Question 3. [70 points] Amy's preference over good X and good Y are given by U(x, y) = xy². (1) Sketch the indifference curves of her preference. (draw 3 indifference curves) (10pts) (2) When she consumers 2 units of X and 3 units of Y, what is her level of utility? (5pts) (3) Calculate the marginal utility of X, the marginal utility of Y and the marginal rate of substitution (MRS).(15pts) (4) What is the marginal utility of X when X =2 and Y= 3? What is the MRS at this consumption bundle? (5pts) (5) What is the graphical interpretation of MRS? What is the economic interpretation of MRS? (5pts) (6) For Amy's preference, if we move along an indifference curve from upper left to lower right, how does the MRS change? What is the economic interpretation of this phenomenon? (5pts) (7) Suppose now the price of X is $1 and the price of Y is $2, and Amy's income is $100. Write down Amy's budget constraint. Sketch the budget line for the two goods. (When drawing a graph, always label the x-intercept, y-intercept and the slope. Use the horizontal axis for good X and vertical axis for good X (10pts). (8) Find Amy's optimal consumption choice of X and Y, find this point on the budget line in (7), and add the indifference curve passing through this optimal consumption point on the budget line in (7). (15pts)