1 Cobb-Douglas demand Suppose that an agent has Cobb-Douglas utility over X = R1 : U($1=332) = mfZEiaa where 0 0 and faces linear prices p1,p2 > 0 for each good. 1. Find the agent's optimal consumption bundle, as a function of 0:, w, p1, pg. 2. What fraction of the agent's total wealth does she spent on each good? Does this change with prices or wealth? 3. Suppose that or = 1/3, p1 = 1, p2 = 4, and w = 3. 0 Draw a diagram illustrating the solution to the utility maximization problem. Your diagram should include the budget constraint and an indifference curve going through the optimal bundle. 0 Using your diagram, graphically illustrate why the tangency conditions for opti- mality fail if the agent consumes only a single good. 4. Now suppose oz = 4/5 and the agent faces quantity markups on each good: If she wants to purchase 3:,- units of good 2', she must pay $53,; per unit. 0 Find the agent's optimal consumption bundle, as a function of the agent's wealth w