Referencing Styles : Not Selected Suppose that Sally’s preferences over baskets containing milk (good x), and coffee (good y), are described by the utility function U(x,y) = xy +2x. Sally’s corresponding marginal utilities are, MUx = y + 2 and MUy = x. Use Px to represent the price of milk, Py to represent the price of coffee, and I to represent Sally’s income. Question 1: Suppose that the price of milk is Px = $1 per litre, the price of coffee is Py = $4 per cup, and Sally’s income is I = $40. Without deriving the optimal consumption basket, show that the basket with x = 16 litres of milk, and y = 6 cups of coffee, is NOT optimal. (2 Marks) Question 2: Derive the expression for Sally’s marginal rate of substitution. (1 Mark) Question 3: Derive Sally’s demand for coffee as a function of the variables Px, Py and I. (i.e. Do NOT use the numerical values for Px, Py and I, from question 1.) For the purposes of this question you should assume an interior optimum. (3 Marks) Question 4: Derive Sally’s demand for milk as a function of the variables Px, Py and I. (i.e. Do NOT use the numerical values for Px, Py and I, from question 1.) For the purposes of this question you should assume an interior optimum. (1 Mark) Question 5: Describe the relationship between Sally’s demand for milk and, (a) Sally’s income; (b) the price of milk; (c) the price of coffee. Your answers must reference the demand function that you derived in question 4, AND use the correct term to describe the relationship. (6 Marks) Question 6: Suppose that Px = $1 and I = $40. Find the equivalent variation for an increase in the price of coffee from Py1 = $4 to Py2 = $5. (7 Marks)