1. (25 points) Avery has preferences over gum () and lollipops (x2) with her utility function given by u(x1,x2) = 0.25 ln x + 0.75 ln x2. Further, the price of gum is given by p and the price of lollipops is given by p2 and income is denoted by y. a) Suppose that given utility and prices, Avery gum and lollipops in such a way that x=2.5 and x2=1 when income is 8. How many lollipops (x2) is Avery willing to give up to get an extra unit of gum (x2)? b) If pi = 2 and p2 3, is the choice from a) affordable? How many lollipops does Avery have to give up to get an extra unit of gum? c) With the aid of a diagram, explain why this choice is not optimal. Should Avery consume more gum? d) What is Avery's optimal choice of gum and lollipops in terms of p1, p2, and y? What are these choices when p = 2, p2 = 3, and y = 8? = e) If Avery's income falls to y 4, how is consumption of both goods affected? Illustrate graphically. Are gum and lollipops "normal" goods?