Consider an agent with perfectly substitutable utility over R1: U(Jc1, NJ\") 2 231 + + x\". The agent has total wealth w > 0. 1. Suppose the agent faces positive linear prices and that p1 1. What is the agent's optimal consumption bundle? Show that the KKT conditions are satised for this bundle. . Suppose instead she faces the same linear price for every good. Describe the set of optimal consumption bundles. . Now suppose she faces the nonlinear price schedule P(L') 3:190? What is the agent's optimal consumption bundle? . Now the agent faces the price schedule P(:23) 2 21:1 Describe the set of optimal consumption bundles. Show that the KKT conditions are satised for each Optimal bundle. . Finally, suppose n = 2 and the agent faces the price schedule P(:c) = 2J1): + @. Identify all bundles which satisfy the KKT conditions, and nd the agent's optimal consumption bundle. Illustrate the solution to the Optimization problem with a dia- gram