3 Long-Form 1. Julia's preferences for goods X and Y can be described by U(X, Y) = X +21 +XY. Julia has an income of $20, and faces prices Px = Py = $5. (a) Use the Lagrangian method to derive Julia's utility maximizing bundle given her budget constraint. (b) Now suppose the price of X increases to $15. Find Julia's new opti- mal bundle. You are not required to be the Lagrangian method for this part of the question. (c) On one graph, depict your answers to parts (a) and (b) using in- difference curves and budget lines. Be sure to clearly illustrate how Julia's MRS of X for Y compares to the MRT of X for Y at both utility maximizing bundles