Suzette purchases food (F) and other goods (Y) and has a utility function U=FY. Assume that her income is I, the price of food is Pf and the price of other goods is Py.
a. Set up the objective function and constraints faced by Suzette if she wishes to maximize her utility given her budget constraint.
b. Re-write (a) as an unconstrained problem using the Lagrangian equation. Define λ as the Lagrange multiplier.
c. Write the first order conditions that solve the Lagrangian equation and use them to derive Suzette’s demand equations for food and other goods.
d. Assume that her income is $12 and the prices are Pf= $2 and Py = $1. How much food and other goods will she purchase to maximize her utility? What is the highest utility level given her optimal purchase of food and other goods?