3 Perfect substitutes Consider an agent with perfectly substitutable utility over 1R1: U(:L'1, ...,:L'n) = 331 + +1rrn. The agent has total wealth to > 0. 1. Suppose the agent faces linear prices and that 301 1. What is the agent's optimal consumption bundle? What fraction of her wealth does she spend on each good? Show that the tangency conditions for optimality are satisfied1 for the bundle you've found. . 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(:r:) = Z\" 3:2 What is the i=1 1' agent's optimal consumption bundle? . Now the agent faces the price schedule P(:1:) 2 21:1 $137. Describe the set of optimal consumption bundles. Show that the tangency conditions for optimality are satised for each Optimal bundle. . Finally, suppose n = 2 and the agent faces the price schedule P (at) = 2\\/:171+1 /:1:2. What is the agent's optimal consumption bundle? Illustrate this solution with a diagram. Show that the tangency condition for Optimality is satised for this bundle