Jin purchases only two commodities. Her preferences are characterized by the utility function U(x1, x2) = x 3/5 1 x 2/5 2 Suppose that p1 = $15, p2 = $10, and M = $50. a) Write down Jin's budget equation. b) Find Jin's optimal consumption bundle (x 1 , x 2 ) using the Lagrangian method. You must form the Lagrangian equation as part of your solution for full credit. c) Now suppose the price of commodity increases to p2 = $20. Find Jin's optimal choice using the MRS Method.

2. Daniel purchases only two commodities. His preferences are characterized by the utility function U(x1, x2) = x 3/5 1 x 2/5 2 Suppose that p1 = $8, p2 = $24, and M = $30. a) Write down Daniel's budget equation. b) Find Daniel's optimal consumption bundle (x 1 , x 2 ) using the Lagrangian method. You must form the Lagrangian equation as part of your solution for full credit. 1

3. Jason purchases only two commodities. His preferences are characterized by the utility function U(x1, x2) = min{4x1, x2} Suppose that p1 = $8, p2 = $3, and M = $100. a) Write down Jason's budget equation. b) Find Jason's optimal consumption bundle (x 1 , x 2 ) using the MRS method.

4. Earl purchases only two commodities. His preferences are characterized by the utility function U(x1, x2) = x1 + x2 Suppose that p1 = $8, p2 = $3, and M = $100. a) Write down Earl's budget equation. b) Find Earl's optimal consumption bundle (x 1 , x 2 ) using the MRS method.