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 = Y^2andMUy = 2XY

1. Briefly explain what is meant by the statement that "preferences are transitive". Use the bundles A = (X,Y) = (1,1), B = (X,Y) = (2,2), and C= (X,Y) = (3,3) to illustrate that for these bundles John's preferences are transitive while clearly explaining your reasoning. 2. Plot John's indifference curve that goes through the point (4, 6). Explain your reasoning. Briefly explain whether John's preferences exhibit a diminishing marginal rate of substitution. 3. Suppose that John's income is I = 30. Suppose also that the price of good X is Py = 1 and the price of good Y is Py = 2