3. (20 points) With homothetic preferences, all indifference curves have the same shape. (1) Give a geometric illustration that when preferences are not homothetic, marginal rate of substitution depends on both relative ratio and absolute quantities of the two goods. (2) Assume the utility function is of the form U(x, y) = xy. Show that the logarithm transformation is a monotonic transformation and marginal rate of substitution of InU(x, y) depends only on the relative ratio. 3. (20 points) With homothetic preferences, all indifference curves have the same shape. (1) Give a geometric illustration that when preferences are not homothetic, marginal rate of substitution depends on both relative ratio and absolute quantities of the two goods. (2) Assume the utility function is of the form U(x, y) = xy. Show that the logarithm transformation is a monotonic transformation and marginal rate of substitution of InU(x, y) depends only on the relative ratio