good Y and draw the uncompensated demand curve (). On the same graph, draw two hicksian demand curves for Y,and, whereis the hicksian demand with Mark's utility from consuming(* , * ), andEVis the other hicksian demand with Mark's utility from consuming(F , F )whenY is $3. Make sure to include two coordinates for each of the three demand curves.