A consumer has the utility function over goods X and Y,U(X; Y) = X^1/3Y²

Let the price of good x be given by P_x = $3 let the price of good y be given by P_y = $2

and let income be given byI = $21.

(a) Derive the consumer's demand for good X and good Y. This question requires you to show your work and produce a mathematical answer.

(b) Is good Y normal or inferior? Explain precisely?

(c) What is the Utility given the answer to #1a? This question requires you to show your work and produce a mathematical answer.

(d) Why does Utility higher if income is increased to $30?