Ron and Harry are traveling on the Hogwarts Express. They are pur- chasing Chocolate Frogs (X) and Bertie Botts Every Flavored Beans (Y). Suppose Ron's ordinary demand function for Chocolate Frogs (X), depending on the price of Chocolate Frogs Px, the price of the Every Flavored Beans Py, and his income M, is as follows: Py. M Px. (Px + Py) Suppose Harry's ordinary demand function for Chocolate Frogs (X), is as follows: XHarry (Px, Py, M) = 10 M - Py Px XRon (Px, Py, M) : = Let's also assume 10 > M > Py > Px > 0. a. [18 Points] Determine for Ron whether Chocolate Frogs (X) are normal or inferior, ordinary or Giffen, and whether Bertie Botts Every Flavored Beans (Y) are substitutes or complements to X. Prove your answers or provide numerical examples to justify your answers. b. [12 Points] Determine for Harry whether Chocolate Frogs (X) are normal or inferior, whether they are ordinary or Giffen. Prove your answers or provide numerical examples to justify your answers. c. [10 Points] Prove a Giffen good must be inferior. [Hint: you can use the Substitution-Income- Total effect chart from class.] (I have always wondered how economics works in the Harry Potter world. If you feel the same, make sure to start/participate in a new thread on our class discussion forum.)