2. Jacob's preferences for goods X and Y can be described by U(X,Y) = X+2Y+XY. Jacob has an income of $20 and faces prices Px=PY = $5. a. Derive Jacob's utility maximizing bundle given his budget constraint. Use the Lagrange method or simply the optimality condition. b. Now suppose Jacob's income falls to $5. Redo part a. c. Calculate Jacob's MRS of X for Y at this new utility maximizing bundle. How does it compare to the market trade-off of X for Y? d. On one graph, depict Jacob's utility maximizing bundles using indifference curves and budget lines, both before and after his income decreases.