Suppose a price-taking consumer chooses goods 1 and 2 to maximize her utility given her wealth. Her budget constraint could be written as p1x1 + p2x2 = w, where (p1, p2) are the prices of the goods, (x1, x2) denote quantities of goods 1 and 2 she chooses to consume, and w is her wealth. Assume her preferences are such that demand functions exist for this consumer: xi(p1, p2, w), i = 1, 2. Prove these demand functions must be homogeneous of degree zero.