2. Ms. V consumes Good X and Good Y. Her utility function is given by U(q y) = 5-xy2. a. Compute Ms. V's MRS(x, y) function. Show your work. You should find that MRS(x, y) = y/(2x). b. Suppose Px = 3, Py = 2, I = 120. Find Ms. V's utility-maximizing quantities of x and y. C. Suppose Py = 2 and I = 120, but that Px is not specified. Instead, we are going to allow the Px to vary. (L.e., we are going to treat P, as a variable, along with x and y.) Rewrite the two equations you used to solve the problem in part (b), but this time do not use 3 in place of Px. Instead, leave P, in the two equations. You will have two equations in three unknowns, x, y and Px. d. Find the equation for the price-consumption line as Px is allowed to vary. To do this you will need to reduce your two equations in three unknows to one equation in two unknowns. Since the price consumption line shows a relationship between x and y, you will need to eliminate Px from the equations. Warning: you will get a strange result. Describe the significance of this result. e. Find the equation for Ms V's demand function for x. Go back to the two equations in three unknowns in (c), but this time eliminate y from the system so that you are left with an equation relating x and P, (i.e., a demand equation). Write it with x on the left hand side of the equation, solving for x. f. If Px =1, according to your demand function, what quantity of X does Ms. V demand? Do the same for Px = 2, 4, 5, 8, 10, 20 and 40. Draw a rough sketch of her demand curve. g. If the price of Good Y changes, will Ms. V's demand curve for Good X shift? Think about how you found this demand function. h. If Ms. V's income changes, will Ms. V's demand curve for Good X shift? Think about how you found this demand function. i. If Ms. V's preferences change, will Ms. V's demand curve for Good X shift? Think about how you found this demand function