The following graph is found in most economics texts and it illustrates how an economy can get outside its PPF through free trade. Solving this problem is a straight-forward application of Lagrange. The Gains From Trade A YE B u* PPF Trading Line" XE X* X Figure 1: Skippy lives on a samll island full of resources that lets her produce two goods: x and y. Her production possibility frontier (constraint) is given by x2 + y2 = 300. Skippy works alone to maximize her utility which is given by U(x, y) = xy. (1) Set up the Lagrangian function for Skippy and solve for and y. Use your solution to calculate U. (2) Carefully graph and label the PPF and Indifference Curve at the optimum