2. Tom always begins his day with a strawberry milkshake. He makes it by mixing milk (x) with five strawberries (y). The secret of a really good milkshake lies in the optimal proportion of milk and fruit: one glass always comes with five strawberries. (a) Plot Tom's representative indifference curves. Depict three indifference curves that pass through the following bundles (5, 1), (10, 10) and (15, 4). What is the MRS at each of these points? (b) What utility function represents these preferences? On the graph from (a), indicate the level of utility corresponding to each indifference curve. (c) Multiply your utility function by ten and add two to it. How did the indifference curves change? How was the level of utility associated with each indifference curve affected? 3. Kate has two favorite kinds of apples: Fuji (x) and Gala (y). Kate loves them both and actually does not distinguish between the two kinds. (a) In a graph, show Kate's indifference that pass through (2, 3) and (3, 3). (b) Suggest two different utility functions that represent Kates preferences. (c) Find the marginal rate of substitution. 4. Suppose the set of bundles is given by B = {B1, B2, B3, B4, B5}. Also suppose that the preferences of a consumer are given by B1 B2 B3 and B4 B5. Can you represent these preferences by a utility function? If you can give a utility function that does so. If not, explain why you cannot. Suppose now we also have the information B5 B1: Now, can you represent it with a utility function? If so, provide one. If not explain. 5. Suppose a consumer's preferences can be represented by the following utility function; u(x, y) = x + y. (a) Show that the utility function v(x, y) = 10x + 10y represent the same preferences with u, that is, v and u are monotonic transformations of each other. (b) Show that the utility function z(x, y) = x + y 2 does not represent the same preferences with u, that is, z is not a monotonic transformation of u