Please answer all the questions in the image below.

QUESTION 1: COBB-DOUGLAS -......20 points. (2 points) (a) Suppose we have preferences U(X, Y) - X1/3 Y2/3. Create a table and graph/sketch the indifference curve through the bundle X - 10 and Y = 10 (2 points) (b) Show that the Marginal Rate of Substitution is MRSxy = - Y/2X. Interpret what this means and what it implies about convexity of the indifference curves. I (2 points) (c) Let prices be Px - 10, Py = 20 and income M - 1000. Draw/sketch the budget constraint. Interpret what the slope of the budget line means in economic terms. (1 points) (d) Suppose the consumer wanted to maximize utility subject to their budget constraint. State the consumer's maximization problem and express this in words. (3 points) (e) What are the two conditions (equations) identify the optimum? Sketch this in a figure and explain. (4 points) (f) Let U(X, Y) = X /3 Y23 and Px = 10, Py - 20 and income M - 1000. Find optimal X, Y and the resulting Utility. (3 points) (g) Now let Px - 12. Find the new optimal X and Y and the resulting Utility. Discuss why Utility falls. (3 points) (h) Why didn't the rise in Px affect consumption of good Y? What is the idea