Suppose that Sally's preferences over baskets containing coffee (good x), and milk (good y), are described by the utility function U(x,y) = 40√x+y. Sally's corresponding marginal utilities are, MUx=20/√x and MUy=1. ? ? The price of coffee is Px = $4 per cup, and the price of milk is Py = $1 per litre. Sally's income is I = $200.
Question 1: Without deriving the optimal consumption basket, show that the basket with x = 25 cups of coffee, and y = 50 litres of milk, is NOT optimal.
Question 2: Derive the expression for Sally's marginal rate of substitution.
Question 3: Find Sally's optimal consumption basket.
Question 4: Find Sally's new optimal consumption basket if the price of coffee increases to Px = $5 per cup.
Question 5: Is coffee a Giffen good for Sally? Briefly explain. Your answer must reference the consumption baskets you found in questions 3 and 4.
Question 6: Find the income and substitution effects associated with an increase in the price of coffee from $4 to $5 a cup.
Question 7: Describe the relationship between Sally's demand for coffee and her income. Your answers must reference the your previous answers, AND use the correct term to describe the relationship.