Derive the expression for sallys marginal rate of

Question

Assignment Questions

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,

MU_x = 20/√x and MU_y = 1.
The price of coffee is P_x = $4 per cup, and the price of milk is P_y = $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.