(a) Suppose we have preferences U(X, Y) = X¹ Y³. Make a table and graph/sketch the indifference curve through the bundle X = 10 and Y = 10. What is the utility at (10, 10)?

(b) The Marginal Rate of Substitution is MRS_XY = - Y/3X. Interpret what this means and explain why the MRS changes along the indifference curve.

(c) Let prices be Px = $5, Py = $10 and income M = $500. Draw/sketch the budget constraint. Explain what the slope of the budget line means in economic terms.

(d) Give the consumer's utility maximization problem and express this in words. What are the two conditions (equations) that identify the optimum? Sketch this in a figure and explain.

(e) Show and explain why these preferences imply that the consumer will spend of her income on Good X and of her income on Good Y

(f) For the income and prices in (c), what is optimal X and Y? Show your work.

(g) Suppose Px rises to $6 and Py falls to $8 but income stays at $500. Does consumer utility rise or fall? Show and explain.

(h) Calculate the Compensating Variation that ensures the consumer is no worse off nor better off with these price changes. Show and explain your work