The preferences of a consumer are represented by the utility function U (x, y ) = xy² Recall that for this function the marginal utilities are given by MU_x (x, y) = y² and MU_y(x, y) = 2xy. Assume that the prices of the goods are p_x = p_y = 2.

(a) Find the equations for the Engel curves of goods x and y and graph them.

(b) Is good x normal or inferior? What about y? Explain.