1 - Optimal demand and price changes (41 points) Let Zoe's preferences over consumption bundles x = (x1, x2) be represented by the utility function u (x1, x2) = x1x2. Zoe has income m = 24. The price of x2 is one dollar, that is p2 = 1. The price of good 1 is p1 = 4. 1. Carefully showing your work, solve for Zoe's optimal consumption bundle and explictly state the following: (a) State Zoe's optimal consumption bundle x. (b) State Zoe's utility in her optimal consumption bundle u(x). 2. The price of good 1 increases to p 1 = 9. All else remains the same. (a) Solve for Zoe's new optimal consumption bundle, x. (b) Solve for Zoe's utility level in her new optimal bundle u(x). (c) Comment on how the good 1 price change from 4 to 9 has impacted demand for goods 1 and 2, respectively. Include discussion of income and substitution effects in your comments. 3. Calculate how much income Zoe would require so as to be perfectly compensated for the good