8. Consider the following utility function: (POINTS: 15) u(x, y) = x² + √√y (a) Does it satisfy any kind of monotonicity? If so, which one? Prove your answer providing the necessary math. (You can provide only the intuition for partial credit.) (Points: 7/15) Now, consider the following problem of utility maximization, for which the only constraints are the non-negativity constraints: max х.у s.t. x 20 and y≥0 (b) What quantities an agent solving this problem would choose? Provide an economic intuition for this result along with the math argument. (Points: 8/15)