2. Douglas Cornfield's preferences are represented by the utility function U (X2, X2) = X32X32 The prices ofX; and X2 are P; and P2 (10 pts.) a. The slope of Corneld's indifference curve at the point (X 2, X 2) is (2 pts.) b. If Cornfield's budget line is tangent to his indifference curve at (X 2, X2), then P2X; P2X: = Hint: Look at the equation that equates the slope of his indifference curve with the slope of his budget line). When he is consuming the best bundle he can afford, what fraction of his income does Douglas spend on X 2 and X2 ? (4 pts.) c. Other members of Doug's family have similar utility functions, but the exponents may be different, or their utilities may be multiplied by a positive constant. If a family member has a utility mction U (x, y) = 6X\" 2X13, where a, b, and c are positive numbers, what fraction of his or her income will that family member spend on X; and X2? (4 pts.)