Answer to Question #66830 in Microeconomics for Carina

Question

Suppose that Billy's preferences over baskets containing milk (good x), and coffee (good
y ), are described by the utility function U(x; y ) = xy +2x. Billy'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
Billy's income.
Question 1: 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.
Question 2: 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.

Answer 1

U(x; y) = xy + 2x, MUx = y + 2 and MUy = x, Px - price of milk, Py - price of coffee, I - income.
Question 1: Sally’s demand for coffee as a function of the variables Px, Py and I is Qy = I - a*Px - b*Py, where a, b some coefficients.
Question 2: Sally’s demand for milk as a function of the variables Px, Py and I is Qx = I - c*Px - d*Py, where c, d some coefficients..