Years have passed. You are now working with a prestigious think tank on K-Street. Early one morning, you find yourself in a heated discussion with one of your brightest colleagues. He gets very upset with you, because you are trying to make the point that, ceteris paribus, it is possible for a decrease in price to result in a decrease in quantity demanded. He argues that you are simply wrong.

Task: Using budget lines and indifference curves, prove to your colleague that he is wrong.

Decompose the change in price into two components: pure substitution effect, and income effect.