Consider an agent with perfectly substitutable utility over R1: U($1, ...,:I:n) = :61 + + as... The agent has total wealth to > 0. 1. Suppose the agent faces positive linear prices and that p; 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. 11. . Now suppose she faces the nonlinear price schedule P[zr:) : 21:1 331?. What is the agent's optimal consumption bundle? Now the agent faces the price schedule P(m) = 21:21 Jae3. Describe the set of optimal consumption bundles. Show that the KKT conditions are satised for each optimal bundle. . Finally7 suppose we : 2 and the agent faces the price schedule P(:.t) : 2J1? + '/mg. 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