Assignment Questions
Suppose that Sally's preferences over baskets containing milk (good x), and coffee (goody ), are described by the utility function U(x, y ) = xy + 2x. Sally's corresponding marginalutilities 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 representSally's income.
Question 1: Suppose that the price of milk is Px = $1 per litre, the price of coffee isPy = $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.
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 andI. (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.
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.
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.
Question 6: Suppose that Px = $1 and I = $40. Find the equivalent variation for anincrease in the price of coffee from Py1 = $4 to Py2 = $5.