John's preferences for good X and good Y are described by the following utility function:U(X, Y) = XY^2where X and Y are the respective amounts of good X and good Y John consumes.The following are the formulas for John's marginal utilities:MUx = y2andMUy = 2XY

3. Suppose that John's income is I = 30. Suppose also that the price of good X is PX = 1 and the price of goodY is Pr = 2. Calculate the numerical values of John's optimal choice of X and Y. Careilly explain your reasoning. Draw a graph that illustrates J ohn's optimal choice and the utility level attained. Briey discuss how your graph illustrates his optimal choice. Now consider the effects of a price change on John's choices. In all the following questions, you should assume that the price of good Y, Py = 2 and John's income, I = 30, remain the same. However, we now consider the case where the price of good X increases from PX = 1 to P x = 2. Calculate numerical values for John's optimal bundle after the price change. What is the \"total effect\" of the price change on the amount of good X that John's consumes? Ir _. . . V an LL