A consumer has the following utility function: U = X . Y (then her MUX = Y and her MUY = X). The price of X is 3 (PX = 3), the price of Y is 1 (PY = 1), and her income is 120 (M = 120).
a. What is this consumer’s optimal consumption choice? Verify that the two conditions for constrained utility maximization hold for your answer.
b. If the price of good X decreases to 1 (PX = 1) and the price of good Y increases to 2 (PY = 2) but her income is also still 120 (M = 120), what would be her new optimal choice? Verify that the two conditions for constrained utility maximization hold for your answer.