QUESTION 3: An individual has a utility function defined over two goods as 20.7570.25 U(Z1, Z2) = 21. The price of Z1 is P1 and the price of Z2 is P2 and income equals I. a. Set up the maximization problem and derive the First Order Conditions. (3 marks) b. What is the economic interpretation of the equation you derive when you combine the first two FOCs? (3 marks) c. If I = 180, p1 = 3 and P2 = 2 find the actual consumption for the two goods and the associated utility for this bundle. (4 marks) d. Derive the demand equations for Z1 and Z2 and present in a graph the optimal consumption bundle. (5 marks) e. How would your answer change if P2 = 4? How much more money would you need to keep the previous bundle? Show in the graph the substitution and income effects (10 marks)