(a) Suppose we have preferences U(X,Y) = X + Y. Graph/sketch the indifference curve through X = 10 and Y = 10. What is the utility and explain why it looks the way it does. (b) What is the Marginal Rate of Substitution for these preferences? Explain and interpret the value. (c) Suppose the consumer wanted to maximize utility subject to their budget constraint. State the consumer's maximization problem and express this in words. (d) Let U(X,Y) = X + Y. with Px = $8, Py = $3 and income M = $200. Find optimal X, Y and the resulting Utility. Draw a sketch of your solution.

(e) Now suppose we offered a discount so that good X was prices at $5 for the first 10 units but rise to $8 for any quantity above that. Draw the new budget line (f) Find the optimal X, Y and the resulting Utility given the availability of the discount. Compare to the non-discounted case and discuss why it is different/the same.