thanks in advance

2. Consider the Cobb-Douglas utility function u(s, y] = 321:2. Let the budget constraint be pg + pug = I. where papa, are the prices and I denotes the income. {a} Write the Lagrangian for this utility maximization problem. {in} Solve the rst-order conditions to nd the demand hmctions for both good a: and good y. [Hint Your results should only depend on the pa- rameters :3... pg. L] {c} In the optimal consumption bundle, how much money is spend on :c? How much on 3;? Express your answer in proportion of the total income I. {d} OPTIONAL: Check the second order conditions. Comparative statics: (e) Assume the price p1, increases. How does the optimal consumption bun- dle change? {f} Assume the price of good .1: doubles. How does the optimal consump- tion bundle change? {g} Are the goods complements! substitutes? (h) Assume the income doubles. What is the new optimal consumption bundle? How does your answer in 2c change? i.e., How does the spend- ing proportion change? {i} Solve now this maximization problem using the method of substitution. Compare your result with those derived using the method of Lagrange. (j) Now, consider the utility function \"(3314) = min {Mr by} . where o, b s- 0. Web can only employ the method of substitution. Find the optimal solution