3. Abe consumes Good X and Good Y. His utility function is given by U(x, y) = x - (3/y). Compute Abe's MRS(x y) function. Show your work. You should find that MRS(x, y) = >(y?). b. Suppose Px =144, Py = 48, I = 864. Find Abe's utility-maximizing quantities choice of x and y. c. Suppose Py = 48 and I = 864, but that Px is not specified. Instead, we are going to allow 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 144 in place of Px. Instead, leave Px in the two equations. You will have two equations in three unknowns, x, y and Px. d. Find the equation for the price-consumption path 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 P. from the equations. It will be easiest to write this with x being a function of y (i.e. backwards). e. Find the equation for Abe'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 = 144, according to your demand function, what quantity of X does he demand? Do the same for Px = 4, 9, 16, 36, 64 and 576 and draw a rough sketch of his demand curve. If the price of Good Y changes, will Abe's demand curve for Good X shift? Think about how you found this demand function. h. If Abe's income changes, will Abe's demand curve for Good X shift? Think about how you found this demand function. i. If Abe's preferences change, will Abe's demand curve for Good X shift? Think about how you found this demand function